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Ultrafast Optical Spectroscopic Study of Semiconductors in High Magnetic Fields

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Title: Ultrafast Optical Spectroscopic Study of Semiconductors in High Magnetic Fields
Physical Description: 1 online resource (190 p.)
Language: english
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: exciton, magnetooptics, quantumwell, semiconductor, superfluorescence, ultrafast
Physics -- Dissertations, Academic -- UF
Genre: Physics thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: We studied the magneto-excitonic states of two-dimensional (2D) electron and hole gas in InxGa1-xAs/GaAs multiple quantum wells (MQW) with continuous wave (CW) optical spectroscopic methods, including transmission and photoluminescence spectroscopy, in high magnetic field up to 30 Tesla. Interband Landau level (LL) transitions are clearly identified. The anticrossing behavior in the Landau fan diagram of the transmission spectrum is interpreted as dark and bright exciton mixing due to Coulomb interaction. With the unique facility of ultrafast optics at National High Magnetic Field Laboratory, we are able to change the 2D electron hole gas into 0D and increase density of each quantum state as well as the actual sheet carrier density in the quantum well (up to 1012cm-2) dramatically. Under these conditions, interactions between electron and hole pairs confined in 0D system play a very important role in the electron hole recombination process. With high power pulsed lasers and cryogenic equipment, we studied the strong magneto photoluminescence emission from InxGa1-xAs/GaAs MQW in high magnetic field. By analyzing the power dependent, field dependent and direction dependent PL spectrum, the abnormally strong PL emission from InxGa1-xAs/GaAs MQW in high magnetic field is found to be the result of cooperative recombination of high density magneto electron-hole plasmas. This abnormally strong photoluminescence from InxGa1-xAs/GaAs MQW in high magnetic field under CPA excitation is proved to be superfluorescence. We studied CW spectroscopic properties of ZnO semiconductors including reflectivity and photoluminescence at different crystal orientations. A, B excitonic states in ZnO semiconductors are clearly identified. Also, with time resolved pump probe spectroscopy, we studied the carrier dynamics of excitonic states of A and B in bulk ZnO as well as ZnO epilayer and nanorods.
General Note: In the series University of Florida Digital Collections.
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Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Reitze, David H.

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Permanent Link: http://ufdc.ufl.edu/UFE0019805/00001

Material Information

Title: Ultrafast Optical Spectroscopic Study of Semiconductors in High Magnetic Fields
Physical Description: 1 online resource (190 p.)
Language: english
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: exciton, magnetooptics, quantumwell, semiconductor, superfluorescence, ultrafast
Physics -- Dissertations, Academic -- UF
Genre: Physics thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: We studied the magneto-excitonic states of two-dimensional (2D) electron and hole gas in InxGa1-xAs/GaAs multiple quantum wells (MQW) with continuous wave (CW) optical spectroscopic methods, including transmission and photoluminescence spectroscopy, in high magnetic field up to 30 Tesla. Interband Landau level (LL) transitions are clearly identified. The anticrossing behavior in the Landau fan diagram of the transmission spectrum is interpreted as dark and bright exciton mixing due to Coulomb interaction. With the unique facility of ultrafast optics at National High Magnetic Field Laboratory, we are able to change the 2D electron hole gas into 0D and increase density of each quantum state as well as the actual sheet carrier density in the quantum well (up to 1012cm-2) dramatically. Under these conditions, interactions between electron and hole pairs confined in 0D system play a very important role in the electron hole recombination process. With high power pulsed lasers and cryogenic equipment, we studied the strong magneto photoluminescence emission from InxGa1-xAs/GaAs MQW in high magnetic field. By analyzing the power dependent, field dependent and direction dependent PL spectrum, the abnormally strong PL emission from InxGa1-xAs/GaAs MQW in high magnetic field is found to be the result of cooperative recombination of high density magneto electron-hole plasmas. This abnormally strong photoluminescence from InxGa1-xAs/GaAs MQW in high magnetic field under CPA excitation is proved to be superfluorescence. We studied CW spectroscopic properties of ZnO semiconductors including reflectivity and photoluminescence at different crystal orientations. A, B excitonic states in ZnO semiconductors are clearly identified. Also, with time resolved pump probe spectroscopy, we studied the carrier dynamics of excitonic states of A and B in bulk ZnO as well as ZnO epilayer and nanorods.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Reitze, David H.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0019805:00001


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UJLTRAFAST OPTICAL SPECTROSCOPIC STUDY OF SEMICONDUCTORS INT HIGH
MAGNETIC FIELDS























By

XIAOMING WANG


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2008
































O 2008 Xiaoming Wang

































To my wife and my daughter









ACKNOWLEDGMENTS

First of all, I would like to express my deep gratitude to my advisor, Professor David

Reitze, for his supervision, instruction, encouragement, tremendous support and friendship

during my Ph.D. He guided me into a beautiful world of ultrafast optics. His profound

knowledge of ultrafast optics, condensed matter physics and his teaching style always impress

me and will help me all through my life.

I wish to thank my supervisory committee, Prof. Stanton, Prof. Tanner, Prof. Rinzler and

Prof. Kleiman, for their instructions for my thesis and finding errors in my thesis manuscript.

I would like to give my sincere thanks to the visible optics staff scientists at the National

High Magnetic Field Laboratory, Dr. Xing Wei and Dr. Stephen McGill, for their excellent

technical support for our experiments. I learned plenty of knowledge about spectrometers, fibers,

cryogenics, magnets and LabView program from them. Also I give my special thanks to Dr.

Brandt, former director of DC facility at NHMFL, for his great administrative assistance.

I appreciate the experimental and theoretical supervisions we received for our research

proj ects from Prof. Stanton from University of Florida, Prof. Kono from Rice University and

Prof. Belyanin from Texas A&M University. Special thanks should be given to my research

collaborators, Dr. Young-dahl Cho and Jinho Lee. Our research proj ects would not be so

successful without their contribution.

This work is supported by National Science Foundation and In House Research Program at

the National High Magnetic Field Laboratory.

Finally I want to send my warmest thanks to my wife and my daughter, my parents and

parents in law for their endless love and support. I could not complete my studies without their

emotional and financial support.











TABLE OF CONTENTS


page

ACKNOWLEDGMENTS .............. ...............4.....

LIST OF TABLES ........._..... ...............8.._._. ......

LIST OF FIGURES .............. ...............9.....

AB S TRAC T ........._. ............ ..............._ 14...

CHAPTER

1 INTRODUCTION AND OVERVIEW ................. ......... ...............16. ....


1.1 Semiconductors and Quantum Wells ................. ...............17........... ...
1.2 Magneto-spectroscopy in High Magnetic Fields ................ .... .. ................... 1
1.3 Motivation for Performing Ultrafast Spectroscopy in High Magnetic Fields ..............19
1.3.1 Quantum Optical Processes in Semiconductors--Superfluorescence ................19
1.3.2 Studies of Technologically Interesting Materials .............. .....................2

2 HIGH FIELD MAGNETO-OPTICAL TECHNIQUES AND FUNDAMENTALS OF
MAGNETO-OPTICAL SPEC TRO SCOPY ................. ...............24........... ...

2.1 Introduction ................... ........... ... ............ .............2
2.2 Basic Background of Optical Response of Solids ................. ................ ........ .24
2.3 Magneto-spectroscopy of Semiconductors--Methods ............ ... .... ................._27
2.3.1 Transmission Spectroscopy .............. ...............27....
2.3.2 Reflection Spectroscopy .............. ...............28....
2.3.3 Photoluminescence (PL) Spectroscopy ................. .............. ......... .....29
2.4 Time-resolved Spectroscopy of Semiconductors ................. ................ ......... .29
2.5 CW Optical Experimental Capabilities at the NHMFL ............................. ..... ..........32
2.6 Development of Ultrafast Magneto-optical Spectroscopy at NHMFL .......................34
2.6.1 Introduction of Ultrafast Optics ................ .......___.........__ ...........3
2.6.2 Magnet and Cryogenics for Ultrafast Optics at NHMFL ................. ...............35
2.6.3 Ultrafast Light Sources .............. ........ ...............36
2.6.3.1 Ti:Sapphire femtosecond oscillator............... ...............3
2.6.3.2 Chirped pulse amplifier............... ...............3
2.6.3.3 Optical parametric amplifier .............. ...............38....
2.6.3.4 Streak camera ................ ...............39........... ....


3 ELECTRONIC STATES OF SEMICONDUCTOR QUANTUM WELL IN
MAGNETIC FIELD ................. ...............57.................

3.1 Introduction ............... ... .. ......... .... .. ........ ... ....... .... ........5
3.2 Band Structure of Wurzite and Zinc Blend Structure Bulk Semiconductors. ...............57
3.3 Selection Rules............... ...............60.











3.4 Quantum Well Confinement .................. .. .......... ........ ...... ...............6
3.5 Density of States in Bulk Semiconductor and Semiconductor Nanostructures ............63
3.6 Magnetic Field Effect on 2D Electron Hole Gas in Semiconductor Quantum Well ....64
3.7 Excitons and Excitons in Magnetic Field............... ...............66.
3.7.1 Excitons............... ...............66
3.7.2 Magneto -excitons ................. ...............67........... ....

4 MAGNETO-PHOTOLUMINESCENCE IN INGAAS QWS IN HIGH MAGNETIC
FIELD S ................ ...............78.................

4.1 B background ............... .. .... ... .. ..... ...... .......................7
4.2 Motivation for Investigating PL from InGaAs MQW in High Magnetic Fields
Using High Power Laser Excitation ................. ...............81........... ...
4.3 Sample Structure and Experimental Setup ................. ...............82...............
4.4 Experimental Results and Discussion ................. ........... .. ............... 82....
4.4.1 Prior Study of InxGal-xAs/GaAs QW Absorption Spectrum .................. ...........82
4.4.2 PL Spectrum Excited with High Peak Power Ultrafast Laser in High
M agnetic Field .............. ...............84....
4.5 Summary .............. ...............87....

5 INVESTIGATIONS OF COOPERATIVE EMISSION FROM HIGH-DENSITY
ELECTRON-HOLE PLASMA IN HIGH MAGNETIC FIELDS .............. .....................9

5.1 Introduction to Superfluorescence (SF) .............. .. ...............98.
5.1.2 Spontaneous Emission and Amplified Spontaneous Emission..........................99
5.1.3 Coherent Emission Process--Superradiance or Superfluorescence .................101
5.1.4 Theory of Coherent Emission Process--SR or SF in Dielectric Medium........106
5.2 Cooperative Recombination Processes in Semiconductor QWs in High Magnetic
Fields ................ ... ........... ........ ..... ...... ... ... ...... .......... 0
5.2.1 Characteristics of SF Emitted from InGaAs QW in High Magnetic Field......110
5.2.2 Single Shot Random Directionality of PL Emission ................. ..................1 12
5.2.3 Time Delay between the Excitation Pulse and Emission ............... .... ..........._113
5.2.4 Linewidth Effect with the Carrier Density ................. .......... ...............113
5.2.5 Emission intensity Effect with Carrier Density ................. ............ .........113
5.2.6 Threshold Behavior. ................. ... ......... .......... ...... ......... ........1
5.2.7 Exponential Growth of Emission Strength with the Excited Area ..................1 14
5.3 Experiments and Setup ................. .......... ...............115 ....
5.4 Experimental Results and Discussion ................ ............. ...............117 ....
5.4.1 Magnetic Field and Power Dependence of PL .................. .... ..... ....... ..........1 17
5.4.2 Single Shot Experiment for Random Directionality of In Plane PL................1 19
5.4.3 Control of Cherence of In Plane PL from InGaAs QW in High Magnetic
Field .............. ...............120....
5.4.4 Discussion ............ ...... ._ ...............121...
5.5 Summary ............ _...... ._ ...............125...

6 STUDY OF CARRIER DYNAMICS OF ZINC OXIDE SEMICONDUCTORS WITH
TIME RESOLVED PUMP-PROBE SPECTROSCOPY .......... ................ ...............140











6.1 Introduction .................. .... ... ....... .. .. ........ ..... .... ... ............4
6.2 Background of Crystal Structure and Band Structure of ZnO Semiconductors .........141
6.3 Valence Band Symmetry and Selection Rules of Excitonic Optical Transition in
ZnO Semiconductors ............... .. .. ...._ ....... .. ..... .................14
6.4 Impurity Bound Exciton Complex (I line) in ZnO and Zeeman Splitting ..................1 44
6.5 Samples and Experimental Setup for Reflection and PL Measurement ................... ..146
6.6 Re sults and Di scussi on ................. .... ........ .. ..... .......... .................14
6.7 Time Resolved Studies of Carrier Dynamics in Bulk ZnO, ZnO Epilayers, and
ZnO Nanorod .............. .. ..... ..............14
6.8 Experimental Results and Discussion ........._. ........._._._ ........... ............5
6.8.1 Relaxation Dynamics of A-X and B-X in Bulk ZnO ........._....... ......_.. .....151
6.8.2 Relaxation Dynamics of A-X and B-X in ZnO Epilayer and Nanorod........... 152

7 CONCLUSION AND FUTURE WORK ................. ...............172........... ...

APPENDIX

A SAMPLE MOUNT AND PHOTOLUMINESCENCE COLLECTION ........._ ................176

B PIDGEON-BROWN MODEL .............. ...............179....

LIST OF REFERENCE S ................. ...............182................

BIOGRAPHICAL SKETCH ................ ............. ............ 190...










LIST OF TABLES


Table page

1-1 Some band parameters for some III-V compound semiconductors and their alloys.........22

3-1 Periodic parts of Bloch functions in semiconductors ................. ................ ........ .70

3-2 Selection rules for interband transitions using the absolute values of the transition
matrix elements ................. ...............71.................

5-1 Some experimental conditions for observation of super fluorescence in HF gas............126

6-1 Some parameters of ZnO bulk semiconductors ................. ...............155........... ..










LIST OF FIGURES


Figure page


1-1 Physical and energy structure of semiconductor multiple quantum well ..........................23

2-1 Transmission spectrum of InGaAs/GaAs MQW at 30 T and 4.2 K .............. .................40

2-2 Reflection spectrum of ZnO epilayer at 4.2K ................. ...............41..............

2-3 e-h recombination process and photoluminescence spectrum in semicondcutros .............42

2-4 Simple illustration of optical pump-probe transient absorption or reflection
experiment. ....._._................. ........._._.........43

2-5 Experimental setup for optical pump-probe spectroscopy and TRDR spectrum of
ZnO .............. ...............44....

2-6 Time resolved photoluminescence spectrum of InxGal-xAs/AlGaAs MQW at 4.2K .......

2-7 Technical drawing of the 30 Tesla resistive magnet in cell 5 at NHMFL............._._._.......46

2-8 Technical drawing of cryostat and optical probe for CW optical spectroscopy at
NHM FL ........._.__...... ..__ ...............47....

2-9 Block diagram of the CW magneto optical experiment setup at the NHMFL. ........._......48

2-10 Schematic diagram of modified magneto optical cryostat for direct ultrafast optics. .......49

2-11 Technical drawing of the 17 Tesla superconducting magnet SCM3 in cell 3 at
NHM FL ........._.__...... ..__ ...............50....

2-12 Technical drawing of the special optical probe designed for superconducting magnet
3 in cell 3 at the NHM FL ........._... ...... ..... ...............51..

2-13 Schematic diagram of Coherent Mira 900F femtosecond laser oscillator .......................52

2-14 Schematic diagram of Coherent Legend-F chirped pulse amplifier (CPA) ................... ...53

2-15 Top view scheme of layout of the optical elements and beam path in TOPAS OPA........54

2-16 Operation principle of a streak camera ......._..__ .... ...............55._.__ ...

2-17 Block diagram of ultrafast optics experimental setup in cell 3 and 5 at NHMFL .............56

3-1 Band structure of Zinc blend semiconductors ................. ................. ........ ...._72

3-2 Band structure of wurzite structure semiconductors ................. ................ ......... .73











3-3 Schematic diagrams of band alignment and confinement subbands in type I
semiconductor quantum well. ............. ...............74.....

3-4 Density of states in different dimensions ................. ....___ ...............75..

3-5 Electronic energy states in a semiconductor quantum well in the presence of a
magnetic field............... ...............76.

3-6 Calculation of free electron hole pair energy and magneto exciton energy of InxGal.
xAs/GaAs QW as function of magnetic field ................. ...............77........... ..

4-1 Magneto abosorption spectrum and schematic diagram of interband Landau level
transitions. .............. ...............88....

4-2 Magnetophotoluminescence experimental results of band gap change and effective
m ass change. ............. ...............89.....

4-3 Valence band mixing of heavy hole and light hole subbands in semiconductor
quantum well ......__................. .........__..........9

4-4 Structure of In0.2Gao.sAs/GaAs multiple quantum well ................. ....__. ...............91

4-5 Faraday configuration in magnetic field ................. ...............92...............

4-6 Energy levels of electron and hole quantum confinement states in InxGal-xAs
quantum well s ........... ..... ._ ...............93...

4-7 Magneto-photoluminescence spectrum of InxGal-xAs quantum well at 10K ................... .94

4-8 Landau fan diagram of absorption and PL spectrum of InxGal-xAs quantum well in
magnetic field up to 30 T. .............. ...............95....

4-9 Magneto-PL and excitation density dependence of the integrated PL in InxGal-xAs
quantum well s at 20 T and 10 K ................. ...............96..........

4-10 Theoretical calculation and experimental results of PL in high magnetic field ........._......97

5-1 Spontaneous emission and amplified spontaneous emission process of a two level
atom system .............. ...............128....

5-2 Four steps in the formation of collective spontaneous emission--SF in N atom system.129

5-3 Schematic diagram of the configuration for collection of in plane PL from InGaAs
multiple QW in high magnetic field .............. ...............130....

5-4 Experimental schematic showing the configuration for a single shot experiment on
InxGal -xAs QW s ................. ................. 13......... 1....










5-6 Fitting method to determine line widths using a Lorentzian and Gaussian function for
the sharp peak and broader lower-energy peak ................. ...............133........... ..

5-7 Excitation power dependent PL spectrum and fitting results of in plane emission.........1 34

5-8 Excitation spot size effect on the in plane PL emission............... ...............13

5-9 Single shot directionality measurement of in plane PL emission in SF regime ..............136

5-10 Single shot directionality measurement of in plane PL emission in ASE regime ...........137

5-11 Schematic diagram of the configuration of control of emission directionality in
InxGal-xAs multiple QW .............. ...............138....

5-12 Control of coherence of in plane PL emission in InxGal-xAs QW ................. ................139

6-1 Top view of the lattice structure of a wurtzite ZnO crystal............_ ........._ .......156

6-2 The orientation of light polarization with respect to the ZnO unit cell ........................... 157

6-3 Band structures and symmetry of each band of a ZnO semiconductor. ..........................158

6-4 Schematic of types of impurity bound exciton complexes ........._. ..... ..._._..........159

6-5 Energy diagram of Zeeman splitting of neutral bound excitons in ZnO ........._.............160

6-6 Schematic diagram of Voigt configuration of c-plane ZnO in magnetic field ..............161

6-7 Reflection spectrum of a-plane bulk ZnO semiconductor for different linear optical
polarization at 4.2K............... ...............162.

6-8 The magneto-PL spectrum of a and c-plane bulk ZnO sample and Zeeman splitting
at 4.2K............... ...............163.

6-9 Comparison of reflection and PL spectrum of c-plane bulk ZnO .............. ................1 64

6-10 Comparison of reflection and PL spectrum of c-plane epilayer ZnO at 4.2 K ................165

6-11 Schematic diagram of the pump-probe experimental setup for measuring TRDR of
ZnO semiconductors. ............. ...............166....

6-12 TRDR plots of a-plane bulk ZnO semiconductor at 4.2K and exponential decay
fitting line............... ...............167.

6-13 Fast decay in TRDR of A-X in a-plane bulk ZnO and the fitting with convolution of
Gaussian function and exponential decay function .............. ...............168....

6-14 Temperature dependent TRDR of A-X recombination in c-plane bulk ZnO ........._......169










6-15 TRDR plots of excitonic recombination in ZnO epilayer for different exciton states.....170

6-16 Experimental TRDR plot of ZnO nanorod sample at 10K and fitting result ................... 171

A-1 Detailed schematic diagram of sample mount and PL collection used in the
experiment. .........._.. .. ...............178.__..........









LIST OF ABBREVIATIONS

BEC Bound exciton complex

CCD Charged coupled device

CPA Chirped pulse amplifier

CW Continuous wave

DOS Density of states

LL Landau level

MQW Multiple quantum well

NHMFL National High Magnetic Field Laboratory

OPA Optical parametric amplifier

PL Photoluminescence

PMT Photomultiplier tube

SCM Superconducting magnet

SF Superfluorescence

TRDR Time resolved differential reflectivity

X Exciton









Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

UJLTRAFAST OPTICAL SPECTROSCOPIC STUDY OF SEMICONDUCTORS INT HIGH
MAGNETIC FIELDS


By

Xiaoming Wang

May 2008

Chair: David H. Reitze
Major: Physics

We studied the magneto-excitonic states of two-dimensional (2D) electron and hole gas in

InxGal-xAs/GaAs multiple quantum wells (MQW) with continuous wave (CW) optical

spectroscopic methods, including transmission and photoluminescence spectroscopy, in high

magnetic field up to 30 Tesla. Interband Landau level (LL) transitions are clearly identified. The

anticrossing behavior in the Landau fan diagram of the transmission spectrum is interpreted as

dark and bright exciton mixing due to Coulomb interaction. With the unique facility of ultrafast

optics at National High Magnetic Field Laboratory, we are able to change the 2D electron hole

gas into OD and increase density of each quantum state as well as the actual sheet carrier density

in the quantum well (up to 1012Cm-2) dramatically. Under these conditions, interactions between

electron and hole pairs confined in OD system play a very important role in the electron hole

recombination process. With high power pulsed lasers and cryogenic equipment, we studied the

strong magneto photoluminescence emission from InxGal-xAs/GaAs MQW in high magnetic

field. By analyzing the power dependent, field dependent and direction dependent PL spectrum,

the abnormally strong PL emission from InxGal-xAs/GaAs MQW in high magnetic field is found

to be the result of cooperative recombination of high density magneto electron-hole plasmas.









This abnormally strong photoluminescence from InxGal-xAs/GaAs MQW in high magnetic field

under CPA excitation is proved to be superfluorescence.

We studied CW spectroscopic properties of ZnO semiconductors including reflectivity and

photoluminescence at different crystal orientations. A, B excitonic states in ZnO semiconductors

are clearly identified. Also, with time resolved pump probe spectroscopy, we studied the carrier

dynamics of excitonic states of A and B in bulk ZnO as well as ZnO epilayer and nanorods.









CHAPTER 1
INTRODUCTION AND OVERVIEW

During the past few decades, the transport and optical properties of electron (e) hole (h)

gas in two-dimensional (2D) semiconductor quantum well (QW) in magnetic field have been

studied extensively in theory and experiments [1-5]. However most of the magneto-optical

studies are based on continuous wave (CW) optics or low magnetic field.

In this dissertation, we first investigate the magneto-excitonic states of 2D electron and

hole gas in InxGal-xAs/GaAs multiple quantum wells (MQW) with CW optical spectroscopic

methods, including transmission and photoluminescence (PL) spectroscopy. With the unique

facility that exists at National High Magnetic Field Laboratory (30 Tesla magnetic field

combined with intense ultrashort pulse lasers), we are able to change the 2D electron hole gas

into a quasi-0D system, and increase carrier density of states of each quantum state as well as

actual sheet carrier density dramatically. Under these conditions, the excitonic effect is

suppressed because the Coulomb interaction between high-density e-h pairs is screened, while

the interactions between e-h pairs confined in this quasi OD system play a very important role in

the recombination process.

With high power pulsed lasers and cryogenic equipment, we studied the strong magneto-

PL emission from InxGal-xAs/GaAs MQW in high magnetic fields. With analyzing the power

dependent, field dependent and single shot direction dependent PL spectrum, the abnormally

strong PL emission is found to be result from a cooperative recombination process of high

density magneto e-h plasmas, which is called superfluorescence (SF).

The second part of this thesis focuses on the CW and ultrafast optical spectroscopic study

of ZnO semiconductors. Due to its unique band gap (~3.3 5 eV) and large exciton binding energy

(~60mev) at room temperature [6-10], these are promising materials for optoelectronic










applications, such as blue and ultraviolet emitters and detectors. By analyzing the CW spectra,

the band structures, excitonic and impurity bound excitonic states are identified. By using pump-

probe spectroscopy, the dynamics of different excitonic states are studied in bulk ZnO, ZnO

epilayer and nanorods.

1.1 Semiconductors and Quantum Wells

By using epitaxial growth such as molecular beam epitaxy (MBE) and metal organic

chemical vapor deposition (MOCVD), modern science and technology have provided us the

methods of manufacturing a very thin epitaxial layer (~nm) of a semiconductor compound on

another different semiconductor with interface of very high precision (atomic precision), thus

allowing for 'quantum-engineered' materials and structures.

The optical properties of semiconductor QWs have been extensively studied [1 1-15], and

many physical phenomena have been investigated thoroughly, i.e. interband transitions, inter-

subband transitions.

Figurel1-1 shows physical and band structure of III-V or II-VI group semiconductor

multiple quantum wells, composed of periods of ABAB..., A and B are two layers of different

type of semiconductor compounds, i.e. InxGal-xAs and GaAs. The bandgap of compound B (the

well) lies within the bandgap of the compound A (the barrier). The thickness of barrier A is

typically greater than 10 nm, so that carriers will be confined in the QW layers. This particularly

unique property of semiconductor heterojunctions provides us an ideal system for studying the

interesting physics and application of device in two dimensional electron gas system--carriers in

QWs are confined in the : direction, the growth direction of QW, and still move freely in the

quantum well plane, or x-y direction. The interface between barrier and well imposes

confinement on carriers in QWs, which results in the formation of discrete quantum states in

both conduction and valence band. In a semiconductor, if an electron in valence band is excited









to conduction band as a free electron, a hole will be left in valence band. Through the Coulomb

interaction, this electron hole pair can form a hydrogen atom (H) like quasi-atom system: an

exciton (X). In a semiconductor QWs, due to the spatial confinement and discrete quantum state

confinement, excitonic effects are more pronounced than semiconductor bulks [16-20]. These

discrete excitonic states of exciton provide a unique system to study quantum optical processes

of carriers in semiconductor quantum wells.

1.2 Magneto-Spectroscopy in High Magnetic Fields

In the presence of a high magnetic field, the cyclotron energy Amie of a charge carrier is

greater than the exciton binding energy Eb (for GaAs, Amc~,=4Eb above 20T1). Thus, we open a

new regime to study semiconductor magneto-optics, where the magnetic field effect due to the

formation of Landau levels (LLs) will suppress the exciton effect. Also, in high magnetic field,

electrons and holes populate on LLs, which provide us a system to study the mid infrared light

driven intraband LL transitions. Many new physical processes can be explored in semiconductor

quantum wells at high magnetic fields [21-25].

Another impact that applied high magnetic fields have on a semiconductor QW is an

alteration of the carrier confinement. Free carriers are confined in QW plane since the magnetic

length IB is on the order of a few nm. At high magnetic fields, the density of states (DOS) of a

two dimensional electron gas system will evolve into a zero dimensional system, like a quantum

dot; the separation between LLs varies with the intensity of magnetic field. Magneto-excitons (or

magneto-plasmas) confined in quasi-nanorods in semiconductor QWs at high magnetic field

provides us with an atomic-like system with tunable internal energy levels to study quantum

optics in solids.









In early studies of magneto-optics in semiconductor quantum wells, light sources used in

the experiments were usually continuous wave (CW) white light or CW lasers (see Chapter.2.5

for detail), which provided static spectroscopic information only. In the past twenty years, with

the development of ultrafast laser technology and magnet technology, time resolved

spectroscopic studies of magneto optical experiments like time resolved Kerr rotation or time

resolved Faraday rotation can be carried out in a split coil superconducting magnet [26-30].

However, time resolved dynamics of magneto-excitons populate on LLs in semiconductor QW

has been carried out at Hields less than 12 T [31-33] and not yet been realized at higher magnetic

Shields. Furthermore, in high magnetic Hields, sheet carrier density in QW can also increased

dramatically due to the OD like DOS at each LL. If the excitation power of the pulsed laser is

very large, i.e., as that achievable with amplified ultafast laser systems (CPA) as the excitation

light source, we can create a carrier density in excess of 1013/Cm-2 in the QWs. In this case, the e-

h response in the QW will be dominated by plasma-like instead of exciton-like behavior. These

high-density magneto-plasmas confined in QWs interact with each other and correlate to each

other before they start to recombine. This leads to many new and exciting physical phenomena,

as we discussed later.

1.3 Motivation for Performing Ultrafast Spectroscopy in High Magnetic Fields

1.3.1 Quantum Optical Processes in Semiconductors--Superfluorescence

In high magnetic field, e-h pairs are confined in a quasi OD structure. Therefore, we can

use this atom like system to study quantum optics in electron hole pair in high magnetic field, i.e.

strong electromagnetic field induced energy splitting--AC Stark Effect [34] and cooperative

recombination process--Superfluorescence [35].

In an atomic ensemble, if the atoms are in excited state, they will relax down to ground

state through emission of photons. This process is called spontaneous emission if there is no









interaction between atoms during the emission. In the case where the decoherence time of the

atom is significantly greater than the spontaneous emission time, due to the interaction between

atoms, the atomic ensemble can evolve into to a coherent state and emit a burst of photons

through a cooperative radiative process called superfluorescence. This type of emission,

characterized by its short pulse width and high intensity compared to spontaneous emission, has

been observed in rarefied gas systems [36], however, due to very short carrier decoherent time in

solid, superflorencence has not been observed so far.

1.3.2 Studies of Technologically Interesting Materials

In order to study quantum optics in semiconductor QW in high magnetic field, the intrinsic

properties of semiconductor material are very crucial to observe quantum processes. These

properties include band structure, electron and hole effective masses, QW structure, and barrier

and well compositions.

Among all the III-V group and II-VI group semiconductor materials, III-V group

compounds such as InxGal-xAs/GaAs, InxGal-xAs /InP, InxGal-xAs /AlGaAs and GaAs/AlGaAs

QW series are the best materials to study quantum optical phenomena of e-h pairs in

semiconductor QWs.

These materials have been thoroughly studied using magneto-optical spectroscopy and

their band structures are well known [37, 38]. First, their band gaps energy are in the near

infrared region, which is very suitable for excitation with Ti: Sapphire ultrafast lasers; second,

the electron subband and valence hole subband are separated reasonably well which cause less

band complexity; third, the electron and hole effective mass in these materials are relatively

small and the exciton binding energy are relatively large (~10 meV), which make it easy to

observed higher LLs in high magnetic field. Some band structure constants of some III-V group

semiconductors are listed in Table 1-1.










In this dissertation, we selected InxGal-xAs/GaAs MQW for the host material for 2D e-h

gas. The behaviors of high density e-h pairs under high power excitation in high magnetic field

are the main result in this dissertation.









Table 1-1. Some band parameters for some III-V compound semiconductors and their alloys.
Parameters GaAs InAs InP
ac(A) 5.651 6.051 5.87
Erg,(mev) 15191 4171 14231
Exg (mev) 19811 14431 14801
Aso(mev) 3411 390] 1081
m*e(r) 0.0671 0.0261 0.07951
m*e(X) 1.91 0.641 0.0771
m*hh(me) 0.451 0.411 0.641
m*1h(me) 0.0821 0.0261
Reference [37]
ac is the crystal lattice constant in c direction.
Erg and Exg are the band gaps at r and X point.
Aso is the spin orbit interaction, m"e(T) and m"e(X) are the electron effective mass at r and x
pomnt.
m~hh and m*1h are the effective mass of heavy hole and light hole.












_


A BA B A B A

(a)


I~


(b)
Figure 1-1. Physical and energy structure of semiconductor multiple quantum well.(a) Physical
structure type I semiconductor multiple quantum well, (b) Energy structure of type I
semiconductor multiple quantum well









CHAPTER 2
HIGH FIELD MAGNETO-OPTICAL TECHNIQUES AND FUNDAMENTALS OF
MAGNETO-OPTICAL SPECTROSCOPY

2.1 Introduction

In this chapter, we introduce the basics on optical response theory, including

optical complex dielectric constant e and refractive index n. We then give a background

in the techniques used to study optical properties of semiconductors, discussed the

experimental techniques of CW measurements on semiconductors, including

transmission, reflection and photoluminescence spectroscopy.

To understand the carrier dynamics in semiconductors, pump-probe spectroscopy is

employed. By understanding the how the dielectric constant e and refractive index n

change with carrier density N, we can study the time resolved differential transmission

and reflection spectroscopy.

In addition, a detailed description is provided for the existing CW spectroscopic

experimental setup at the NHMFL that will be used for our measurements. Finally and

most importantly, to extend our research regime in high magnetic fields and ultrafast

lasers, we have developed an ultrafast facility at the NHMFL to study the ultrafast

magneto optical phenomena in high magnetic field. In this chapter, we give and overview

of the ultrafast facility and describe the technical details.

2.2 Basic Background of Optical Response of Solids

In a solid state system, including semiconductors, the optical response such as light

transmission and reflection is determined by the complex dielectric constant e. Coupled

with an underlying model for the physics that relates to the dielectric function, the

knowledge of the dielectric function over a given spectral range completely specifies the

optical behavior of the material. In Drude's model [39], e is given by [40]









4m-e r or i
E(0i) = E' (m)+ iE"(mi) = 2-1
nzes or +1'

where Nis the electron density, e is the electron charge, me is mass of electron, r is a

phenomenological relaxation time constant corresponding to the mean time between

carrier and ion collisions, and e, is dielectric constant at high frequency (-o m). The

refractive index n is [40]


n(m) = e'+[ (e) (") -

And the intensity absorption coefficient is [40]


a(m)~ = &"0,2-3
cn(u,

where a is also the absorption coefficient in Beer Lambert' s law [40]

I(z)=I, exp(-acz). 2-4

The expression for optical reflection is given by


R = '2-5


where nl and nz are the refractive index on both sides of a solid and the incident beam

light is perpendicular to the solid surface.

In the low frequency of optical frequency regime, corresponding to the infrared part

of spectrum where er~ << 1, we have [40]


e~m)a ie(m)= 4me r2-6


and


n2(W)= 2-









for the index of refraction and


acu)mJE -

for the absorption coefficient.

In high optical frequency regime where or~ >> 1 corresponding to ultraviolet part of

spectrum, we have [40]



4~/-~2


where my~ is plasma frequency.
E-me

For 0 ,> 0i,, we have [40]


n~m)= .2-10

The relation between dielectric constant e and optical susceptibility X is [40]

e(m)= 1+4?Xy~m), 2-11

7 is a complex parameter, given as

X(m) = X'(mL)+ iX1"(U). 2-12

Since the dielectric function e and optical susceptibility X have both real and

imaginary components, both of them will contribute the optical response such as the

transmission T and reflection R. Therefore, the optical resonant frequencies

correspondent to e~co are not necessarily directly related to absorption peaks or dips on

the transmission and reflection spectrum. However, Kramers-Kronig transformations [40]

allow us to determine the real part of optical response function from the imaginary part at









all frequency and vice versa, so that we are able to figure out the frequency of optical

resonance in the spectra.

The real part and imaginary part of optical susceptibility X are related by [40]


g'm) Pr dw' u2 2xl(,
0 2-13




and


Pr dm' =IXIW li W e+de21
g22) 22 we2 2 'I 21


where Pr refers to the principal part of the complex integral.

2.3 Magneto-spectroscopy of Semiconductors--Methods

In magneto-spectroscopic studies of semiconductors, many experimental

techniques have been developed. These spectroscopic methods include transmission and

reflection spectroscopy, photoluminescence (PL) and photoluminescence excitation

(PLE) spectroscopy, and optical detected resonance spectroscopy (ODR). Here, we will

restrict our discussion to the methods that have been applied in this dissertation.

2.3.1 Transmission Spectroscopy

Transmission spectroscopy [40-44] is very useful tool in the study of electronic

states in quantum well (discussed later in Chapter 3, 3.6). The first investigations of

GaAs/AlGaAs quantum wells used this method. From Eq. 2-3, we can see that a(co) is

related only with e" so that we can find the resonant frequency directly from transmission

spectrum. In transmission spectroscopy, a white light beam is incident on the

semiconductor sample, which is usually placed in a cryostat, and the transmitted white

light is collected and sent to a spectrometer. The spectrum will be resolved with the










spectrometer and the intensity of each wavelength is detected by either a CCD array or a

photomultiplier. Using the CW optical setup at NHMFL, a typical transmission spectrum

of GaAs/AlGaAs multiple quantum well in high magnetic field 30 Tesla and 4.2K is

shown in Fig. 2-1. In this figure, we can clearly resolve several quantum states, which

will be interpreted in detail in Chapter 4. The dips in spectrum correspond to specific

interband transitions, which are the positions of excitonic states (see section 4.4). Using

transmission spectroscopy, we can directly mark the energy positions of Gaussian shape

absorption dips as excitonic states on the spectrum. However, care should be taken for the

band gap of substrate and barrier materials that they are high enough from the well

material band gap to avoid overwhelmed by the continuum states of the barrier and

substrate materials.

2.3.2 Reflection Spectroscopy

Reflection spectroscopy is also an important method to study the optical properties

of semiconductor materials [45-48]. In reflection spectroscopy a white light beam is

incident on a sample and the reflected light is collected and sent to a spectrometer for

frequency resolution. Compared with transmission spectroscopy, this method offers a few

advantages. It has a good signal noise ratio and not affected by the substrate materials

unless the optical depth of quantum well is large, and it is a good method to study the

above band gap excitonic features in semiconductors possessing very high absorption

coefficient, since in transmission spectrum these features will be overwhelmed by the

high absorption coefficient. Reflection spectroscopy has a significant disadvantage: the

refractive index n shown in Eq. 2-2 has both e and a ", which have different contributions

to reflection so that the location of resonant electronic state position is not completely

straightforward and further analysis is needed. Fig. 2-2 is a reflection spectrum of a 400









nm thick ZnO eplilayer at 4.2 K, the energy positions of electronic states are not clearly

resolved However, for a very good approximation, we can identify the states at the arrow

points shown on the figure as the energy positions of electronic states.

2.3.3 Photoluminescence (PL) Spectroscopy

PL spectroscopy is also very important method to study excite states in

semiconductors [49-53]. In transmission and reflection spectroscopy, information about

the optical absorption processes is obtained. They cannot be used to provide information

about the photon emission process. In PL spectroscopy, electrons in valence band are

excited with photons whose energy is higher than the band gap of semiconductor sample,

followed by relaxation down to the bottom of conduction band. This leads to

recombination with holes on the top of valence band, which undergo a similar energy

relaxation, simultaneously producing a photon, which has the energy of the transition

(See Fig. 2-3(a)). From the photon emission, we can use PL spectroscopy to understand

the excited states in conduction and valence bands. Fig. 2-3(b) shows a typical PL

spectrum measured with the ultrafast magneto-optical setup at NHMFL, we can observe

clearly PL peaks in the spectrum. The detailed physics of this spectrum will be discussed

in Chapter 3, 4 and 5.

2.4 Time-resolved Spectroscopy of Semiconductors

The CW optical spectroscopic techniques described above provide a wide range of

methods to study the optical properties of photoexcited carriers in semiconductors.

However, these methods provide the information of static states in semiconductors only.

In order to understand the dynamical processes of photoexcited carriers, time resolved

spectroscopic techniques need to be employed. Since the 1970's, extensive studies of









time resolved carrier dynamics in semiconductor have been reported [54-58], which have

opened a new research area for semiconductor optics.

The most common time resolved spectroscopic method used to investigate the

carrier dynamics in semiconductors are pump-probe spectroscopy and time-resolved

photoluminescence spectroscopy.

In Fig. 2-4, a basic illustration of degenerate (equal wavelength) ultrafast pump

probe experiment is shown in transmission geometry. The laser pulses (in our case of

duration ~100 fs) are split into two pulses called the pump pulse and probe pulse, and

pump pulse is much stronger than probe pulse. The pump and probe pulses are spatially

overlapped on the sample with an optical focusing lens. Pump pulses are absorbed by the

sample and excite carriers, which change the optical properties such as refractive index n

(See equation 2-1, 2-2). After a controlled time delay At, the probe pulse reaches the

sample, the transmission of this probe pulse will be recorded. By changing the time delay

At between pump and probe, we can record the intensity of transmission of probe pulse at

different time delays. The absorption coefficient a~co is time dependent, it changes after

pump pulses excitation and will go back to original value. Therefore, the transmission of

probe light also manifests the dependency on time delay At, because the relationship

between T and a~co is


T I exp(-a(co)L,) 2-15


Generally speaking, in optical pump-probe spectroscopy, the pump pulse excites certain

optical process in a sample and the probe is used to map out the dynamics of this process.










A typical pump-probe spectroscopy experimental setup is shown in Fig. 2-5. In this

spectrum resolved pump-probe setup, either the transmission or reflection of the probe is

sent to a spectrometer before it reaches the PMT (Photo Multiplier Tube), so that change

of probe light at different wavelength can be resolved and detected. The intensity of

reflection or transmission of probe beam will be recorded at different time delay between

pump and probe pulse by changing the relative optical path of pump beam. The

spectrometer is used to select specific wavelengths to probe.

In many cases, the change of probe induced by pump pulses is normalized to see

the magnitude of the effect. These techniques are called differential transmission

spectroscopy (DTS) or different reflection spectroscopy (DRS), and the signals are given

by

AT T T
T T,
o a 2-16
AR R R
Ro Ro


For DTS, because of Eq. 2-15, we have

AT
= exp(-Aa(m)~L)-1= -Aa(mi)L 2-17


However, for the DRS, the expression is quiet complicated because R is associated with

both real and imaginary part of dielectric constant (see Eqs.. 2-1, 2-2 and 2-5). Thus, by

measuring the time resolved DTS and DRS, we can infer the carrier dynamics in

semiconductors. Fig. 2-5(b) shows a typical degenerate time-resolved differential

transmission (TRDR) spectrum of ZnO epilayer at 4.2K.









Time-resolved differential transmission (TRDT) and reflection (TRDR) provide an

indirect method to study the carrier dynamics with very good time resolution (~100 fs

and shorter). However the mechanism of carrier recombination processes can not be

inferred, i.e. the radiative and nonradiative carrier recombination processes cannot be

distinguished from a pump-probe spectroscopy since both of them will contribute to

carrier recombination. To solve this problem, alternative techniques are required to

perform time-resolved study of the radiative processes. In time-resolved

photoluminescence, PL emitted from sample is sent to a streak camera, with which

temporal information of PL emission is acquired. The resolution of this method (~ps) is

not as high as pump-probe spectroscopy. The combination of pump-probe spectroscopy

and time resolved PL spectroscopy will give us a thorough understanding of photoexcited

carrier dynamics in semiconductors.

Fig. 2-6 shows a TRPL spectrum measured from InxGal-xAs/AlGaAs MQW at

4.2K taken using a Hamamatsu streak camera. These time-resolved figures are typical

data we use in this thesis and the detailed physics will be discussed in the following

chapters .

2.5 CW Optical Experimental Capabilities at the NHMFL

Since the construction of the DC magnetic field facility at the National High

Magnetic Field Laboratory (NHMFL), there has been high demand for research in

magneto-optics, and many research proj ects have been accomplished with the well-

developed CW magneto-optical techniques that have been established [59-68]. In this

dissertation, many experiments were carried out to characterize InxGal-xAs/GaAs MQW

sample by using the CW magneto optical setup at NHMFL in Tallahassee.










In order to reach high magnetic fields, we used a 31 Tesla resistive magnet in cell 5

at NHMFL. Fig.2-7 shows the schematic diagram of this magnet. This magnet is a

resistive magnet consists of a few hundreds of thin copper disks (Bitter disks). The Bitter

disks are connected electronically and electric current can flow through Bitter disks in a

spiral pattern. In Fig.2-7, we can see that there are four coils of Bitter disks in the magnet

housing. There are huge flows of electric current (~37KA) in the magnet coils when they

are in operation at full field, at the same time, cold water flows continuously through

holes punched on the Bitter disks to remove the huge amount of heat (~MW) generated

by the electric current.

In many magneto-optical experiments, low temperatures are usually required to

measure transmission, reflection and photoluminescence. Specially designed cryostats

and probes have been designed to work at liquid helium temperatures with these resistive

magnets with bore size around 50mm. The technical drawing of a cryostat and probes are

given in Fig. 2-8. This cryostat has a long tail, so that the probe/sample can reach the

position of highest magnetic field. In this cryostat, liquid helium is stored in the center

space and enclosed by liquid nitrogen or nitrogen shield and vacuum jacket, which

significantly reduce heat leaking into the helium reservoir. In Fig 2-8, an optical probe is

inserted into the liquid helium reservoir of this cryostat, and the sample inside the probe

is cooled down by back filling low-pressure helium exchange gas into probe. Light is

delivered to the sample through an optical fiber, and temperature of sample is measured

with a Cernox temperature sensor and controlled with a heater mounted on sample

mount.









In Fig. 2-9, the layout of a typical CW magneto-optical experiment setup at

NHMFL is shown in a block diagram. An optical probe is inserted in the cryostat, which

is positioned on the top of a Bitter magnet. A Lakeshore temperature controller controls

the temperature of the sample via a sensor and heater co-located next to sample. The

input light and output signal light are delivered to sample and spectrometer respectively

through two optical fibers. In the case of transmission, reflection measurements, CW

white light sources (Tungsten or Xenon lamps) are used for input illumination while

lasers (He-Ne, He-Cd, Argon and Ti:Sapphire) are used as input excitation light for

photoluminescence (PL) experiments. The transmission, reflection and PL signal light are

collected with the output optical fiber mounted next to the sample and analyzed by a 0.75

m single-grating spectrometer (McPherson, Model 2075) equipped with single channel

photon counting electronics PMT as well as a multi-channel CCD detector. All of the

control units in this setup, including magnet controller, temperature controller,

spectrometer controller, PMT and CCD controller are managed by an Apple computer

through GPIB interfaces.


2.6 Development of Ultrafast Magneto-optical Spectroscopy at NHMFL

2.6.1 Introduction of Ultrafast Optics

With the existing CW magneto optical setup at NHMFL, many experiments have

been done successfully. However, there is still a drawback of this experimental setup -

time-resolved magneto-optical information can not be acquired due to large stretch effect

of multimode optical fibers, which expand the pulse width of ultrafast laser pulse

dramatically (from ~100fs to ~20ps) and results in a significant loss of time resolution. In

order to obtain time-resolved magneto-spectroscopy in high magnetic fields, a new









facility needs to be developed, which includes a new magnet, cryostat, probe as well as

new ultrafast light sources and detection methods.


2.6.2 Magnet and Cryogenics for Ultrafast Optics at NHMFL

Note that in a standard pump-probe experiment, while the excitation (pump) and

probe pulses must be delivered to the sample through free space to preserve the temporal

resolution, the collection of the light from the sample can be accomplished using standard

fibers.

To preserve the temporal duration of a femtosecond laser pulse before it reaches the

sample, direct optical propagation in free space is required. We also needed to modify

current cryostat so that it can be used on resistive magnet for ultrafast magneto optical

experiments. A technical drawing of modified optical cryostat is shown in Fig. 2-10. We

mount an optical window on the bottom of outer tail of the cryostat, open the bottom of

nitrogen shield, weld a copper sample mount right on the bottom of helium tail so that

samples can be cooled down with a cold sample mount. For the collection of light after

excitation of the sample, optical fibers positioned right on the top of sample are used to

deliver transmission or PL to spectrometer or detector. With this configuration, the

ultrafast laser pulse can reach the sample directly through resistive magnet bore and

optical window, while the sample can still be as cold as 10K (for more details see

appendix A).

In addition to resistive magnet, a superconducting magnet was also developed and

commissioned by us to carry out magneto-optical experiments, especially for the ultrafast

magneto-optics laboratory. We redesigned the cryostat for a 17 Tesla superconducting

magnet such that femtosecond laser pulses can be steered into the center magnet bore and









excite sample directly at field center. Fig 2-11 shows the section view of this

superconducting magnet. There is a stainless steel center bore welded on the cryostat and

going through the center of magnet. This bore isolates the sample chamber and helium

reservoir, which make it possible to do direct optics with this superconducting magnet.

The cold stainless steel bore is sealed with an optical window on the bottom and a

specially designed probe loading system on the top, shown in Fig. 2-12. With this probe

loading system, we can change sample without causing air leak into the center bore

merged in liquid helium. The sample on probe is cooled down with backfilling low-

pressure helium exchange gas in the center bore.

2.6.3 Ultrafast Light Sources

In addition to the development of cryogenics and magnet system, we also set up

several femtosecond pulse laser systems for time resolved magneto-spectroscopy These

ultrafast laser systems include a Ti:Sapphire femtosecond oscillator, a Ti: Sapphire

chirped pulse amplifier (CPA) and an optical parametric amplifier (OPA).

2.6.3.1 Ti: Sapphire femtosecond oscillator

Fig. 2-13 shows the schematic diagram of Coherent Mira 900 F femtosecond laser

system. In this laser system, a prism pair compensates dispersion caused by broad

bandwidth of laser emission. This passive mode locking ultrafast oscillator laser acquires

self-mode locking with Kerr Lens effect, and the shaker in the cavity works as a trigger to

initiate the mode locking. The pulse width of this ultrafast laser oscillator is around 150fs

and the energy per laser pulse is around 4nJ. This laser is tunable from 700 to 900 nm and

runs at 761VHz repetition rate. We use this ultrafast laser to get second harmonic









generation from BBO nonlinear crystal and carry out degenerate pump probe experiments

on ZnO semiconductors as described in Chapter 6.

2.6.3.2 Chirped pulse amplifier

In many optical experiments, strong ultrafast laser pulses (up to mJ per pulse) are

needed for either nonlinear effect like self phase modulation (white light generation) and

parametric amplification or for high carrier density generation in samples. Most of our

experiments were done with the Clark-MXR 2001 CPA. However, because of reliability

problems the Clark -MXR laser was later replaced by the Coherent laser in early 2007.

The current Coherent Legend-F chirped pulse amplifier (CPA) is set up in cell 3 at

DC facility for research in ultrafast magneto optics. Fig. 2-14 shows the schematic

diagram of this CPA femtosecond laser system. This CPA itself consists of three basic

components: a pulse stretcher, a regenerative amplifier cavity, and a pulse compressor

(see Fig.2-14). There are two external lasers for this CPA system, a Coherent Vitesse

oscillator (similar to the Mira described above), which generates a high repetition rate

ultrafast seed pulse train for amplification and an Evolution, which is a Q switch laser

used to pump Ti:Sapphire crystal inside regenerative amplifier cavity at a variable (but

typically 1 k
following manner. First, a 150 fs seed pulse train is generated in Vitessee laser and sent

into pulse stretcher. This seed pulse is stretched to approximately 100 ps, so that it will

not destroy the Ti:Sapphire crystal in regencavity as it get amplified. A Pockel cell (PC 1

in Fig. 2-14) then picks off one pulse from the train within the regenerative amplifier

cavity for amplification. The pulse undergoes several roundtrips within the cavity and

through the Ti:Sapphire crystal which is prepumped with the Evolution laser and










experiences a total gain of approximately 106. Once the amplification of seed pulse

reaches its maximum (around 2 mJ per pulse), it is switched out of the regencavity by a

second Pockel cell (PC2 in Fig. 2-14) within the cavity. Finally, the amplified pulse

propagates through a grating compressor (see Fig.2-14) to compress the pulsewidth back

down to 150fs. At the output, we obtain 150fs laser pulses at a 1 k
2 mJ per pulse from this CPA system. As we discuss in Chapter 5, this laser is used to

study PL from high density of carriers in InxGal-xAs/GaAs MQW in high magnetic Hield.

2.6.3.3 Optical parametric amplifier

The Ti:Sapphire oscillator and CPA laser can provide us with ultrafast pulse,

however, their wavelength ranges are limited. Therefore, an optical parametric amplifier

(OPA) is required to convert light to different wavelengths while preserving the short

duration of the pulses. Fig.2-15 shows the layout of a Quantronix OPA laser. This is a

Hyve pass system in total. The first three passes of the pulse occur through a beta barium

borate (BBO) nonlinear optical crystal for frequency conversion, and a signal pulse (at

frequency wsignal) and idler pulse (at frequency widler) are generated. In the forth and fifth

passes through the BBO crystal, signal and idler pulse are parametrically amplified with a

fraction of CPA pulse. The relation between fundamental CPA, signal and idler pulse is

given by

CPm = signwl 8Idler -1

After parametric amplification by CPA pulse, the signal and idler pulses are then used to

generated ultrafast pulses at different wavelength through second harmonic generation

(SHG), mi=20signa, l Or 20iidler, fourth harmonic generation (FHG), mi=40signa, l Or 40iidle,, and

different frequency mixing (DFG),










CP4 signal Idler -1

The five nonlinearly optical processes mentioned above cover wavelength range from

300 nm to 20 Clm.

2.6.3.4 Streak camera

In many cases, time-resolved photoluminescence is a very important method to

study the carrier dynamics since it provides a direct measurement of the radiative

emission of photons as carriers recombine in semiconductors. A picosecond streak

camera is the proper device to measure time resolved photoluminescence. Fig. 2-16

shows the operation principle of a streak camera. We are currently setting up a

Hamamatsu Streak Camera at the NHMFL ultrafast facility. In Fig.2-11 we can see that

conceptually, a PL pulse generated after excitation of a sample is steered into the slit and

then focused on a photocathode, where it is converted into an electron pulse of the same

duration. The electron pulse is then accelerated and passes through a very fast sweep

electrode, which is synchronized with the PL pulse, so that electrons at slightly different

time will be deflected at different angle by the AC high voltage and hit the CCD at

different position. Using this method, the temporal profile of a PL pulse is spatially

mapped on CCD in a spatial profile. By placing a spectrometer at the front end of the

streak camera, the PL can be spectrally and temporally resolved.





I I I I I
1300 1350 1400 1450 1500
Energy (mnev)


Transmission spectrum of InGaAs/GaAs MQW at 30 T and 4.2 K.The
energy position of each dip on transmission curve is correspondent to a
magneto exciton state. Magneto-excitonic states are labeled according to
the convention presented in Chapter 3.


el hh2s


e~llh
I e2HH21


O

I-





Fiue -.















j
ed

a,
o
r


a,


3.35 3.40

Energy(ev)


3.45


Figure 2-2.


Reflection spectrum of ZnO epilayer at 4.2K.Excitonic states and their
symmetry are labeled. In the reflection spectrum, the approximate position
of an excitonic state is marked with an arrow, which is the middle point
between a dip and the peak next to it on the low energy side. on the
reflectance curve. This spectrum will be discussed further in Chapter 5.



























radiative relaxation


condluction band


electron


non red stive relaxation


radiative recambination


hole


valence bardl


~Ennn


. 0


30000

25000

20000

'15000

'10000

5000


1


1.35


Energy (ev)


1.45


1.50


(b)
Figure 2-3. e-h recombination process and photoluminescence spectrum in
semiconductors. (a) Illustration of Photon induced photoluminescence in a
direct bandgap semiconductor, (b) PL of InGaAs/GaAs MQW in high
magnetic field 30Tesla excited with an intense femtosecond laser pulse.


excitai.il hoan


e~mision photDM











tqs t


Figure 2-4.


Simple illustration of optical pump-probe transient absorption or reflection
experiment.Both pump and probe are from pulsed laser and spatially
overlapped on the sample. The time delay between pump and probe is At.
Either the transmission or reflection of probe light is detected. By changing
the delay between pump and probe pulse, time resolved transmission or
reflection spectrum can be obtained.


Sample


pump pulse










Cryustat


o~-0.01



2-0.04

S-0.05


Time Delay (ps)


(b)
Experimental setup for optical pump-probe spectroscopy and TRDR
spectrum of ZnO. (a) Pump probe experimental setup for spectrum resolved
time differential reflectivity. Pump and probe are modulated with frequency
fi and f2 TOSpectively, a lock-in amplified is used to acquire the transient
reflection signal; (b) Time resolved differential reflectivity of ZnO epilayer
at 4.2K. Details will be discussed in Chapter 6.


Figure 2-5.














S400.




S200.

100.


-2)0 0 200 400 600 800

Time Delay (ps)

Figure 2-6. Time resolved photoluminescence spectrum of InxGal-xAs/AlGaAs MQW at
4.2K taken with a Hamamatsu Streak camera. Time resolution is around
5ps.

















































Figure 2-7. Technical drawing of the 30 Tesla resistive magnet in cell 5 at NHMFL.
From National High Magnetic Field Laboratory, www.magnet.fsu.edu, side
view of 31T / 32mm Resistive Magnet with Gradient Coil (Cell 5), date last
accessed September, 2007


Bitter dis ks











optical fiers ~ l~rEe


|- rotator



optical probe




vacuum jacket


liquid


liquid nitrogen



nitrogen shield


Cornox sensor
and heat~


sample


U


Figure 2-8. Cryostat and optical probe for CW optical spectroscopy at NHMFL.The
cryostat has vacuum jacket and liquid nitrogen space for thermal isolation.
An optical probe is inserted in the liquid helium (LHe) of the cryostat,
sample on the end of the probe is cooled down with He exchange gas, the
input light and output light are delivered through multimode optical fibers.







































Figure 2-9.


CW magneto optical experiment setup at the NHMFL. Input light is
delivered to sample in optical probe through fiber, the sample is mounted on
an optical probe, positioned at the field center and cooled down with LHe,
the output light from sample is sent to a spectrometer and the spectrum is
recorded with CCD or PMT. The magnet control and spectrum acquisition
from spectrometer is computerized with GPIB interface.











optical fibers


optical probe





vacuum jacket


liquid


Ig net


?


Modified magneto optical cryostat for direct ultrafast optics. The optical
cryostat is positioned on the top of a resistive magnet and the sample is
right at the field center. A sample mount is attached directly on the LHe
tail of the cryostat, so that the sample can be cooled down. An optical
window is mounted on the bottom of the outer tail of the cryostat, through
which the ultrafast laser can reach the sample without being stretched
significantly. The PL or probe light is delivered to detector and
spectrometer through optical fiber.


CPA/IPA.

Figure 2-10.













He melife valve

N2 exhaust port


to vacuum pump L



LN2 space


vacuum jacket

center hum

LHe reservor





supem~onducting
manget









Pulsed laser


.N2 space


res ervor


shield


window


Figure 2-11i. Technical drawing of the 17 Tesla superconducting magnet SCM3 in cell 3
at NHMFL. Stainless steel tubing is used as the center bore of this magnet,
an optical widow is mounted on the bottom of the tubing, samples on probe
are positioned in the center tubing. Ultrafast laser is steered in to the bore
and excites samples without being stretched much.


KF flange connected to load lock KF flange


I


I












cubic chamber for wires and f r


cap for fiber fit througI



flange conni




SS tubing 3/4"


double oring seal chambi




ondlock




ect to KF 50 on top of







Id to mount wire SIP


ToMum Pmump out port B


G-10 ring


Ii50SP


Laser pulse

Figure 2-12. Technical drawing of the special optical probe designed for
superconducting magnet 3 in cell 3 at the NHMFL. A load lock system is
attached on the top part of this probe, the vacuum in the center bore of the
magnet is not broken when loading and removing the probe from the cold
magnet bore. Temperature of the sample is controlled with a Cernox sensor
and electric heater. Ultrafast laser can reach the sample directly and the PL
or probe light from sample is delivered outside with fibers.










150fs
M2 75MHz,4nJ


BP1
From SW Verdi leser L



2 MS Ti:Sepphire M

M4 M1

BRF
Starter
MS

Figure 2-13. Coherent Mira 900F femtosecond laser oscillator. BPland BP2 is a Bruster
prism pair, Ml and M7 are cavity mirrors, BRF is birefringe filter, MS M7
are spherical mirrors, M2, M3 and M6 are mirrors, L1 is a lens.









130 fs


100ns


Regencavity


Figure 2-14. Coherent Legend -F chirped pulse amplifier (CPA). PC is pockell cell, wp
is waveplate.


Vitessee


EVolutiDR







CPA


CPA


CPA


Signal +idler


.......----ratin


BBI Crystal
Figure. 2-15. Top view of the optical elements and beam path in TOPAS OPA.


g9









Streak Image


t2 t1


Elecrn

Incident light pulses


Photocathorde



Time varying high voltage
Streak Irr age

Figure 2-16. Operation principle of a streak camera. The photocathorde converts light
pulse tl and t2 in to two electron pulses, the two electron pulses have
different positions for streak images because the high voltage bias is time
varymng.





















































Figure 2-17. Ultrafast optics experimental setup in cell 3 and 5 at NHMFL.










56









CHAPTER 3
ELECTRONIC STATES OF SEMICONDUCTOR QUANTUM WELL INT MAGNETIC FIELD

3.1 Introduction

This chapter provides a background in the physics and optics of quantum confinement

induced by structural modifications (quantum wells) and strong magnetic fields. Optical and

electrical transport properties of semiconductor materials are determined by their electronic

states. A background in the fundamental band theory of semiconductors is necessary to

understand the magneto optical spectroscopy, specifically, oflInxGal-xAs/GaAs multiple quantum

wells, a typical III-V group semiconductor material, and ZnO (bulk, epilayer and nanorod),

typical II-VI group semiconductor material. Band structures of Wurzite symmetry (C6v) ZnO and

Zincblende symmetry (Td) InxGal-xAs semiconductors are introduced.

In semiconductor quantum wells, carriers are confined in the two dimensions defined by

the barriers, and the electronic states have new characteristics with respect to bulk materials due

to quantum confinement. The exciton effect, energy states due to quantum confinement and

selection rules of optical transitions in quantum well are given in detail in this chapter.

In a high magnetic field oriented perpendicular to the plane of the quantum wells, further

confinement is introduced to a semiconductor quantum well, and the basic theory of magneto

optical process of semiconductor quantum well is given to understand the optical processes

related with interband Landau level transitions. Also, the density state of 3D, 2D and 1D

systems are given in this chapter.

3.2 Band Structure of Wurzite and Zinc Blend Structure Bulk Semiconductors

In a crystalline solid with N atoms, the electronic states of the N electrons make up

continuous energy bands separated by finite width band gaps. In a crystal, the electron









wavefuction and periodic potential of this crystal remain unchanged under translational

symmetry R (1, m, n), which can be described by the three primitive vectors: a, b and c as

R(1, m,n) = la + mb + nc,

1, m, n are integers. Because of the translational symmetry, the electronic wave functions in a

crystal can be described with "Bloch function" [40]


'F,(r)= er1rk-),3-


v is the index of an electron energy band, k is a reciprocal lattice vector, Nis the total number of

primitive cell unit in the crystal and u is a periodic function inside a primitive cell and has

translational symmetry


up,(r +R) = up,(r) 3-2

In equation 3-1, the Bloch function 'PVK is normalized over the whole crystal and in Eq. 3-2,

u, (r') is a function normalized over the volume of a unit cell. The value of k is limited to the

Wigner-Seitz cell in reciprocal space, which is called "Brillouin Zone".

Semiconductors are also a kind of solid crystal, which has a finite band gap between the

highest and fully occupied valence band and a lowest partially occupied (doped) or totally

unoccupied (undoped) conduction band. The band gap values and band structure of

semiconductors, which determine many optical and transport properties, are very important

parameters. The band gaps of semiconductors vary from near infrared (InAs 0.43eV) to

ultraviolet (ZnO 3.40eV). Among most of the III-V group semiconductors such as GaAs and

InAs, the typical structure is zinc-blende, while for the II-VI group semiconductors like GaN and

ZnO, the most common structure is the Wurzite structure.

In semiconductors, the Hamiltonian of an electron can be described as [71]:










h2k2
H = + V(r) + Hso + H st, 3-3
2m* vsa
where k is the momentum of electron, m*" is electron effective mass, V(r) is periodic potential in

semiconductor crystal, Hso is the spin and orbit interaction, and Hcry1 stlS the interaction between

electron and crystal Hield in an unit cell. Compared to the first two terms, the later two are

relatively small and can be treated as perturbation.

As the prototypical direct gap semiconductor, the first Brillouin zone and band structure of

GaAs (fcc structure) are given in Fig.3-1 (a). (We will be working with In0.2Gao.sAs in this

disseration, but the descriptions given for GaAs are applicable since GaAs and InAs have same

crystal structure.) At the center of the Brillouin zone, the point is labeled as r point (0, 0, 0). X

(1, 0, 0) on k, axis, and L (1/2, 1/2, 1/2) are also the fundamental points. The calculated

electronic band structure of bulk GaAs is shown in Fig. 3-1 (b). The conduction band in GaAs

has absolute minimum value at the r-point and two local minima at the L-point and X-point,

which are referred as L valley and X valley. The conduction band of GaAs does not split since it

is a s-like nondegenerate band, while the valence band split into three bands: heavy-hole, light-

hole and split-off bands since they are p-like three folds degenerate [71]. The degeneracy

between split-off (J=1/2) and heavy-hole and light-hole (J=3/2) is lifted due to the interaction

(Hso) between electron spin (s=il/2) and angular momentum (l=+1 for p-like electron).

However, at the r-point, the degeneracies of light-hole and heavy-hole subbands are not lifted

because of the high cubic symmetry (Td point group) of the GaAs cell (Hcrystal0).

In a Wurzite structure semiconductor such as GaN and ZnO, the first Brillouin zone and

bandstructure are quite different from the zinc-blende structure. Fig 3-2 (a) and (b) present the

first Brillouin zone and band structure of a zinc-blende structure GaN semiconductor. At the T-

point, the valence band of Wurzite structure semiconductors split into three subbands (heavy










hole, light hole, and split-off) due to the hexagonal (Csv point group) symmetry of GaN crystal

cell, which gives an additional perturbation part of Hcrystaf O and lifts the degeneracy.

In the optical transitions in semiconductors, a photon is either absorbed or emitted. This is

based on electron transitions between the top of valence band and bottom of conduction band.

The selection rule for this optical transition is Ak = 0, which expresses the momentum

conservation of crystal. Compared to the crystal momentum, the momentum of photon is very

small and can be neglected.

For direct bandgap semiconductors such as GaAs and ZnO, the valence band absolute

maximum and the conduction band absolute minimum occur at r-point, the center of Brillouin

zone, where interband and intraband (inter-subband) transitions are observed without phonon

emission. The optical transitions from other valley (X or L valley) in conduction band to r-point

of the valence band must be accompanied by the emission of a phonon to conserve the crystal

momentum .

3.3 Selection Rules

In Kane model [72], since in all the II-VI and III-V group semiconductors the chemical

bond are formed with outer shell electrons nsnp, the wave functions of hybridized s-like band

and p-like bands can be represented using 8 band edge Bloch functions (uo, ul,..., us)

|ST>,|XT>I~>|>,|ZT> and |SL>,|XL>, |Y1>, |Zl>. However, after the spin orbit interaction Hso is

considered, a new linear combination of these functions can be formed. In the new functions,

J=L+S and J, are good quantum numbers and H can be diagonalized. The new Bloch functions

basis set [71] is given in Table 3-1. They are taken as a basis set in a Kane model calculation

[72].









The optical transitions between conduction band and valence band due to electro dipole

transitions in semiconductor are described by the transition matrix element [71]


M,- = 'f; E-p'F~d r .3-4


where r is the optical polarization unit vector and p is the electron momnentumn operator. Using

the Bloch functions (Eq. 3-2), M,, can be expressed approximately as [71]:


M, = e- Ziy p ,,) ff*/-d r+e- u, uj ff / dr 3-5

where uf and u,, are the wave functions for the initial and final state(see Eq.3-1),

1 xd it evl fnto oa lj ,,h rnii mti mil


determined by first term in Eq.3-5.


The absolute values of the transition matrix elements (Sc p u ~,, j are listed in table 3-2,

where S is the conduction band wavefunction and u,, is the valence band wavefunction, x, y, and

z are the propagation direction of light, ex, 8, and a are light polarization

-1( Ixl~ -1(I? ) -1(IIJ
and P = ( xX S )= (pz
m m m

3.4 Quantum Well Confinement

In this thesis, we have focused our study on type I quantum well structure described in

chapter 1. The Bloch wave function of an electron or hole confined in the quantum well with

periodic potential V(z) is described as [41]


W, = er k*" z ,( 3-6










here k is the electron wave vector in xy-plane and X(z) is an envelop function along the z

direction, in which the quantum well is grown. We can separate the wave function (Eq. 3-6) into

xy and z directions. In the z direction, we have



2m* dz2 -

The eigenvalues E,, of this equation 3-7 are the energies of different quantum confined

subbands. A schematic diagram of the confinement subbands in a type I quantum well is shown

in Eigure 3-3.

For the states in the xy plane, if we use parabolic bands for kx and k,, the carrier energies in

the quantum wells are given by:


E = E,, +-(k, + k ). 3-8
2m*

The Bloch wave function (Eq. 3-6) for a quantum state labeled by n can be expressed as





here, k and r are the 2D electron wave vector and position vectors in the xy-plane.

With the envelope functions X(z) we can derive the selection rules of the envelope

function from equation 3-5,


,f f = er(k-k i)dr IX, z)7,(z)d'z. 3-9

The first term shows that the optical transition is allowed when the electron momentum k is

conserved

k' = k' .


The second term gives us the selection rule for transition between two different subbands [41]









nZ-n =evenZ.

However, the transitions corresponding to n-nz=0 are far stronger than n-nz=2, 4, 6... [41]. The

optical transitions processes correspondent to n-nz=0 are shown in Fig. 3-3.

3.5 Density of States in Bulk Semiconductor and Semiconductor Nanostructures

A consideration of the density of states is very important for understanding the optical

response of semiconductors. It expresses how many states are available in the system in the

energy interval between e and a de; the maximum number of carriers is reached when all the

density of states is occupied up to Fermi level. This will become particularly important for

understanding the superfluorescence experiments in Chapter 5. The density of states in a bulk

semiconductor is given as [41]


g3D F)= __i 3-10a

In a 2D semiconductor quantum well, the carriers are confined within the well width, so the

density of states is described as [41]:



g2D (F) =C s (c- Ez,). j= 1, 2, 3---. 3-10b

Here, j is the index of quantum confined states and B(E E ) is the step function.

For a 1D system, the density of states is given by [41]:
1
glD 23-10c


Here, jx and j are index of quantum confinement states on : and x direction.


If all the 3 dimensions are quantum-confined for a free carrier, we have a quasi OD system,

and the zero dimensional carrier density of states is given by [41]

gOD /)= 213e 6 3-10d










Here, &, is the energy of the jth quantum confinement state and Sc g) is the Dirac delta

function.


The density of states curves for 3D, 2D, 1D and OD system are plotted in Fig.3-4. We can

see that for 3D and 2D systems, the density of states is continuous, while in 1D and OD, the

continuums collapse and the density of state get discrete and turn into 8 function.

3.6 Magnetic Field Effect on 2D Electron Hole Gas in Semiconductor Quantum Well

In a type I semiconductor quantum well such as InxGaAsl-x/GaAs, electrons and holes are

confined in a potential well defined by the xy-plane. In the presence of magnetic field along the z

direction, an additional quantum confinement is applied to the electrons and holes in the xy-

plane. The Hamiltonian of an electron in a quantum well in the presence of magnetic field along

z direction is given by [71]


H=l (p- -A)2 + V(z), 3-11
2m c

where A = (0, xBR,0) is the vector potential and VT(z) is the quantum well confinemnent potential.

We can separate the electron wave function into xy-plane component and z direction component,

so the wavefunction 7 can be written in the form

'F(x, y, z) = h(x, y) f(z) .

Using this wave function, the Schroidinger equation can be separated in two independent

equati ons :

(I) In :-direction (QW growth direction), we have


2m* dz~l









This is referred to type I semiconductor quantum well confinement and discussed earlier (see

Eqs.3-7, 3-8 and 3-9).

(II) In xy- plane (quantum well plane), we can modify the Schroidinger equation.

Setting h(x, y) = e(rek")p(x'), Eq. 3-12 can be modified into [71]

+A d2m apux') = EBXx'),. 3-13



where x' = x + This is a typical Schroidinger equation for harmonic oscillators and the
Be
solution is well known. The energy of this xy-plane motion is given by [71]

E = N + ha N=0, 1, 2...

Be
where me~ = -is called cyclotron frequency. The quantum states corresponding to the
mc
harmonic oscillator energy states are known as Landau levels.
The total energy including both z- and xy in-plane contributions is


E = E,t +N + h

There are some important lengths and densities that define quantum wells in magnetic

Hel s. he agn ticlen th e i deine as e = The degeneracy of a Landau level is 2 eB/h


where the factor of 2 comes from electron (hole) spin. Typical Landau levels evolve from

electronic quantum confinement energy levels in a quantum well are shown in figure 3-5. The

crossing or anti-crossing effect between 3rd Landau level evolves from El and the 1st Landau

level evolves from E2 State is shown. The crossing or anti-crossing effect depends on the

symmetry properties of wave function of the states and the perturbation at the intersecting point.

For a particular magnetic field, the number of electrons populating a LL is finite. The

electron density on a filly filled Landau level at a magnetic field is given by [71]










eB


The filling factor v is defined as
n nh
ne eB

Physically v/2 at any magnetic field gives the number of fully occupied Landau levels. And

again, the factor of V/2 COmes about because each Landau level has two spin states.

3.7 Excitons and Excitons in Magnetic Field

3.7.1 Excitons

As discussed in Chapter 1, an exciton is a pair of an electron and a hole due to the

Coulomb interaction between them, and its energy states are very similar to a hydrogen atom.

Therefore, the exciton energy levels are expressed as


E~exloni, e a 3-14


where F is the dielectric constant of semiconductor material, n a is the reduced effective mass of

4*
an exciton, n=1, 2, 3..., and R* [41] is called the effective Rydberg energy and

E2h

as ,, is an effective exciton Bohr radius. Similar to the hydrogen system, for a given
nae

quantum number n, the degenerate state has fine structures due to angular momentum l=0, 1, 2,

3.... The fine structure of this exciton is also labeled as Is, 2s, 2p...

In semiconductor quantum wells, the exciton binding energy increases with respect to bulk

semiconductors because the electrons and hole at the bottom of conduction band and holes at the

top of valence band, which form the excitons, are confined in the same well and their wave

function overlap is larger than in the corresponding bulk material. Therefore, the exciton binding

energy depends strongly on barrier height and the well width.









Unlike the exciton binding energy for the 3D bulk case given in equation 3-14, in a

quantum well with well width less than the exciton diameter 2aB*, the confinement has a

significant effect on excitons--one layer of electrons and holes gas are confined in a two

dimensional plane. In quantum wells with extremely narrow well widths, the exciton binding

energy are given by [41]

E2D R 1 3-15
(n + 1-)2

So, in the 2D case, the ground state binding energy of an exciton is 4R*, which is four times that

of the 3D bulk semiconductor [73-76].

3.7.2 Magneto -excitons

In the presence of magnetic field, the excitons in semiconductors are called magneto-

excitons. Due to the existing magnetic field, the electron and holes start to orbit with respect to

each other, and the orbit shrinks if the magnetic field increases. We can expect that the

hydrogen-like exciton wave functions diminish in radius with increasing magnetic field.

The Hamiltonian of an exciton in a quantum well in the presence of magnetic field

perpendicular to the well layer can be depicted as:


H = He + H 3-16



The first two terms are the Hamiltonian of electron and hole in magnetic field, and the third term

is the Coulomb interaction, which depends on the separation between electron and hole in an

exciton. The first two terms can be expressed as [71]:


1
H,, =(p,~,+ e At r))' + V,,,( r), 3-17
2nze.;,










where Ai = ~(rx BR) is the vector potential from magnetic field.


Due to the presence of the potential we cannot separate the Hamiltonian in Eq.3-
e r

16 and the wave function into two parts for : direction and xy-plane to get an analytical solution.

However, if perturbation theory is used to treat the exciton ground state in the presence of

an external magnetic field, we can consider the effect of low magnetic field as small

perturbation. The perturbation caused by magnetic field can be described as [71]:

1 2 E h4
AE~i"" (B) -DIRy 7 B12 3-18
2 4c e~m


where 7 is a dimensionless effective magnetic field in the form of 7 = -, which is the ratio of
R*

cyclotron energy and excition binding energy, me = (mee+o) mch *IS ithe combination of

electron and hole cyclotron energy and D is the dimensionality parameter for the excitons.

Equation 3-18 is often called "diamagnetic shift of exciton" and only valid for 7<1 [71].

In the case of high magnetic field limit, where the magnetic field effect is larger than

exciton effect and 7>>1, the magneto-exciton is more similar to a free electron hole pair in

magnetic field, and the binding energy R, is considered only as small perturbation (See Eq. 3-

16). Therefore, in high magnetic fields, the energy shift due to magnetic field is given by:


AE (B) = Am ~.
ground 2

For a GaAs semiconductor quantum well, where R* is 5.83 meV [77], the value of 7 is

around 5 T. This is a significant point--if we want to study the optical magneto-exctions in GaAs,









it is necessary to use high magnetic fields in excess of 20 T, since the magnetic field effect is 4

times larger than the Coulomb effect.

Figure3-6 shows the calculation results of free electron hole transition energy and exciton

energy oflInxGaAsl-xGaAs (including the band gap E,) in magnetic field. The solid line are

excitonic, which includes the Coulomb interaction between electron and hole pairs that populate

at different Landau levels, while the dashed line are Landau energy levels correspondent to free

electron and hole populate on different Landau levels.

Using this theoretical basis, we turn now to a study of the magneto-optical properties of

excitons in In0.2Gao.sAs/GaAs quantum wells with the goal of understanding emission from

highly excited quantum wells in high magnetic fields.









Table 3-1. Periodic parts of Bloch functions in semiconductors
Quantum number Wavefunction
ul 1 1 i |St>
| s, >
2 2
U2 1 1 i |SJ>
2 2
U3 3 31
'2 2 2|(iY


|(X iY) J>

|(X iY) 1>- |Z T>

- |(X iY) ?>- |Z 1>

|(X iY) 1>+ |Z T>

- |(X-iY) ?>+ |Z 1>


3 3
I'2 2 >

IP >





IP, >
IP, >










Table 3-2. Selection rules for interband transitions using the absolute values of the transition
matrix elements
Propagation Ex Ey Ez Transition
direction
Z P P Impossible hh e
X~J J obdenh
Y P Forbidden hh e


Z P P lh e

X P lh e

Y P 2 h e

Z p p Split-off e

X p p Split-off e

Y Split-off e

















































(b)
Figure 3-1. Band structure of Zinc blend semiconductors. (a) Brillouin zone of zinc blend
structure. (b) Band structure of Zinc blend structure semiconductor in <100> and
<1 11> direction. r, X and L valleys of conduction band are shown. Light hole and
heavy hole are degenerate at r point. From Electronic archive of New Semiconductor
Materials, Characteristics and Properties, loffe Institute, Russia [78]


Energy

r-volley












































k, E Heavy holes k,
Light holes

Split-off band


Wortzite


TEnergy


A-valley


M-L-valleys


(b)
Band structure of wurzite structure semiconductors. Brillouin zone of a wurzite
structure. (b) Band structure of a wurzite structure semiconductor in kx and kz
direction. r, A and M-1 valleys of conduction bandare shown. Degeneracy between
heavy hole and light hole at r point is lifted.From to Electronic archive of New
Semiconductor Materials, Characteristics and Properties, loffe Institute, Russia
[79].


Figure 3-2.











Bar rier


- - I


- - -


Valence hand
lhh2

hlh3


Bar rior

























Ilhi


Ih2


Well


Figure 3-3.


Band alignment and confinement subbands in type I semiconductor quantum well.
el and e2 are subbands in conduction band, hhl, hh2 are the heavy hole subbands
in valence band, lhl and lh2 are light hole subbands in valence band. The solid lines
between conduction and valence band are correspondent to the allowed optical
transitions.


CDnduc~tion barnd



















































__


3d

2d


1 E2


g(E)


lia od
E1 1


Od
2'


(b)
Density of states in different dimensions. (a) Density of states in 3D bulk
semiconductor and 2D QW; (b) density of states inlD (dot line) semiconductor
quantum wire and OD (solid line) semiconductor quantum dot (d).


Figure 3-4.






































Figure 3-5. Electronic energy states in a semiconductor quantum well in the presence of a
magnetic field. The dashed line corresponds to crossing behavior and solid line
corresponds to anti-crossing.


E(mev)











































Figure 3-6.


Calculation of free electron hole pair energy (dash line) and magneto exciton
energy(solid line) of InxGal-xAs/GaAs QW as function of magnetic field.
s, p, d. fare different magneto excitionic states. Solid lines are for the e-h pair with
consideration of Coulomb effect and dash lines are for the e-h pair without
considering Coulomb interaction. Reprint with permission from T. Ando et al.,
Phys. Rev. B 38, 6015-6030, (1988), figure 7 on page 6022.


Magnetic filed (T)









CHAPTER 4
MAGNETO-PHOTOLUMINESCENCE IN INGAAS QWS INT HIGH MAGNETIC FIELDS

4.1 Background

Optical phenomena arising from interband and intraband transitions in 2D electron-hole

gases in III-V semiconductor quantum well have been studied intensively and extensively in

theory and experiments during the past several decades owing to the intense interest in the

physics of low dimension system and their potential applications [81].

In a magnetic field, the quantum-confined states in the conduction and valences band split

into different Landau levels, resulting in electrons and holes populating different Landau levels,

thus, the interband Landau level transitions will dominate optical transitions in magnetic fields.

By observing and analyzing inter-LL optical transitions, we can study the optical transitions of

2D electron hole gas such that detailed information about the conduction and valence band

structures, carrier effective mass and carrier interactions between different Landau levels (such

as crossing and anti-crossing) can be acquired [82-84]. This work will serve as a background to

the next chapter on the nature of light emission from dense magneto-plasmas in quantum wells.

Using relatively weak light sources such as tungsten and xenon lamps, we can measure the

absorption spectrum of optical transitions from valence band Landau levels to conduction band

Landau levels in semiconductor QWs in magnetic fields and determine the energy peaks of each

inter-Landau level transition. In the absorption spectrum, these optical transitions are still

predominantly excitonic, since the separation between two electron hole pairs is relatively larger

than the exciton Bohr radius (d >> axcoon), so that the Coulomb interaction between electron and

hole in a exciton system are not screened.

PL due to recombination of electrons on a conduction Landau level with holes on a valence

band Landau level is necessary to study the Landau level physics of magneto-excitons (at low










densities) or magneto-plasmas (at high densities). In this case, CW excitation (for example, with

a He-Ne laser) is not sufficient since it cannot create a large number of carriers to populate in

higher Landau levels; the only photon emission channel is due to the transition lowest electron

Landau level to highest hole Landau level. Therefore, pulsed lasers such as Q-switched or mode

locked lasers are needed to generate a sufficiently high carrier density so that interband

transitions due to higher Landau levels are observed. During the excitation, the laser pulse

transfers large amount of energy to the semiconductor in a very short time (~ ps), and carriers

can reach high densities before their recombination, which deplete the higher LLs.

III-V group semiconductor quantum wells, especially composed of GaAs or InxGal-xAs, are

widely used to study the physics of magneto-excitons [85]. This group of materials has a

relatively small effective mass nz*~ 0.067nro (mo is the free electron mass), which makes it easy

to observe transitions between higher Landau levels, since the Landau level splitting between

two consecutive levels is given by

eB
AE = Aco~ = A 4-1
na

In addition, for InxGaAsl-x/GaAs quantum wells, the degeneracy of heavy hole and light

hole is lifted at r point due to the existence of strain in the well. This is an effect of degenerate

perturbation in quantum mechanics. The lattice mismatch between well and barrier material

cause a crystal lattice distortion and induce a new static electric field in the Hamiltonian of

electrons on valence bands. This perturbation lifts the degeneracy between heavy hole and light

hole subband.

Since the heavy hole and light hole are separated by ~100 meV, we can observe transitions

between electron LLs and LLs originating from heavy hole and light hole subbands respectively.









Before we start to investigate the inter-LL transitions, the labeling of the inter-Landau level

transitions needs to be defined. A diagram ofinterband LL transitions is plotted in Fig.4-1(b),

which describes the optical processes of each peak in absorption spectrum. We use the hydrogen-

like excitonic notation to represent the transitions, and the meaning of each term is given as

following.

en is an electron on the nth subband, hn is a hole on the nth subband, I or h means heavy

hole or light hole subband and ns means that both electron and hole are on the nth LLs originate

from a subband. This notion well represents the hydrogen like e-h pair bond with Coulomb

interaction. However, under high excitation density, we use 0-0, 1-1 and 2-2 to represent the e-h

inter LL transitions (see Fig. 4-2(a)), since the electron and holes density is high and Coulomb

interaction between electron and hole in an e-h pair is screened so that the electron hole pair is

plasmonic instead of excitonic [89, 86-88].

Ando and Bauer [90], and Yang and Sham [91-92] have theoretically studied magneto-

excitons in 2D electron hole gas in GaAs quantum wells from low to high magnetic field.

Valence band complexity, which due to the mixing between different subbands in valence band

(shown in Fig.4-2(a)) is considered in their calculation of inter-LL transitions to account for

diamagnetic shift at low field, linear dependence of magnetic field at high field and other

experimental results.

Using nanosecond pulsed laser excitation at high powers, Butov, et al. have studied the

photoluminescence of interband -LL transitions in InxGal-xAs quantum well up to 12 T in details

[93]. In his experiments, the photoexcited electron-hole gas is considered as a magnetoplasma

instead of magneto-excitonic at high laser excitation powers (carrier density up to 1013Cm-2 in the

quantum well). In addition to 0-0 transitions, transitions between higher LLs are also observed in









the PL spectrum, as shown in Fig. 4-2(a). In Fig. 4-2(a), the peaks of the LL transitions (n-n)

shift to the low energy side with the increasing of carrier density. This is caused by carrier-

induced bandgap renormalization (BGR), which is considered to be many body effects and can

be interpreted using many body theory instead of single particle theory [93].

4.2 Motivation for Investigating PL from InGaAs MQW in High Magnetic Fields Using
High Power Laser Excitation

While these prior magneto-photoluminescence experiments have revealed several insights

about the physics of high densities of carriers in Landau levels, they were performed in relatively

low Hields (less than 12 T) using either CW optical measurements or nanosecond pulsed laser

excitation, with excitation densities of few GW/cm2. A drawback of using nanosecond excitation

for these experiments is inter-LL carrier relaxation can occur during the excitation pulse,

resulting in an equilibrium distribution of filled LLs. In addition, inter-LL recombination can

actually occur during pumping, reducing the carrier density.

In order to investigate these PL effects in QW in new regimes with higher densities and

larger LL separation (i.e. higher magnetic Hields and high pump power excitation), new facilities

are required. As discussed previously in Chapter 2, we have developed an ultrafast spectroscopy

laboratory at the DC High Field Facility of the National High Magnetic Field Laboratory, with

the capability of probing over the 200 nm-20 Clm wavelength range with 150 fs temporal

resolution in fields up to 31T.

In high magnetic fields, the density of states of 2D electron hole gas will evolve into a OD

hydrogen like system owing to magnetic field confinement (See Chapter 3). We can expect that

all the electron and hole states will populate a very small energy range in a width AE about the

energy E of the LLs resulting in each energy level of this OD system having a very high density









of state (see Fig.3-4). New optical phenomena are expected in this high-density electron hole gas

system at high magnetic field since the Coulomb interaction between e-h is screened.

4.3 Sample Structure and Experimental Setup

InxGaAsl-x/GaAs with x=0.20 semiconductor QW samples were grown via molecular

beam epitaxy (1VBE) method on GaAs substrates. The samples consist of a GaAs buffer layer

grown at 570oC followed by 15 layers of 8 nm In0.2Gao.sAs quantum well separated by 15 nm

thickness GaAs barriers, all were grown at substrate temperature between 390 to 4350. Samples

were provided by Glenn Solomon from Stanford University. The sample structure is shown in

figure 4-4.

Using the CW optics setup and resistive magnet described in Chapter 2 at the NHMFL, the

absorption spectra were measured at 4.2K up to 30 Tesla. The white light source used for

absorption spectrum is tungsten lamp and excitation light source for the CW PL spectroscopy is

a He-Ne laser at 632nm wavelength. Using the ultrafast optics facility and a 31T resistive

magnet, the photoluminescence spectrum was measured for the same sample at T=10 K. The

excitation light sources are the CPA and a tunable OPA as described in Chapter 2. The CPA laser

operates at 775 nm and the OPA was tuned to 1100 nm and 1300 nm respectively. We excite the

sample with different power up to 25 GW/cm2. In both absorption and PL experiments, we chose

the Faraday geometry shown in Fig. 4-5, in which the magnetic field is perpendicular to the

quantum well plane and the propagation of light is parallel to the magnetic field.

4.4 Experimental Results and Discussion

4.4.1 Prior Study of InxGal-xAs/GaAs QW Absorption Spectrum

As a prelude to our investigations, Jho and Kyrychenko [82] have previously studied

InxGal-xAs QW samples used in our high field experiments in high magnetic fields to understand

the complex mixing behavior. For reference, the energy levels of this InGaAs quantum well are









shown in Fig.4-6. The magnetic Hield-dependent absorption spectrum of InGaAs quantum is in

shown in Fig 4-1(a). At zero fields, three exciton levels, elhhl, ellhl and e2hh2, are clearly

resolved, and the shape of absorption curve is a step function, corresponding to a 2D e-h gas

density of state. Between the exciton levels, continuum absorption is also observed. We can see

that the splitting between h1 and 11 hole state is relatively large (~100 meV), induced by the

strain on InxGal-xAs QW, which is caused by the mismatch of crystal lattice between InAs and

GaAs semiconductor. This energy separation reduces the wavefunction mixing between h1 and

11 hole states and permits unambiguous study of the elhl exciton, since elhhl and ellhl exciton

states can be considered separately.

With increasing magnetic Hield strength, the elhhl and ellhl exciton states split into

magneto-exciton states elhhl 1s, elhhl2s, elhhl3 s and e lhlh1s..., using the description of the

magneto-exciton states given above. The corresponding inter-Landau level transitions are given

in Fig.4-1(b). At higher magnetic Hields, we can see from spectrum that the continuum states

between exciton steps collapse and the absorption spectrum curve evolves into OD-like density of

states, indicating that e-h gas system has evolved into a quasi OD system (see Fig. 4-1).

In the absorption spectrum, each excite magneto-.exciton state (2s,3s,4s) originating from

the elhl state shows anti-crossing -like splitting when it intersects with elll1s state, indicated

with arrows. Jho and Kyrychenko have previously modeled this anti-crossing effect [83]. They

found that each excited state shows anti-crossing like splitting when it meets a dark state. This

splitting behavior is independent of polarization, and sensitive only to the parity of the quantum

confined states. They also attribute the origin of this effect (~9meV) to Coulomb interaction

between e-h pair instead of hole valence band complexity. In Fig. 4-4, an example of valence

band mixing is shown. In this figure, the dispersion curve of heavy hole subband crosses the light









hole subband at certain k value, which causes the wavefunctions of heavy hole and light hole get

mixed also.

4.4.2 PL Spectrum Excited with High Peak Power Ultrafast Laser in High Magnetic Field

We now contrast the above spectrum with PL observed using ultrafast laser pulses. Fig. 4-

7 shows magnetic field dependent PL spectrum from InxGal-xAs QW excited with 775 nm, 150

fs laser pulses of 10 GW/cm2, which generates carrier density ~1012Cm-2. At zero field, we

observe elhl and e2h2 interband transitions, and with the increasing of magnetic field these two

PL peaks split into inter-LL transitions ('Landau fan'). We observed PL from well defined inter-

LL transitions up to elhl5s, but the anti-crossing-like splitting between elh ns and el lns in the

absorption spectrum are not observed in this PL spectrum. As mentioned above, the anti-crossing

effect is due to the Coulomb interaction between electrons and holes, therefore, the absent of

mixing of LL states indicated that the Coulomb interaction is screened at high e-h density so that

the corresponding transitions between LL states in Fig.4-7 are not purely excitonic.

For comparison, we plot the Landau fan diagram comparing the absorption spectrum and

PL spectrum under high power excitation in Fig. 4-8. The Landau fan diagram of PL is very

different from the Landau fan diagram of absorption even at high magnetic field. First, for the

same inter-LL transition, the energy position of each PL peak has red shift with that of the CW

absorption peak, which we attribute to carrier density-induced bandgap renormalization [93].

This band gap renormalization is caused by the many body effect of carriers and this many-body

effect gets stronger at high carrier density. Second, at high magnetic field, since the excitonic

effect can be neglected, we have the following form for the energies:

heB
E = Eg + -I(n +1), 4-2
m c









where E is the energy position of peak of a LL at given magnetic field B, E, is the band gap, m*"

is e-h pair effective mass and n indicates the nth LL. We can see that in equation 4-2, E is

linearly proportional to B and 1/m*" is the slope, fitting result shows m*"=0.0672mo, mo is the

electron effective mass. From Fig.4-8, we can see that for a trace of given LL, the effective mass

in the absorption spectrum should be higher than that in the PL line, which indicates that the m*

is higher at low carrier density. Third, in the case of free e-h pairs with no excitonic coupling,

such as in e-h plasma, the traces of all the LLs originate from same subband should converge at

zero field since the Coulomb interaction bind e and h is screened. This effect is consistent with

the traces of LLs in PL spectrum. However, in absorption spectrum, the line of LLs peak

positions do not converge at zero field because of the existing of e-h binding energy. Thus, the

magneto-PL of InxGal-xAs/GaAs QWs excited with high power ultrafast laser pulses is most

likely plasmonic instead of excitonic.

In Fig.4-9, we plot the magneto-PL excited with different excitation intensity for three

wavelengths (a) 1300 nm, (b) 1100 nm and (c) 775 nm at 25 T. For each wavelength, we denote

the lowest and highest excitation intensity in GW/cm2. The peak position are assigned from

lower energy side 0-0 to higher energy side 1-1, 2-2 and respectively. From the Fig.4-9, we can

see that the excitation with 1.1 Cpm and 1.3 Cpm are below InGaAs QW bandgap so that the PL

originates from carriers excited via two-photon absorption into the GaAs barrier and capping

layer as well as the continuum states of InxGal-xAs QW. For 775 nm as well as 1.1 and 1.3 pum

excitation, PL emission occurs after excited carriers relax down to the QW subbands. In Fig. 4-9,

the peak energies of each LL remain at fixed positions and do not show any red shift at high

pumping intensity. This indicates that the many particle interaction effect is not resolved and the

bandgap renormalization effect is suppressed at low excitation power.









In Fig4-9 (a), (b) and (c), we can see that the character of energy peaks 1-1 and 2-2 are

very different from 0-0 peak. At low excitation powers, broad and weak peaks from 1-1 and 2-2

are seen in (b) and (c). With increasing the excitation laser intensity, a narrow peak starts to

appear on the high-energy side of 1-1 and 2-2 peaks and become dominant at high excitation

power. The linewidth of narrow peak of 1-1 is 2.3 meV, smaller than that of 0-0 peak (9 meV),

implying a different emission origin for these two peaks. In addition, we do not observe these

narrow peaks in the magneto-exciton absorption spectrum shown in Fig.4-1.

We plot the 775 nm, 1.1 pum and 1.3 pum laser excitation power dependence of PL intensity

for 0-0 transitions, 1-1 transition, including broad and narrow peaks, in Fig4-9 (d) to (f). For

775nm excitation, the PL intensity from all the three states rise up rapidly at low power

(<2GW/cm2) and then saturates. At 1.1 Cpm and 1.3 Cpm excitations, the PL intensity from 0-0

transition and tail of 1-1 transition increases proportionally to I2pump, Since the excitation requires

a two photon absorption which scales as the square of laser intensity. However, the narrow peak

of 1-1 transition shows very different scaling. In Fig.4-9 (d), the narrow peak of 1-1 LL transition

shows no emission until threshold pump intensity (~13 GW/cm2), which might be an evidence of

stimulated emission processes.

To understand the many particle effect in the high density of electron hole gas generated

with femtosecond lasers, we plot the magnetic field dependent spontaneous emission calculated

with an 8 band in Pidgeon-Brown effective mass model [94](for details, see appendix B) in

Fig.4-10 (a). Fig. 4-10(b) is the correspondent experimental results. By comparing the two

curves, we estimate that the actual carrier density is between 1012/CM2 and 1013/CM2 in OUT

experiments. However, there are several discrepancies between theoretical calculation and our

experimental results.










(I) The energy peaks of higher LL levels are shifted due to the single particle theory, in which the

Coulomb interactions between electron hole and renormalization effects are neglected.

(II). Spin induced splitting in magnetic field is not observed experimentally due to the large

inhomogeneous broadening of the PL peaks.

(III) The theory does not predict the emergence and power scaling of the narrow emission peaks

at 1-1 LL transition,

We suggest that the experimental curves are induced by new emission processes at higher

lying LLs. More systematic studies are presented in the next chapter to elucidate the origin of

these phenomena.

4.5 Summary

With the underlying theory of LL physics, we have elucidated the conduction and valence

band structure of InxGal-xAs/GaAs QW. The anticrossing behavior between LLs originate from

different subbands has been discussed. Previous investigation shows that the anticrossing is due

to Coulomb interaction between e-h excitonic pair. Furthermore, by comparing the CW

experimental magneto-absorption spectrum and magneto-PL spectrum with ultrafast high power

laser excitation, it is found that the interaction between e-h is plasmonic rather than excitonic.

Also new sharp features emerge in the PL spectrum of interband LL transitions, which implies

new optical process in the PL emission. That is the subj ect of Chapter 5.

















c .E.-2






1350 14001450 150

O.E-I~"T~ \ 2 Energy/f (meV)20


P (a)
4 L= 2


Energy L=1---
oL=0
el~i











L= 2


ManeicFild(T

(b)O


Figre4-1 Mgnto boorpio setruman sclhemati digrmofitebndLndulee







Energ diaram o theoptial rnsition Finth mageoasrto pcrmo




InxGal-xAs/GaAs quantum well. Each transition corresponds to a peak in the
absorption spectrum.













u~ I T=4.2 K
0-0 1-1 2-2 3-3 4-4



H4.7x1012








10"-- n=0,5x10a"cm-
1.23 1.33 1.43 1.53
ENERGY (eV')
(a)


0.07
:Inc.2eaGQ.82As GaAs SQW solid dots
Inc~,saoo.47As/inP SQW open dots

y0.06 1 O k=1.5x10'cml'
e~ AA k=2.1x10"cm-'






0.04 -





DENSITY (10'2 om )


(b)
Figure 4-2. Magnetophotoluminescence experimental results of band gap change and effective
mass change. (a) Band gap renormalized at high carrier density, (b) Reduced
effective mass renormalized at high carrier density in InxGal-xAs semiconductor
QW.Reprint with permission from L. Butov et al., Phys. Rev. B 46, 15156 15162
(1992), Figure 2 on page 15158 and Figure 8 on page 15161









ENk~


Figure 4-3. Valence band mixing of heavy hole and light hole subbands in semiconductor
quantum well. Light hole subband crosses with heavy hole subbands.


Light hole















I ~Buffer


Figure 4-4. Structure of In0.2Gao.sAs/GaAs multiple quantum well used in our experiments.


5 Periods

























L


Figure 4-5.


Faraday configuration in magnetic Hield. The light propagates in the direction of the
magnetic Hield B and the electric field polarization E is perpendicular to the
magnetic Hield.


famlll ~Z
Sample


Laser beam


Z


Magnetic Field (B)









Ba~s


- - -


hhl
hh2 100mov Valence hand


hh3


Ga~s





-10mv


1325meV


Figure 4-6. Energy levels of electron and hole quantum confinement states in InxGal-xAs
quantum wells. el,e2, hhl, hh2 denote the electron and hole states due to quantum
confinement.


In~abs


CoDucioiD boHE


-20mev
Ilh
lh2

























1h

ehh


I II
12012 36 4014














poe f120 GW/c 2 16 4 40































0 4 8 12 16 20 24 28 32

Magnetic Field (T)


Figure 4-8.


Landau fan diagram of absorption and PL spectrum of InxGal-xAs quantum well in
magnetic field up to 30 T. The solid squares are the energy positions ofinterband
LL transitions from absorption and the solid triangles are energy positions of
interband-LL transitions from PL spectrum.




















j
m

>I
cl
m
c

E











130


1.45


Figure 4-9.


Magneto-PL (a-c) and excitation density dependence (e-f) of the integrated PL
signal in InxGal-xAs quantum wells at 20 T and 10 K.The left side plots the PL
spectra on a semilog scale excited at (a) 1300 nm, (b) 1100 nm, (c) 775 nm, the
excitation density is marked with arrows. The right side displays the excitation
density dependence at (d) 1300 nm, (e) 1100 nm and (f) 775 nm.


"1.35 1.40

Energy (eV)


Excitation density (Gwicm )











B = 25 Tesla


T = 4.2 K


1


0.1


0.01


1 E- 3


0.1



0.01


c

a

0..


1300 1320 1340 1360 1380 1400 1420 1440 1460 1480


Energy (meV)


Figure 4-10. Theoretical calculation and experimental results of PL in high magnetic field.
Theoretical calculation of the PL spectrum based on an 8 band Pigeon Brown
model (top panel, from Gary Sanders) and experimental results (lower panel) of
magneto-PL emitted from InxGal-xAs with high excitation density at 25Tesla and
4.2K.









CHAPTER 5
INVESTIGATIONS OF COOPERATIVE EMISSION FROM HIGH-DENSITY ELECTRON-
HOLE PLASMA INT HIGH MAGNETIC FIELDS

5.1 Introduction to Superfluorescence (SF)

In this chapter, we consider the unique nature of cooperative electro-magnetic emission

made possible using ultrafast laser excitation of quantum wells placed in high magnetic fields.

This combination allows us to create atomic-like behavior between electrons and holes at carrier

densities well above those which support excitons. As such, these 'simulated atoms' can emit

light cooperatively via superfluorescence.

The nature of the emission of light from atoms and atom-like systems depends sensitively

on the physical environment surrounding them, and can be tailored by controlling that

environment [96-98]. At the most fundamental level, atom-photon interactions can be modified

by manipulation the number density, phase, and energies of atoms and photons involved in the

interaction. A very common example is the laser, in which mirrors are used to provide coherent

optical feedback to a population inverted atomic system, resulting in the emission of photons

with well-defined spatial and spectral coherence properties. Less common but equally

fundamental examples are the "superemission" processes, superradiance (SR) and

superfluorescence (SF), cooperative spontaneous emission from a system of Ninverted two-level

dipoles in a coherent superposition state.

Experiments probing these phenomena in atomic systems have provided significant insight

into the fundamental physics of light-matter interactions [99]. In our experiments, by

manipulating the coherent interactions of electrons and holes in a semiconductor quantum well

using intense ultrashort laser pulses and strong magnetic fields, we generate superfluorescence in

a completely new and unexplored regime. Our experiments begin to approach the question of

whether atom-photon interactions in semiconductors are truly "quantum" as they are in atoms.









5.1.2 Spontaneous Emission and Amplified Spontaneous Emission

The simple illustration of spontaneous emission process is shown in Fig.5-1 (a). For a two

level atom system with a high energy excited state E2 and a low energy ground state El, the

atoms populating the Ez state might spontaneously transit to El state without any external

electromagnetic field perturbation. A photon is emitted with energy Are, = E, E,, where ~co is the

angular frequency of an emitted photon. We can describe this spontaneous emission as [120]

dN
S-A ,N, 5-1


in which Nis the number of atom on excite states Ez and A21 is called spontaneous emission

probability or Einstein A coefficient. The solution of this equation is an exponential decay

function given by


N = N,e ~, 5-2

where No is the initial number of atom on Ez state and re; is the life time of this transition.

Comparing Eq. 5-1 with 5-2, we have z,, = A .

As we know, if atoms are far enough from each other and the interactions between atoms

are neglected, the spontaneous emission that occurs in one atom on excited state is also isolated

from the spontaneous emission from another atom on excited state. Therefore, spontaneous

emission has random directionality. Also as we see from equation 5-1, the intensity of

spontaneous emission is proportional to N, the total number of atoms involved in the transition.

The instinct properties of the atomic system determine the value of z,,, which ranges from pus for

rarified gases to ns for semiconductors. [100-102]

Fig.5-1(b) shows the transition process of amplified emission. In a two-level atom system

as described above, an atom populates the excited state Ez. Before this atom relaxes down to the










ground state El through spontaneous emission, it can be perturbed by the electro-magnetic Hield

of an incident photon, which is emitted from spontaneous emission with energy h v = E, E, .

Under the perturbation, this atom might transit to ground state El, emitting a photon with

energy h v = E, E, This photon emission process is called amplified spontaneous emission

(ASE). After this transition, one photon h v is turned into two photons.

ASE process can be described with the following equation [121]

dN
= -B,,p(v)N, 5-3


where B21 is a stimulated emission probability, called Einstein B coefficient and p(v) is the

distribution function of radiation density of photons at frequency v.

The relationship between Azl and Bz is given by [121]

A, A~i c
5-4
B, ir c2

One important optical property of ASE is that the emitted photon is exactly same as the

incident photon [121]. These two photons have the same optical frequency, spatial phase, optical

polarization, and direction of propagation, which results in the coherence between them.

Through ASE process, weak spontaneous emission can be amplified coherently in active

medium.

However, ASE can occur for any photon created from spontaneous emission, and in a

medium with a sufficiently large density of excited states, many spontaneously emitted photons

can be exponentially amplified in different regions, such that light from different spatial regions

are incoherent since they have different phases, polarizations and propagation directions. If an

optical cavity is used to select a specific mode of ASE, a lasing effect can be observed since all

other ASE processes are suppressed except the preferentially selected ASE mode.









In ASE process, in the low intensity regime, where I(z) << Is, the amplification of emission

intensity in the propagation direction z is written as

I(z)= I(0)egoz, 5-5

in the high intensity saturated gain regime, where I(z) >> I,, the emission intensity is described

by

I(z) = I(0)+ Is,gz 5-6

In equations 5-5 and 5-6, I(0) is the intensity of light propagating in the medium at z=0, Is is the

saturation intensity (which depends on the medium and density of excited states), z is the light

propagation direction, and go N2 21 IS called optical gain, where cr21 is a probability factor

called the stimulated-emission cross-section and usually very small~10-20Cm-2 [96].

From the two equations 5-5 and 5-6, we can see that in low intensity regime, the light

intensity grows as an exponentially along the z direction; in high intensity regime, the intensity

grows linearly along the z direction. The gain is said to saturate in high-intensity regime.

5.1.3 Coherent Emission Process--Superradiance or Superfluorescence

In SE or ASE processes, the separation between two atoms on excite states are relatively

large, so that the electro-magnetic Hield induced by one atom does not interact with the other

atom, and the electric dipole of each transition is not aligned nor has the same phase in the

oscillation, which results in incoherence between different SE processes or ASE originating from

different spontaneous emission processes, also resulting in incoherent emission.

However, in a N-atom ensemble, if the atoms in excited states are brought closer and

closer, so that the electro-magnetic Hield radiated interact with many excited atoms (in

macroscopic scale) simultaneously and all the atomic electro dipoles oscillate in phase before

they start uncorrelated spontaneous emission, a coherent macroscopic dipole state can exist for a









short time. A very short burst of emission will occur, radiating strong coherent light. This

'superemission' process is called superradiance (SR) or superfluorescence (SF), depending on

the nature of the initial formation of the macroscopic coherence. For SR, the coherence of atoms

is from the external excitation source, i.e. polarized laser pulse, and excited atoms preserve the

coherence before they emit photons. For SF, the atoms on excited state are initially incoherent,

the coherence develop in the N atoms due to the interaction between them.

The SF emission is a macroscopic coherent effect in an ensemble of Natoms, in which all

the Natoms radiate photons cooperatively and coherently. Fig.5-2 shows the processes of SF

emission. Initially, an ensemble of N atoms populates the ground state. With photoexcitation

from a laser pulse, the N atoms are excited and populate higher energy states. The N atoms

preserve the coherence from the coherent laser pulses for a very short time and then lose the

coherence before they start to transit to ground state. In this situation, the electro dipoles ofN

atoms are not aligned in phase. However, if the density is high enough, the electro dipoles could

develop the coherence and get aligned and start to oscillate in phase spontaneously due to the

interaction between them. A small number of electro dipoles of the N atoms could be aligned in

phase spontaneously due to quantum fluctuation or thermal effect, and then this coherence of

electro dipoles is developed to all the atoms through a very high gain mode (wL>>1). The N

atoms in the coherent state will emit coherent photons in a very short burst of pulse.

SR was first predicted theoretically by Dicke in 1954 [35] and first observed

experimentally by Skribanovitz et al. [103] in hydrogen fluoride (HF) gas in 1973. Many

experiments about SR and SF have been performed and reported in atom gas system [104-106].

In addition to experiments of SF, more theoretical work elucidating the nature of SF under









different conditions has also been done with either quantum field theory [107] or semiclassical

theory [108].

In Dicke's SR theory, the cooperative emission of electro dipoles takes place under the

following condition,

V ~ 2 .5-7

Where Vis the volume that excited atoms are confined and 32 is the emission light wavelength.

From this condition, cooperative emission exists in a very small active medium volume.

However, Bonifacio et al. [107] and MacGillivrary and Feld [108] extended the SF theory

to optically thick medium (on the order of mm or cm), either a "pencil shape" geometry, in

which the Fresnel number (A/L3A, where A is the cross section and L is the length of active

medium) is not larger than 1 or a "disk shape", in which Fresnel number is much larger than 1.

In the description of SF, there are five time scales are involved: the "dephasing" times T2

an T2, lthe photonI decay urtim z, coouperautiv urtim z and SF radiation rtim (or duration) zR, and

coherent delay time rd. zE is the time of a photon transit time in the active medium, T2 and T2* aef

the coherence relaxation time due to homogeneous and inhomogeneous broadening effect, z is

the characteristic exchange time of electro dipole coupled to radiation field, zR is the pulse

duration of SF emission, and rdis the delay time, during which the spontaneous emission evolves

into coherent emission.

The expressions of these time scales z, zR and zd arT giVen by [108]

iR spontaneous (8m4/ NiL)

re = (Ko ) > Ko =KkO = (ckoP2 /2h) 5-8

d _R-In(2mV)2









where Tsp IS the spontaneous radiation time of an atom transits from high energy state to the

lower energy state, Nis the number density of atomic system, 3A is the transition wavelength, gico

is the coupling factor between electromagnetic field and electric dipole, which is a key factor in

the evolution of coherent emission, ko is wave vector of central frequency of optical transition

and pu is the dipole moment of atomic dipole. Another critical factor in the cooperative coherent

emission is the cooperative length L,, within which all the dipole oscillates in phase, resulting in

the coherent emission. The expression of Le is given by [108]

L~e = c/2go ,~ 5-9

where p is the density of atoms.

In Bonifacio' s theory, the condition for cooperative emission of Natoms ensemble is given

by [108]

re << ZR d
Under this condition, initiated by quantum fluctuations or thermal radiation, a small

number of atomic dipoles oscillates in phase and emit photons spontaneously, then through the

coupling between atomic dipoles and electromagnetic field, the N atom oscillators ensemble

develop into oscillatory phase matching state in delay time rei and radiate a short burst of

coherent emission with pulse width TR. Eq. 5-10 stresses that the emission takes place before the

N atoms oscillator become dephased at time Tz, Tz* and the N atom oscillators develop into

coherent state before they start to recombine.

Bonifacio also mentioned in his theory that the relationship between active medium length

L and critical cooperative length Le









In the case L<
with the atoms, the N atomic oscillators emit a pure SF, the intensity of pure SF is given below

[108]

g2zN2 1)eh~51
I(t) = exp(- )eh ).51
2kV T2 R,

We can see that the peak intensity of SF is proportional to N2 and emission peak is at t-Td.

In the case L Icthe photons travel inside the active medium when the SF

emission takes place, SF is still observable, however the emission pattern is oscillatory pattern in

stead of sech2 pattern [108].

In the case L>Lo, the SF emission starts to get weaker and disappear, the emission process

is dominated by ASE [108].

As shown in Eq.5-10, several requirements and characteristics for a system need to be

satisfied to make SF emission observable. SF pulse duration rr and delay time between

excitation and SF burst zd are much shorter than the spontaneous emission time Tspontaneous and

inhomogeneous dephasing time T* (z, T,
maintain their phase relation and emit coherent light before spontaneous emission occurs. Based

on these requirements, rarified gas atom systems are the most favorable to observe SF emission,

since they have relatively long Tspontaneous and (~ pus), and the SF pulse width and delay time is on

the order of nanoseconds. Table 5-1 shows some of the time constant in the SF experiment done

in Rb gas. By controlling the pressure of the atomic gas, SF emission pattern can be clearly

resolved [109, 110]. However, in a solid-state system, i.e. semiconductors, the dephasing time

T2, T2* are extremely small (~1ps) [111], and the conditions in 5-10 are very difficult to satisfy.

Thus, up until this work, it has been impossible to observe SF emission in semiconductors.









5.1.4 Theory of Coherent Emission Process--SR or SF in Dielectric Medium

In 1964, A. P. Kazantsey [1 12] reported the first theoretical results of collective emission

processes in a two level system of a dielectric medium, such as a semiconductor. He found that if

the electromagnetic field interacts with two level systems resonantly, the field amplitude is

modulated with a characteristic frequency 0R, which is the coupling between electric field and

two level systems. The two prerequisites in Kazantsev's theory can expressed as

E2
7 = ~- <;1, 5-12


Orz >1, 5-13

where z is the relaxation time of two level system, Nhmo~,is the energy stored in N atom system.

Also, three simplifications of the two level system in Kazantsev' s theory are made, (1) the

dielectric medium is infinite and sufficiently rarefied, in which case the DR<
is a two level system and (3) there is no dissipation in the two level system so that 1/r~0, only the

early time (t<< z) is considered.

With the conditions shown above, the intensity of radiation is given by


IE(t)' 2 ~ EO 2 OXp(ta)

022 ~ Nd2 i0 5-14

where Eo is the initial value of electric field, d is dipole momentum, Nis the density of activated

atoms and wo is the transition frequency. It can be seen that the intensity of field increases

exponentially and dramatically if the collective modulation frequency DR is large enough.

Zheleznyakov and Kocharovsky [113] applied the idea of cooperative frequency, which

couples the electric magnetic field and optical polarization P in the medium, to the coherent









process of polarization wave function in dielectric medium, and the cooperative frequency is

given by

me = 8md Mm, /3h), 5-15

Where AN=N2-N;, which represents the maximum population inversion density in the two

level system.

Belyanin et al [114-118] calculated the Maxwell-Bloch equations for resonant interactions

between active medium and radiation field in semiconductors. In the mean field approximation,

the slowly varying electromagnetic field E(k), macroscopic polarization wave Pk, and inversion

density ANk can be described via a coupled set of equations:


d ?+--~+wzE = -47iP, 5-16a
dt2 T dt ka

d:P 2 dP 2 mfE
+ k g=5-16b
dt2 T dt 47r


d~ k f) 2 .d 5-16c
dt 7 m dt

Here, E is the electric field and Pk is the optical polarization oscillating at frequency m ~, The

sub script k refers to electron-hole pair with quasi-momentum k, TE is the photon life time for a

given field mode, Ty is the relaxation time of excited state, Tz is the dephasing time of dipoles, d

is the transition dipolep moment, nis the ref~cracTPTtive inex nd1 h is the inversionn depnsity

excited by pumping.

From these three equations, we can see that E and P are coupled, with the cooperative

frequency coc (and thus the density) determining the coupling strength and resulting emission.

The left hand side of 5-16 (a) and (b) for E and P are harmonic oscillators with damping factors










TE, T2, and right hand sides are driving force on the oscillators. However, the increasing rate ofE

and P strongly depends on the value of wc, which couples the E and P and dominates the

increasing rate of E and P. The driving force we on RHS of 5-16 (b) should be associated with

excited atom density and electric dipoles, and transition frequency in the E and P resonant

interaction, as shown in Eq.5-15. If an initial value of we is sufficiently large, equation 5-16

exhibit instability with respect to the growth of small initial oscillations of the E and P.

Given that


c > -5-17
E T,

equations 5-16 can be solved approximately in two regime [111].

First is amplified spontaneous emission regime. In this case, we have

ml
<< 5-18
2 T2

and the growth rate is given by



01


In order to get amplified, then we should have mi" = W T2 >0.
4 T

Second is SF regime. In this case, we have


c >> -5-20
2 T,

and the maximum growth rate of emission intensity is given by


m"~l= Oc.5-21










The SF pulse width TR and coherent length Le can be estimated with the value of coc, also

the delay time tD, which characterize the coherent generation can be given as [111]





L -x Log( factorl0 20) 5-22
mi~"n

log(


From the cooperative frequency me~, many parameters can be derived. The SF pulse

duration scales as


rF ~ -~ N 2, 5-23


and the peak intensity of SF scales as

AmiN
I,, N 5-24


The line width of cooperative recombination, which is determined by the band filling of

particle states in QW or QD scales as

Am ~ me ~N ".5-25

5.2 Cooperative Recombination Processes in Semiconductor QWs in High Magnetic
Fields

Naturally, in solid-state systems such as semiconductors, it is quite difficult to observe SR

or SF since Tz in solid-state system is very small (on the order of ps). The ensemble of dipole

oscillators formed by electrons and holes cannot build up coherence before they undergo phase

breaking, since the electron and holes are not localized and easily be involved in collisions such

as electron-phonon, electron-electron, and electron-hole collisions. However, Belyanin pointed

out that in quantized semiconductors, such as a semiconductor QW in high magnetic field or QD,









the electron and hole are spatially confined. This confinement reduces the collision probability

and can dramatically increase the dephasing time Tz. Meanwhile, the density of states of QW and

QD increase dramatically compared to that of a 3D bulk semiconductor (see chapter 3, equation

3-10 and Fig.3-4). This effect implies that instead of populating in the continuum states in a bulk

semiconductor, electrons and holes mainly confine themselves around the quantized energy

levels because the continuum states are depleted in QW and QD structure. In this case, the

number of dipoles formed by electrons and holes increase significantly at QW energies level El,

Ez, which satisfy the high density of "atoms" requirement of SF (see equation 5-20).

In a high magnetic field, the electron-hole pairs in a InxGaAsl-x QW are effectively

confined in a quasi-zero dimensional state, and manifests this OD effect in the absorption

spectrum and PL spectrum (see Fig. 4-4 and 4-7). The electron-hole pair only populate at

discrete LL states, ensuring that the spreading of the electron-hole pair energies is small, favoring

SF generation. Moreover, the density of state ofLL levels for InxGaAsl-x/GaAs QW is high

(~1012/CM2 at 20T, see Chap. 4, equation 4-13), which also give rise to the generation of

cooperative phenomena.

5.2.1 Characteristics of SF Emitted from InGaAs QW in High Magnetic Field.

As mentioned before, semiconductor nanostructures such as QWs or QDs are an ideal

system to observe cooperative recombination of electron-hole pairs, therefore we chose

InxGaAsl-x/GaAs multiple QWs as our emission medium, using ultrafast excitation and high

magnetic field in combination to observe SF. The structure of this sample has been discussed in

4-3 and Fig.4-2.

According to the results shown above (Eqs. 5-17 to 5-21), the key term that determines the

growth rate of emission intensity I, which corresponds to the cooperative emission process is the

cooperative frequency coc.









In a two-dimensional semiconductor quantum well structure, the cooperative frequency is

modified into the following form [114],

83r 2d ANTc
m 5-26
c An 2L,

Here L,,, is quantum well of thickness, 31 is emission wavelength, 7 is the effective overlap

factor of electromagnetic field with the quantum well in the direction perpendicular to well

plane, n is the refractive index and d is the transition dipole. The maximum photo excited

electron-hole density is AN ~Ne-h.

Based on the theory presented above, we can estimate the parameters for SF emission in

the InxGaAst-x/GaAs used in these experiments.

Ln-J
The photon decay time is TE ~2x10-13 S-1, where L is the active medium length, F


is the Fresnel number. In reality, 4x10-13 S-1 Seems to be a better estimate because the excited

medium can guide the SF emission into the active medium. This waveguide effect is generated

after medium is excited, due to an enhancement in the refractive index medium in the active area

from the magneto-plasma, In this case the electro magnetic field will couple more with optical

polarization.

The cooperative frequency at initial time is given by equation 5-26, where ANis carrier

density in the quantum well plane, and r is around 1/3. The estimation of cooperative is


me ~ Nx3x1013S-1. In equation 5-20, in order to make the condition for SF satisfied, Tz
101 cm2

is ~ 10-13 S-1, and we need N> 5x10"1 cm-2, which can be realized at high magnetic field

(~20Tesla) and ultrafast pumping (see chapter 3, equation 3-14).









Below, we present investigations of the magneto-PL spectrum obtained from high-density

electron-hole plasmas in InxGaAsl-x /GaAs QW in high magnetic fields, in which propagation of

PL is perpendicular and parallel to the QW plane. Perpendicular to the QW plane, abnormally

sharp and strong emission lines from 0-0 and 1-1 LLs are observed as discussed in chapter 4. As

we have discussed above, there is possibility that this emission is from ASE or macroscopic

cooperative recombination--SF. Since the electron-hole pairs are mainly populating in the QW

plane, the in-plane PL should be much stronger than the PL collected perpendicular to the plane

because the spontaneous emission should be amplified when propagating in the in-plane path.

Thus, we have developed experiments in new configurations to measure the in plane PL from

InxGaAsl-x /GaAs QW.

In order to show definitive evidence of cooperative recombination in QWs in high

magnetic fields, there are a number of experimental signatures that uniquely characterize SF

emission. These are listed in Table 5-2. For comparison, we also include the ASE characteristics

in the Table 5-2, since PL emission in InxGaAsl-x /GaAs QWs at high magnetic fields could be

due to either emission mechanism. From these six characteristics, we can distinguish a pure SF

process from ASE processes, and they are given as follows.

5.2.2 Single Shot Random Directionality of PL Emission

In an SF emission process, the coherent collective emission builds up stochastically from

spontaneous emission, which can be emitted in any direction, and a specific SF burst will follow

the propagation direction that the first spontaneous emission takes. It is essential to note that

since this is a probabilistic quantum electro-dynamic process, each SF burst forms independently

on each subsequent excitation laser pulse. By contrast, in ASE processes many spontaneous

emissions could be amplified, therefore, in a single shot, the PL emission should equally

distribute in all direction and no random directionality is expected.









5.2.3 Time Delay between the Excitation Pulse and Emission

As we seen in Eq. 5-21, the SF emission is given after the excitation pulse, the delay time

between iS Td, during which the spontaneous emission develops into SF through an extremely

high gain mode. This delay occurs because of the inherent build up time for the coherence form

from the initially incoherent dipole population. In ASE, the emission process start in a short time

(on the order of nl c < Td, where c is the speed of light and I is the length of activated medium

and n is the refractive index) immediately after the excitation pulse disappears, therefore, no time

Td delay is expected to be observed.

5.2.4 Linewidth Effect with the Carrier Density

In the formation of ASE, spontaneous emission is amplified when travels through medium,

however, the amplified emission linewidth depends on the gain function G~co, which is given

below,

I(m)~ = I, (0)~ exp(G(mi)L). 5-27

Where lo~co is the initial intensity function in frequency domain and L is active medium that

light get amplified. Usually, G~co has Gaussian or Lorentz shape, which result in the center

frequency in I~co get amplified more than frequency off center. This gain narrowing effect

reduces the emission linewidth in ASE process.

In SF process, as mentioned above in Eq. 5-22, the linewidth of cooperative emission is

broadened at high densities, Ami ~ Ne-a U2, Since more carriers are involved in the cooperative

emission.

5.2.5 Emission intensity Effect with Carrier Density

In an ASE process, emission is amplified linearly with N, so that the emission intensity

should increase linearly with the increasing of carrier density N. In an SF process, according to










equation 5-23 the emission is a short burst and given coherently, superlinear increasing of the

emission intensity is expected when carrier density Nis increased.

In magnetic field, the carrier density N depends on the magnetic field strength B (see

chap.3, equation 3-14), the linear relation between them is N~B, so a superlinear relation, I~B ,

between emission intensity and magnetic field is expected in SF emission.

5.2.6 Threshold Behavior

Both ASE and SF exhibit threshold behavior with respect to laser excitation intensity.

However, in ASE, the threshold is at the point where optical gain G 0, while in SF, the

threshold is the point where coherence is built up among carriers.

5.2.7 Exponential Growth of Emission Strength with the Excited Area

Both ASE and SF will be amplified in the form of I ~ I, exp(a L), so that the emission

strength increases exponentially with respect to the excited area. Therefore this doesn't

distinguish between be ASE and SF, but does show that an exponential process is occurring.

We expect to see cooperative emission from high carrier density electro-hole plasma in

InxGaAsl-x /GaAs QW in high magnetic field, however, in order to fully fill the LL and make the

carriers populate on LL before they start to recombine (time scale ~100ps), a high power

(GW/cm2) ultrafast CPA laser is needed to generated enough carrier density in a very short time

(~ps). It is also critical to note that the initial excitation at 800 nm, is well above (240meV) the 0-

0 LL levels that we probe (at 920nm). In fact we excite electrons carrier into GaAs barrier

continuum states and InxGal-xAs well continuum stats., Most of electrons carriers populating in

barrier are dumped into the InxGal-xAs QW layer and increase the carrier density in well layers.

Carries in QW layers will relax down to 0-0, 1-1....LL levels and there are many collisions

during the energy relaxation (and momentum relaxation) which completely destroys the initial









coherence of carriers imposed by the laser. Thus, we can are truly probing SF as opposed to SR.

After energy relaxation to the QW LLs, the carriers, now tightly confined both in space and

energy, develop into a coherent state with interacting with the electromagnetic Hield from initial

spontaneous emission and give a burst of SF emission. This process shows the key signature of

SF instead of SR.

5.3 Experiments and Setup

To understand the PL emission processes in InxGaAsl-x/GaAs QWs excited with high

intensity short laser pulses at high magnetic Hields, several experiments have been carried out.

Magnetic Hield and excitation power dependent in-plane PL

Single shot experiment for random directionality of in-plane PL

Control of coherence of the in plane PL from InxGal-xAs QW in high magnetic field.

In all the experiments, we use the ultrafast magneto-optics facility developed by us at the

NHMFL (see chap2, Figs.2-2, 2-3, and 2-4.). All the experiments are done at liquid helium

temperature with the Janis optical cryostat designed for a resistive magnet. The InxGaAsl-x/GaAs

QW sample is mounted on the liquid He tail of cryostat for direct optics, in which laser beam can

travel in free space and then excite the sample without being chirped.

For most of the experiments, the ultrafast CPA laser system is the excitation light source,

which has been introduced in Chap.4, 4.3. The excitation laser is focused on the InxGal-xAs QW

sample with one 1 m focal length lens, and the spot size on sample is around 500 pum.

The configuration of the in plane PL collection geometry is shown in Fig. 5-3. In order to

collect the PL travels in the QW planes, a small right angle roof prisms is mounted on the edge

of the QW sample, which can steer the in plane light into the optical multimode fiber mounted

right on the top of the prism. The area of prism is 1.0xl.0mm2, and the fiber diameter is 600 pum.









The collection angle for this prism is approximately 40o. With this configuration, PL emission

travels in the QW plane is effectively and efficiently collected and delivered to a McPherson

spectrometer for analysis. In addition, for comparison with the in-plane PL, PL emission

perpendicular to the QW planes is collected via a fiber on the back face of the sample.

The magnet used for study of cooperative emission is Bitter resistive magnet located in cell

5 at NHMFL, a 25 Tesla (upgraded to 31 Tesla now) wide bore (50 mm) magnet (see Fig.2-1).

Most of our spectra were collected by averaging over multiple shots (1000 shots in most

cases). However, to probe the directionality of the emission, in which the PL propagation is

different from pulse to pulse, single shot experiments need to be performed to resolve this

phenomenon. Thus, we measured the PL from InxGaAsl-x/GaAs QWs excited by one single laser

pulse. An electro-optical Pockel cell was employed in this experiment. As shown in Fig. 5-4, the

laser beam propagates through two crossed polarizers and gets rej ected at the second polarizer.

However, there is fast transient high voltage bias nonlinear crystal positioned between the two

polarizers, which operate as a transient half wave plate when the high voltage bias is on. Each

time when the high voltage is on, the high voltage biased crystal changes the polarization of laser

beam by 90 degree and let it go through the second polarizer. With this device, we can control

the number of laser pulses and the repetition rate of the pulses that are sent to the sample and

collect PL from a single excitation pulse.

Also, in order to compare the PL intensity at different in plane directions, two small right

angle prisms are mounted at cleaved edges 900 apart of InGaAs/As QW, which will

simultaneously collect the PL excited with one CPA pulse and steer into two fibers mounted on

top of roof prism. The excitation geometry of single shot measurement is shown in Fig.5-8









5.4 Experimental Results and Discussion

5.4.1 Magnetic Field and Power Dependence of PL

We measured the field dependency in plane PL emission spectrum oflInxGal-xAs/GaAs

QW excited with 150fs CPA laser pulses at a constant laser fluence (Flaser~ 0.62 mJ/cm2) up to

25 Tesla. Experimental result is shown in Figure 5-5(a). For comparison, PL collected at the

same conditions with the center fiber is also shown in Fig. 5-5(b). The sharp in the edge

collection PL spectrum is a lot stronger than the PL from center collection. Broad PL emissions

due to spontaneous emission from inter band LL transition are observed up to 12 Tesla. This

broad linewidth (~9 meV) is due to inhomogeneous broadening, which originates from the

inhomogeneities and possibly defects in the multiple QW layers. The magnetic field dependent

PL features above 13 T change dramatically, and sharp peaks (around ~2 meV) are observed on

high energy side of broad feature of each interband LL transition. These sharp peaks dominate

the PL at high magnetic field. However, each inter LL transition PL peak consist of overlapping

broad and sharp peaks, shown in Fig.5-6. The sharp peaks are believed to be ASE or SF and their

linewidth is determined through homogeneous broadening, since the emission concentrates

around a narrow frequency. We fit the field dependent PL strength of 0-0 LL transitions with a

combination of Gaussian function (for inhomogeneous broadening line width) and Lorentz

function (for homogeneous broadening line width) given below.

Gaussian function


I(co)>= A exp( ") 5-28


where 1.386 w is the FWHM (full width at half maximum) linewidth, coo is the center frequency

of PL transition.

Lorentzian function










I(m)~ = B( ), 5-29


where w is the FWHM and coo is the center frequency of PL transition.

The fitting results of sharp peak emission strength (black dot) and linewidth (red dot) of PL

from 0-0 LL transitions vs. the magnetic Hield strength are shown in Fig.5-5 (c). In Fig.5-7(a) at a

Eixed magnetic Hield of 20 T, the PL spectrum of interband LL transition vs. excitation laser

fluence is plotted. It is observed that below certain laser fluence (0.01 mJ/cm-2), Only broad PL

peaks with linewidth (~9 meV) exist, but with the increasing of laser Fluence, a sharp peak starts

to emerge on the high energy side of broad peak. At the highest excitation laser fluences, the

sharp peak dominates the PL emission spectrum. With the same fitting procedure as used for the

magnetic field dependent PL spectrum, laser fluence dependent emission strength and linewidth

of sharp PL peak from interband 0-0 LL transition are obtained and shown in Fig 5-7(b).

Identical field and laser fluence dependent PL spectra are seen when collecting from the

center fiber above the pump spot, i.e., out of plane, although at a much lower signal level

(~1/1000). Also, increasing or decreasing the pump spot size resulted in the emergence of sharp

PL features in the spectra at a given fluence. Thus, the observed behavior is not due to a spatially

or spectrally inhomogeneous distribution of carriers.

Comparing the fitting results in Fig. 5-5(b) and 5-7(b), we can see similar patterns in

curves of magnetic field or laser fluence dependent emission strength and linewidth. There are a

few regimes in the two set of curves. First, below 12 T (or 0.01 mJ/cm2), narrow emission is not

observed. In the range 12-14 Tesla or (0.01-0.03 mJ/cm2), the narrow peak signal strength S

grows linearly (S~B or FEaser, see green lines)) with respect to both B and Faser. Second, above 14

T (0.03 mJ/cm2), the emission strength S starts to show a superlinear increase (S ~ B3 2, See blue

lines) with respect to B or FEaser. Above 0.2 mJ/cm2 (See Fig. 5-7(b)), the signal resumes a linear









scaling. Also, the field and Flaser dependent PL linewidths curve (red circles) plotted in Figs. 5-

5(b) and 5-7(b) reveal a remarkable correlation with the field and fluence dependent emission

strength curve. In the linear regime, the linewidth decreases monotonically both versus B and

Flaser until the emission becomes superlinear at the threshold point (B=12T and Flaser=0.01ImJcm-2

) where the PL linewidth begins to increase.

At a 20 Tesla, setting the excitation spot diameter at 0.5mm, 0.1mm and 3mm, we also

measured on fluence dependent PL spectrum respectively. The fitting results of emission

strength and linewidth at different excitation spot sizes are plotted inFig.5-8 (b) (c) and (d),

narrow emission was observed, but both the integrated signal S and the linewidth exhibited

qualitatively different scaling for each different spot size. The curve in Fig. 5-8(b) shows the

increasing pattern with increasing laser fluence as shown before (See Chap. 5-4, II) however,

the emitted signal S in (c) and (d) shows an almost linear relation with respect to the Flaser

(S~Flaser), and in both of (c) and (d), and the linewidth curves monotonically decreased with

increasing fluence.

5.4.2 Single Shot Experiment for Random Directionality of In Plane PL

With a optical Pockel cell, we are able to reduce the repetition rate of CPA laser to very

low frequency (~20Hz) so that we can use the mechanical shutter (speed ~20 ms) on McPherson

spectrometer to record the PL spectrum from a single CPA laser pulse excitation. Also we collect

the in plane PL with two optical fibers simultaneously (the fibers are mounted on QW edges

perpendicular to each other (see Fig. 5-4)), then deliver them to spectrometer to resolve the PL

spectrum propagating in different directions in QW. This measurement is crucial for determining

the correlation of the emission and single shot directionality of the in plane PL emission. Figure

5-4 presents the directionality measurements of the emission for a single pulse excitation. Figure

5-9 (a) illustrates a series of spectra upon single pulse excitation at a given fluence in the










superlinear emission regime (Flaser 9.7 mJ/cm2, B=25 T) for a 0.5 mm diameter spot size. The

spectra are collected through fibers on edge 1 (black) and edge 2 (red). We can see that the

relative height between the red and black curve changes from shot to shot, which indicates that

the propagation direction of in plane PL could be different from pulse to pulse since the two

optical fibers are mounted to collect PL propagating in different directions. Since the two optical

fibers have different collection efficiency, in Fig.5-9 (b) we displayed the maximum peak height

from each edge (normalized to 1.0) versus shot number for the pumping conditions shown in Fig.

5-10(a). The maximum observed emission strength in Fig. 5-9(b) fluctuates as much as 8 times

the minimum value, far greater than the pump laser pulse fluctuation (~2%). This strong

anticorrelation between signals received from different edges indicates a collimated but

randomly changing emission direction from pulse to pulse, as expected for cooperative

spontaneous emission.

At a lower excitation fluence in linear increasing regime Flaser~- 0.02 mJ cm2 (Obtained with

a 3 mm spot), we also measured the shot to shot PL spectra collected with the same configuration

discussed above and show it in Fig 5-10(a). We observed qualitatively different emission

strength behavior from high power excitation shown in 5-10(a). In Fig.5-10(a), the emission

strength of different shot from the same optical fiber do not fluctuate as much as high power

excitation. In Fig. 5-10(b) we can see that the normalized (to 1) shot to shot PL emission strength

at different collection direction are highly correlated instead of anti-correlated in high power

excitation. Fig. 5-10(b) shows omnidirectional emission on every shot, as expected for ASE or

SE.

5.4.3 Control of Cherence of In Plane PL from InGaAs QW in High Magnetic Field

As discussed in Chap. 5.3, the intensity of cooperative emission or ASE increases

exponentially with respect to the active length of medium in the propagating direction. We










shaped the excitation laser pulse and probed the spatial and directional characteristics of the PL

emission process (see Fig.5-11). Using a cylindrical lens to focus the excitation laser beam on

the QW sample, we generate an elliptically shaped spot ('pencil geometry') for the excitation

region. When the cylindrical lens is rotated, we change the active medium length of PL emission

propagating towards the two right angle roof prisms. The emission strength collected from the

prisms should change according to the rotation angle. We define the 0 degree angle at the point

where in plane PL from edge one is at maximum. We measured the signal as a function of angle

from 0 to 180 degree for Flaser ~ 0.02 mJ cm2 and B~ 25 T (shown in Fig. 5-12), from which we

can see that the PL emission strength change dramatically with respect to the angle cylindrical

lens. In the experiment, the maximum signal from edge one, which correspondent to activated

length 1.5mm is at 90 degree, the minimum signal from edge one is at 0 degree, correspondent to

activated length 0.5mm. The ratio of signal strength max= 20 corresponds to exp(1.5/0.5) ~ 20,


which is consistent with exponential increasing of emission strength vs. activated medium length

in ASE or SF..

5.4.4 Discussion

With the analysis of all the experimental result shown in Fig. 5-5, 5-7, 5-8 and 5-10, we

found that for the interband 0-0 LL transition, the scaling of the emission strength S, the

linewidth evolution, and single shot emission directionality indicate the following evolution

processes as excitation power Flaser and magnetic field strength B are increased: (i) In the low-

density limit (B 12 T, Flaser 5puJ cm2), excited e-h pairs relax and radiate spontaneously

through interband recombination. The emission is isotropic with an inhomogeneous Gaussian

shape linewidth of ~9 meV. This broad spontaneous emission can be seen in both Fig.5-5(a) at

low magnetic field and in Fig. 5-7(a) at low laser fluence. (ii) At a critical fluence 0.01 mJ cm2









(at 20 T) and magnetic field B~12 T (at Flaser~- 0.6 mJ/cm2), a carrier population inversion is

established with increasing magnetic field and excitation laser fluence, which increases the

carrier density in QW (since N~Flaser and N~B, see equation 3-14). In this case, ASE develops,

leading to the emission of amplified pulses. Fig. 5-10 shows that ASE is simultaneously emitted

in all directions in the plane. The reduction in linewidth with increasing fluence results from

conventional gain narrowing discussed in section 5-2-1, in which spectral components near the

maximum of the gain spectrum are preferentially amplified than components with greater

detuning [see Figs. 5-5(a) below 17 T and Fig.5-7(a) below 0. 03mJ cm2]. In this high-gain

regime, the spectral width reduces to 2 meV (FWHM), still larger than 2 T2. (iii) If we keep

increasing the magnetic field and laser fluence, since the DOS and physical density in QW are

sufficiently high at high magnetic field (at B~20T, N~1012Cm-2), the cooperative frequency we

exceeds 2 (T2T241 2, the build-up time of coherence between transition dipoles are shorter than

the decoherence time. The e-h pairs establish a macroscopic dipole after a short delay time and

emit an SF pulse through cooperative recombination (or a sequence of pulses, depending on the

pump fluence and the size of the pumped area).

According to the theoretical expression of Aw, in cooperative emission regime, the

linewidth of emission increase with increasing of laser fluence due to reduced pulse duration of

cooperative emission, until eventually saturation (due to the filling of all available states) halts

the further decrease in pulse duration (shown in Fig.5-7(b), above 0.2mJcm-2). The transition

from ASE to cooperative emission at 0.03 mJ cm2 at 20 Tesla is shown in Fig. 5-7(b), we can see

that the linewidth of emission starts to increase significantly, which is consistent with Awc

increasing with increasing of carrier density (predicted in Eq. 5-29).









In ASE, the spontaneous emission is amplified during propagation in certain direction.

However, since there are many spontaneous emission photons propagating in different directions

with subsequent amplification, we observe that in a single shot measurement, ASE emission

distribute in all directions. Significantly, we find that unlike ASE, which should be emitted in all

directions with the same intensity [see Fig. 5-10(b)], in this super linear regime the initial

quantum fluctuations grow to a macroscopic level to establish coherence and lead to strong

directional fluctuations from shot to shot [see Fig. 5-9(b)] This is consistent with the random

direction distribution discussed in ChapS, 5.2. 1 a. The linear scaling of linewidth vs Flaser above

0. 1 mJ cm2 is a combined result of absorption saturation of the pump and saturation of SF

emission.

As discussed in Chapter 5, the intensity of cooperative emission increasing super linearly

with respect to increasing of carrier density (I~N3 2). Since the carrier density is proportional to

Flaser or B, we should expect observe I~B3 2 Or I~F3 21aser in the experiments. However, since the

data was collected in a time-integrated fashion with spectrometer and CCD, we cannot directly

probe the peak SF intensity scaling mentioned before because the SF emission is on the order of

hundreds femtoseconds. However, there are two lines of evidence indicating that the observed

superlinear scaling is related to the formation of multiple SF pulses from the 0-0 LL transition.

The superlinear increase for the 0-0 LL emission is accompanied by an emission decrease from

higher LLs, indicating a fast depletion of the 0-0 level through SF followed by a rapid relaxation

of e-h pairs from higher LLs and subsequent reemission. Also, in the single pulse measurements

shown in Fig. 5-9, data shows that the PL emissions collected from two fibers on different edges

of QW sample are either correlated or anticorrelated in roughly equal proportion. This result

indicates that fast relaxation from higher LLs refills the 0-0 LL, resulting in a second pulse of SF









emission in a random direction. On average, the two SF pulses in one excitation pulse are

collected in two different edge takes 50% shots, and for the other 50% shots, the two SF pulse

from one excitation go to the fiber on only one edge. This is in qualitative agreement with

observations, in which 50% shots are correlated and 50% are anticorrelated.

One could argue about weather the observed emission characteristics are consistent with

pure ASE lasinging"'), but this can be ruled out by examining the excitation power dependent

experiments at 20 T at different excitation spot sizes. In Fig. 5-8(b), (c) and (d) three spot sizes

0.5 mm, 0. 1 mm and 5 mm are selected for the experiments. We can see that, only in the S vs.

Flaser curve with excitation with 0.5mm spot size, linear and super linear increasing behavior (the

signature of cooperative emission) emerge. Also a gain region of 0.5 mm is consistent with the

theoretical predication of coherent length L, ~ c zLn(I, /I,), which is found to be a few

hundred micrometers. However, in the S~Flaser curve with 5mm excitation spot size, we only

observe linear increasing behavior, this is a typical ASE process, also the linewidth of the PL

emission keeps decreasing with increasing ofFlaser,, which is the gain narrowing effect in ASE.

In the curve with excitation spot 0.1Imm, we can see that the linewidth decreases up to certain

Flaser,(~0.6mJcm-2), then it stop decreasing. Also we can see that the emission strength S is

neither linearly nor superlinearly increasing with Flaser, increasing. The PL emission with 0.1 mm

excitation spot might be a combination of ASE and SF or early stage in SF. In the case that the

excitation spot size is either much larger or much smaller than the coherent length, and none

optical cooperative emission signature is observed.

We can conclude that collimated, randomly directed emission and superlinear scaling are

observed only when the pumped spot is 0.5 mm, approximately equal to the theoretically










predicted coherence length for SF emission in QWs. They are not observed for 0.1 and 3 mm

spot sizes.

Finally, contrary to popular opinion in the quantum optics community, pure SF does not

require a rod like geometry. As shown in ref. [119], cooperative recombination is not constrained

by the geometry of the excitation region, omnidirectional superfluorescent emission has been

observed in cesium. Moreover, the disk-like geometry of the pumped active region allows us to

observe the key evidence for SF, namely, strong shot-to-shot fluctuations in the emission

direction. Previous experiments almost exclusively employed a rod-like geometry, in which the

only direct signature of SF is the macroscopic fluctuations of the delay time of the SF pulse and

pulse duration.

In a semiconductor system the SF pulse duration and delay time for cooperative emission

would be manifested on the ps and sub-ps scale and we need to employ ultrafast spectroscopic

method such us pump probe spectroscopy, time resolved upconversion PL spectroscopy and time

resolved PL spectroscopy with a streak camera to observe these time parameters. Those

experiments are underway at present.

5.5 Summary

In this chapter we have reported on a series of experiments to generate SF in

semiconductor quantum wells. Excited with high peak power CPA laser, we observed

extraordinarily strong in-plane PL emission from InxGal-xAs/GaAs multiple quantum wells at

high magnetic field. With increasing carrier density, there are three regimes in emission from

the interband 0-0 LL transition, spontaneous emission, amplified spontaneous and cooperative

superfluorescent emission. In the SF regimes, all the experimental observations are in consistent

with the optical signatures of cooperative emission process.










Table 5-1. Some experimental conditions for observation of super fluorescence in HF gas.
The time unit is nanoseconds, L is the length of activated gas, and d
is the size of laser beam.


Active length
(cm)


d
(rmn)


TE ZR


5.0 432 5 0.17 0.15
3.6 366 32 0.07 0.15
2.0 273 5 0.35 0.12
Reprint with permission from M. Gibbs et al., Phys. Rev. Lett. 39


6-20
5-35
6-25
(1977), page 549.









Table 5-2. Characteristics of SF emitted from InGaAs QW
Characteri sti cs Superfluorescence(SF)


in high magnetic field
Amplified Spontaneous
Emission(ASE)
No


Shot to shot random
directionality
Pulse delayed by zd
(~10ps)
Emission linewidth
increase with carrier
density N
Emission strength increase
with excitation density
Threshold behavior
Exponential growth with
area (~exp(gL))


Superlinear (~I1.)


Linear (~I)


Yes
Yes


Yes
Yes





















Eo 7 c = E, Eo


Transition








Figure 5-1. Spontaneous emission and amplified spontaneous emission process of a two level
atom system.(a) Spontaneous emission (SE); (b) Amplified spontaneous emission
(ASE).













O O
0 0
O O
9 O
0" O
O00
O00
0 O


Excitation


(a) (b) (c) (d)
Figure 5-2. Four steps in the formation of collective spontaneous emission--SF in Natom
system. (a) N atoms are excited by light absorption;(b) After excitation, the
dipoles of the N two level atom randomly distribute in all direction; (c) Electric
dipoles are aligned and phase matched; (d) All the electric dipoles emit
simultaneously a burst of coherent light pulse.


)+r d t


rI)
SF










Center
col election


Edge
collection


Prism


Figure 5-3.


Configuration for collection of in plane PL from InGaAs multiple QW in high
magnetic field.One right angle prism is positioned at the edge of QW sample to
collect in plane PL.


























P


Figure 5-4. Configuration for a single shot experiment on InxGal-xAs Multiple QWs.


tr~n 1


rumpl ai
1 KHz











3"

ir,
.3,


5T






3T


1 .?.5 '1_40 1i 45 .o
Energy, (eV) Energy (eV)


-3



E
-2:


Linear Fit

m


5 5


. -


(00)


20
Magnetic Field (T)


(c)
Magnetic field dependent PL spectrum and fitting results of in plane emission.
(a) Field dependent PL emission spectrum from edge collection; (b) Field
dependent PL emission spectrum from center collection and (c) Fitting results of
emission strength and linewidth.


Figure 5-5.


Edge


Ce nter
























Figure 5-6. Fitting method to determine line widths using a Lorentzian and Gaussian function
for the sharp peak and broader lower-energy peak.The broad peak (blue line) is
Gaussian shape originates from spontaneous emission, while the sharp peak (pink
line) is Lorentz shape originates ASE or SF.


*Exp.
Lorentz ian
- Gaussian










7 at 20 T






IS 0 14G
/1 2n

:~~~ 0067 C -d-)
,~~~~~~~ 0074L ne r
14 30i, 1 35~ 1 0 1 50.1 0
Enrg (e)Fune(n)m

(a (b)1~ Q
Fiue57 xiaio oe eedn L setmanftigrsusoinpne emsin
(a exiainpwr deenen L eiso pcrmat2 el n b
fitn reut ofeiso srnt ndlnwdh
























MaIg netic Field (T1) Fluence


(Ia) 0.5 mm spot size


(b) 0.5 mm spot size


-


0.1 1
(mJ/cm')

1 spot size


(c) 5 mm spot size
a Exp.
Lmecar Fit








" "" i "'I """1
0.01 0.1 1
Fluence (m)/cm")


0.01 0.1 1
Fluence (mJ/cm )


Figure 5-8.


Excitation spot size effect on the in plane PL emission.Emission strength and
linewidth of the narrow peak from the 0-0 LL versus (a) B and (b), (c), (d) Flaser for
different pump spot size at 20 Tesla. Both B and F are on log scale.





































(00) -Edge 1
Edge 2


1.4


Shot Number


(b)
Single shot random directionality measurement of in plane PL emission excited
with one CPA pulse in SF regime.(a) Four representative emission spectra from
edge 1 (black) and edge 2 (red) fibers, excited from single laser pulse and measured
simultaneously. (b) Normalized emission strength from the Oth LL versus shot
number in the SF regime.


Figure 5-9.


1.4 1.3
Energy (eV)


























V(a






1.3- -. Edge 1.




.C -= Edge 2





-u 0 10 20 30 40
w Shot Number

(b)
Figure 5-10. Single shot random directionality measurement of in plane PL emission
excited with one CPA pulse in ASE regime.(a) Four representative
emission spectra from edge 1 (black) and edge 2 (red) fibers, excited from
single laser pulse and measured simultaneously (b) Normalized emission
strength from the Oth LL versus shot number in the ASE regime.










































Figure 5-11. Configuration of control of emission directionality in InxGal-xAs
multiple QW with cylindrical lens.










-*- Edge "1 --I- Edge 2


II


0."1


180O


Figure 5-12. Control of coherence of in plane PL emission in InxGal-xAs QW. Edge emission
strength of 0-0 LL transition from two orthogonally aligned fibers vs. the rotation
angle 6. 6 is the angular separation between the logner beam axis and the direction
of the edge 2 fiber as shown in the Fig. 5-12..Emission strength of the 00 LL is
plotted for edge 1(black) and edge 2 (red) as a function of angle.


60 120
An~gle (Degree)









CHAPTER 6
CARRIER DYNAMICS OF ZINC OXIDE SEMICONDUCTORS WITH TIME RESOLVED
PUMP-PROBE SPECTROSCOPY

6.1 Introduction

The II-VI group wide band gap semiconductor alloys such as ZnO, ZnMgO are recognized

as important materials for potential applications in optoelectronic devices in the ultraviolet

spectral range as well as for integrated optics substrates. Since the exciton binding energy of

ZnO is 60mev [122-126], which is very high compared to GaN (~30mev) [127] or

GaAs(~8mev)[128], the radiative electron hole recombination process in ZnO is even visible at

room temperature[129]. Due to these unique properties, ZnO semiconductor materials are of

interest in applications such as UV light emitting diodes (LEDs) and laser diode (LDs) [130].

Also, ZnO crystal is excellent substrate material for growing another important wide band gap

semiconductor [131-132], GaN, since the lattice mismatch is relative small. For ZnO we have

a=b=3.249A and c=5.206A, while for GaN, we have a=b=3.189A and c=5.185A.


The dynamics of carriers in ZnO semiconductor, which are critical for high speed electro

optical device design, have recently been investigated by ultrafast time-resolved pump-probe

spectroscopic method or time resolved photoluminescent spectroscopy [133-134] with above

band gap excitation.

In our study, we have performed a comprehensive set of measurements on bulk ZnO, ZnO

epilayers and nanorods. We measured the reflectivity and PL spectra of bulk ZnO, ZnO epilayer

and nanorod from 4.2 K to 70K. In order to understand the excitonic states in ZnO materials,

magneto reflection and PL spectra are also measured at 4.2K. Compared with previous studies

[135], we identify and label the excitonic state on each spectrum. Via spectrally resolved

degenerate pump-probe spectroscopy, we measured the time resolved differential reflectivity









(TRDR) of the A and B excitonic states in bulk ZnO, ZnO epilayer and nanorod. We find the life

time of the A exciton (A-X) is approximately 130ps and while the B exciton (B-X) is ~ 45ps at

for bulk ZnO at 10 K. We also measured the temperature-dependent TRDR of A-X in bulk ZnO

up to 70K, we find that the life time of A-X is still around 100ps, which indicates that relaxation

processes do not change significantly at higher temperatures. This is associated with the

properties of neutral donor bound X (DoX). The life time of A-X (50ps) and B-X(20ps) in ZnO

epilayer are very different from bulk ZnO, which is caused by different neutral donor bound X

(DoX) states in epilaer. The relaxation process of ZnO nanorod is fitted with stretch exponential

decay curve, indicating different relaxation dynamics of Xs from bulk ZnO and ZnO epilayer.

The coherent process in a very short time range (~2ps) on the TRDR of A-X in bulk ZnO is

analyzed with convolution of probe pulse with Gaussian function shape and carriers response

with exponential decay curve.

6.2 Background of Crystal Structure and Band Structure of ZnO Semiconductors

ZnO crystallizes stably in a wurtzite structure with C6v pOint group symmetry. This typical

semiconductor lattice structure is shown in Fig. 6-1. In the x-y plane, the atoms in a unit cell

form a hexagon, and the zinc atoms form hexagons and oxygen atoms form hexagons stack along

the z-axis, called (0001) direction.

In the x-y plane, since ZnO possesses hexagonal symmetry, many physical and optical

constants are isotropic, while along the z-direction they are different. However, we can use a, b

and c unit vectors to label the unit cell of ZnO, where c is along z-axis and a, b are in x-y plane.

In the study of optical properties of ZnO semiconductors, the polarization of absorption or

emission light are very critical to probe since they are associated with the selection rules of

transition and band structure symmetry. We define 2n linear polarization parallel to the c axis of









ZnO and a linear polarization perpendicular to the c-axis. The geometry and definitions of

polarization with respect to ZnO unit vectors are plotted in fig. 6-2.

As mentioned in chapter 3, a Hamiltonian with C6v Symmetry will couple the s states and

form lowest conduction band and px, p, and p, states into three valence bands. The band structure

of ZnO semiconductors is shown in Fig 6-3.

At the center of Brillouin zone, the conduction band is s-like, which has r7 symmetry,

while the p-like conduction band splits into three doubly degenerate bands due to spin-obit (Aso)

and crystal-field interaction (Acr). In the valence bands, the top valence A band has T9 Symmetry

while the B and C bands have r7 symmetry. The excitonic states formed with electron in

conduction band and holes in A, B and C valence bands are called A-X and B-X respectively. In

Fig. 6-3, the total angular momentum (J=L S, L is orbit momentum and S is spin momentum) of

each r points are shown. The A, B and C valence band states at r point can be expressed as:

33 1 1\
A: +- +- X +iY +-
2/ i12 2/
31 1 1 1
B:- Xfi,-- Z +-6-
2: 2 + X i, 2 2

':1 1 1 1 1
22 2/ 2

We can see that each valence band at r point are degenerate, each band will split in to doublet

states (spin up"+" and spin down"-") in magnetic field.

6.3 Valence Band Symmetry and Selection Rules of Excitonic Optical Transition in
ZnO Semiconductors

The optical properties of bulk ZnO have been studied for over 40 years, and for the most

part are well understood. However, there remains ambiguity and controversy in the assignment

of symmetries of the A, B and C valence band states. In Thomas and Rodina' s assignment[1 36-

137], the symmetry of A, B and C valence bands are r7, T9 and r7 since they considered that P,









component is mixed into the A band, which results the reverse of the order of r7 and T9 in typical

II-VI group semiconductors. In contrast, after carefully studying of the absorption, reflection and

PL spectra as well as the Zeeman splitting of excitonic states of ZnO semiconductor [138],

Reynolds have concluded that the order of top two valence bands in ZnO do not reverse.

Therefore, in Reynolds's assignment of the order of valence bands in ZnO semiconductor, A, B

and C bands have T9, r7 and r7 symmetry respectively. In this case, A band is pure Px and P,-,

and the only optical transition from A band to conduction band optical transition is expected to

be a polarization (k//c and E l c k is the direction of light propagation, c is c-axis). For the B

band, the optical transition could be either o- polarization (k // and E Ic ) or 2n polarization

(k ic and E//c).

Based on group theory [18], the symmetry and selective rules of optical transition between

conduction band and A, B and C valence bands in ZnO semiconductor are given as follows:

A-X: 9 7 + ,6.2(a)

B-X: OF + F F ,6.3(b)

C-X: OF + F F,,6.2( c)

where rg is allowed in polarization and r1 is allowed in Fr polarization. The optical transition

r6 and r2 are prOhibited and r1 is very weak [139].

In order to resolve the controversy of valence band ordering, a magnetic field was

employed to observe Zeeman splitting of different optical transitions, since the Zeeman splitting

for r9 7 r transition and r, a r, transitions are very different--r6 is a doublet and splits into

two in magnetic field while T1 is a singlet and does not split in a magnetic field. Reynolds

clarified the symmetry of the top valence band by studying the splitting behavior of PL emission









line from A-X in magnetic Hiled at configuration [139]. In this thesis, we will consider the order

of valence band according to the Reynolds assignment.

6.4 Impurity Bound Exciton Complex (I line) in ZnO and Zeeman Splitting

In bulk semiconductor materials there are many types of defects and localized states. Some

of these states can bind excitons, resulting in a bound exciton complex (BEC).

Conceptualizations of an exciton bound to an ionized donor (D X), a neutral donor (DoX) and a

neutral acceptor (AOX) are plotted in Fig.6-4. The binding energy E of these bound excitons

usually increases according to [40]


ED X < EnoX < EAoX 6-3

These BECs have many emission lines in the PL spectrum of bulk ZnO, termed 'I' lines. Also,

when the free excitons or BEC optical transitions couple with longitudinal optical (LO) phonon,

the phonon replica can be observed in the PL spectrum at energy position

E' = E mheniLO 6-4

where E' is the positions of phonon replica, E is the energy of optical free exciton or BEC

transition which is coupled with LO phonons, m is an integer, and AmLO, is energy of LO phonon.

However, these phonon replica emission peaks are usually much weaker than the BEC emissions

or free X emissions.

In a magnetic Hield, a quantum state with spin will split into two states, spin up and spin

down. The energy splitting between the two states are called Zeeman splitting. However, in the

case of free excitons or BEC, both electrons and holes can be involved in Zeeman splitting,

which makes the interpretation of energy splitting of ZnO semiconductor in magnetic Hield more

complicated than free electrons.

Zeeman splitting in ZnO can be express as










AE = g,,cyB, 6-5(a)

where pu is Bohr magnon, B is magnetic field strength and gc factor is Lande factor and can be

written as:

gexc = Ke + KA. 6-5 (b)

For an electron, the g factor is isotropic, while for a hole the g factor is anisotropic (g and gL),

and typically gL is nearly zero [136]. In above expression, // means the c-axis of ZnO is parallel

to the magnetic field B and I means the c-axis is perpendicular to the magnetic field.

In the case of BEC, the Zeeman splitting is qualitatively different than free excition

Zeeman splitting since the splitting of ground states of Do and Ao has to be considered in addition

to the splitting of electron and hole in an exciton. Rodina and Reynolds [139] have studied the

splitting of BEC in ZnO and the results are shown in Fig. 6-5.

As shown in figure 6-5, the excited state ofDoX consists of a donor defect, two electrons

and one hole, with the two electrons spins antiparallel. The Zeeman splitting of the excited state

is determined by the anisotropic hole effective g factor, while the Zeeman splitting ground state

Do is given by the effective g factor of electron ge. Therefore the splitting of optical transition of

DoX in the Faraday geometry (B//c and k//c) (see Fig.6-6) is given by

AE = (g, g,, )puB, 6-6(a)

and the splitting in Voigt geometry (Bic and k//c) (see Fig.6-6(b) )is

AE = g, pB 6-6(b)

Also the Zeeman splitting should be linear in magnetic field. In the case of the acceptor bound

exciton AoX, the Zeeman splitting has similar form.









6.5 Samples and Experimental Setup for Reflection and PL Measurement

The ZnO samples we used for magneto optical spectroscopic studies are bulk ZnO (grown

by MTI Crystal Co.), ZnO epilayers (grown by David Norton' s group at University of Florida),

and ZnO nanorod grown in GIST in South Korea). The size of bulk ZnO is 5x5x0.5mm and the

orientations of the crystals are c-plane (c-axis perpendicular to the plane) or a-plane (a-axis

perpendicular to the plane and c-axis in the plane) configurations. The bulk ZnO crystal was

grown with hydrothermal method. The 400nm thick ZnO epilayer samples were grown on a c-

plane sapphire substrate via the MBE method and the self-assembly ZnO nanorod sample with

rod diameter 8nm is grown with laser deposition. All the ZnO samples were nominally undoped.

We measured the reflection spectrum of all the ZnO samples with polarized light to

identify the excitonic states. We used a Deutrium lamp with the output polarized using a Glan-

Laser polarizer. In the reflection spectrum measurements, ZnO samples were put in a cold finger

style optical cryostat, in which the samples can be cooled down to 4.2K with liquid helium.

In magneto-optical spectrum measurements, we used the cw magneto-optical facility at

NHMFL shown in Fig.2-2, 2-3. The ZnO was mounted inside the helium tail of a Janis cryostat

and cooled down with helium exchange gas. The light was delivered to ZnO sample through

multimode optical fiber, and the reflection and PL emission were collected with another

multimode optical fiber. Here, we used a UV Xenon lamp for measuring the reflection spectrum

and a He-Cd laser (325nm wavelength) for exciting the sample to measure the PL spectrum.

Both the reflection light and PL emission were delivered to a 0.75m McPherson spectrometer

and the spectrum was recorded with a charge-coupled device (CCD). In the temperature

dependent measurement, the sample temperature was measured and controlled by a Cernox

sensor, a Cryocon temperature controller and a heater with 50 W maximum power output.









6.6 Results and Discussion

In Eigure 6-7, the reflection spectrum of a-plane bulk ZnO at 4.2K obtained using a and 2n

polarized light. The excitonic optical transitions obey the transition rules listed in equation. 6-2,

where A-X (T9), B-X (r7) and C-X (r7) are activated in a polarized light and C-X (r7) is

activated only in xn polarized light. However we cannot specify the exact energy positions of free

excitons peaks since the complexity in reflection spectrum (see Chapter 2).

In Eigure 6-8(a), the magneto-PL spectrum of c-plane bulk ZnO is plotted for the Faraday

configuration (B//c, k//c, Elc). We can see that the PL emission feature is a sharp peak sitting on

the top a broader and weaker peak, which caused by inhomogeneous broadening. There is no

significant magnetic splitting observed, although the sharp PL peak becomes broader (possibly

due the onset of splitting) and the PL intensity becomes lower with the increasing of magnetic

Hield strength. Figure 6-8(b) shows the PL spectrum of the same sample at Voigt configuration

(Bic, k//c, Elc). It is clearly evident that the sharp PL peak split linearly into two peaks with the

increasing magnetic field. The energy position vs. magnetic field of the peaks is plotted in figure

6-8(c). This is Zeeman splitting and will be discuss further in the following section, however,

since we use multi-mode fiber to delivered light, no polarization information can be obtained

from the two PL peaks and the spin states can be resolved.

In order to understand the PL emission spectrum, we plot the reflection and PL emission at

zero field in figure 6-9(a). We can assign the PL emission peak at 3377 meV to the

recombination of free A-X, indicated by an arrow in the figure. The other PL peaks at lower

energies are assigned as emission from impurity bound A-X, the strongest bound exciton PL

peak is at 3360 meV and has been reported to be neutral donor bound exciton (DoX) [140].









In figure 6-9(b), the reflection and PL emission spectrum of the c-plane bulk ZnO in both

Faraday and Voigt configurations at 30 Tesla are plotted. From this data, we can conclude that

the A-X and its bound state do not split in Faraday geometry while they split into two peaks in

Voigt geometry. At 30 T, the splitting of PL peaks from A-X donor bound state is ~3.4 meV.

The magnetic splitting of A-X and DoX can be interpreted with the splitting process shown

in figure 6-5 and equation 6-6 as following. In the Faraday geometry, according to Eq. 6-6, the

magnetic Zeeman splitting of A-X and DoX is determined by Lande factor gex, which is ge-

gh=0.7[16], therefore the Zeeman splitting at 30 Tesla is around 1.2 meV, which is smaller than

the resolution of spectrometer and thus can not be observed with our spectrometer.

However, in Voigt geometry the Lande factor gex=ge, since gh=0, therefore the Zeeman

splitting at 30 T is ~3.38 meV, which is in agreement of our observation 3.08 meV. In Fig.6-

8(d), we plot the experimental and calculated results of AE vs. B, the results are in good

agreement if we take into consideration that the resolution of spectrometer is around 1meV. This

agreement strongly proves that the dominant PL emission peak comes from neutral bound

exciton.

In the case of the ZnO epilayer sample, we plot the reflection and PL spectrum at zero

fields in figure 6-10(a), we can clearly resolve the A-X and B-X in the reflection curve. In the PL

spectrum we observe a strong emission at 3355 meV, which is also from bound exciton

transition, however the PL peak is asymmetric and has a long tail at the low energy side, and in

addition the PL linewidth is much broader (5~6 meV) than the bulk ZnO (2 meV). All of these

observations imply that the optical quality of this ZnO epilayer is not as good as bulk ZnO, with

more defect states present which cause more inhomogeneous broadening and carrier trapping

below the bandgap, and result in the PL linewidth broadening and an asymmetric line shape. At









3285 meV, we observe a PL emission peak due to LO phonon coupled with bound exciton

transition, since the LO phonon energy is 70 meV in ZnO. Due to the fact that the PL emission

linewidth is larger than the predicted Zeeman splitting, we cannot resolve and observe the PL

peak splitting in neither Faraday geometry nor Voigt geometry in this ZnO epilayer sample as

shown in Fig.6-10(b).

6.7 Time Resolved Studies of Carrier Dynamics in Bulk ZnO, ZnO Epilayers, and ZnO
Nanorod

As introduced in chapter 2, time resolved spectroscopy is a very important tool for

understanding the dynamics of carriers and excitons in semiconductors, critical for applications

in electro- optical device.

From Chapter 2, the changes to the dielectric function e are given by [141]

AN, (t)e2
Ae(cy, t) = 6-7
E,,711 0

Where wL is the laser frequency, AN, (t) is the carrier density in the ith energy band and m, is the

carrier mass of the ith band. Since ZnO is a wide bandgap semiconductor, the high-frequency

limit (w~t>>1) is satisfied, therefore the differential reflectivity is proportional to the change in

carrier density in each energy band divided by the mass of the band, summed overall bands,

which is shown in equation 6-8,

AR AN,
(I >). 6-8
R ,m

This shows clearly that the differential reflectivity measurements effectively probe the changes

in carrier density in different ZnO energy bands.

In the recombination of an electron and hole pair, both radiative and nonradiative

recombination processes are usually involved, and the rate equation can be expressed as follow










1 dN A, A,
N t Tadrahre nonradrahre

where N is the carrier density, Trdar and Tnnadar are radiative and nonradiative relaxation

times, A, A, is corresponding efficiency. In radiative recombination, photons are emitted as the

carriers recombine to conserve energy, while in nonradiative processes, electrons and holes

recombine through emission of acoustic phonons.

As we have seen that bulk and epilayer ZnO exhibit different reflectivity and photo-excited

emission characteristics due to the presence of defect states, we now turn to investigations of

how those differences impact dynamical carrier processes. We measured the time resolved

differential reflectivity (TRDR) spectrum of ZnO semiconductors, including bulk with different

orientation, c-plane epilayer and nanorod samples with 8 nm rod diameters. Since the absorption

coefficient of ZnO is very high, it is very difficult to get good transmission signal from thick

samples, we use reflection geometry to get TRDR signal.

The experimental setup for measuring the TRDR of ZnO semiconductors is shown in

figure 6-1 1. We used ultrafast laser pulses 150fs in duration at a wavelength of 730 nm from a

Coherent Mira 900-F laser system with 76 MHz repetition rate. The laser beam was focused onto

a nonlinear /7-barium-borite (BBO) crystal to frequency double the pulses into the near UV

around 365nm via second harmonic generation (SHG). The UV laser pulses were then split into

pump and probe beams using a sapphire plate. Both the pump and probe beam propagated

through waveplates and Glan-Laser polarizers to make them parallel or perpendicularly polarized

before they were focused down to 50pum on the ZnO samples, mounted in an optical cryostat.

Liquid helium flows into the cryostat during the measurements, by which we can cool down the

ZnO samples to down to 4.2K and reduce the thermal broadening effect and phonon effects. The









pump beam was time delayed with respect to probe beam using a Newport stage controlled by

computer. To obtain the best signal-to-noise ratio, the pump and probe beams were chopped with

a differential frequency fi = 2KHz and f2 = 1.57KHz, and the probe reflectivity signal was

detected using photodiode via a lock-in amplifier demodulating the signal at fi-f2.

6.8 Experimental Results and Discussion

6.8.1 Relaxation Dynamics of A-X and B-X in Bulk ZnO

In figure 6-12, the TRDR at 10K are plotted for A-X and B-X in a-plane bulk ZnO

semiconductor, both the probe beam and pump beam set to a polarization (perpendicular to c-

axes), in which A-X and B-X are optically activate. The DR curve decays exponentially. We fit

the two curves exponentially with equation 6-9 and obtain the following results,

rg = 130 fl0ps and ry = 45fIlps .

The sharp peaks in figure 6-12(a) and (b) at t-0 ps most likely arises from a coherent

artifact due to the collinearity of the pump and probe polarization. More discussion about this

fast relaxation process will be given in the following.

However, the relaxation time r is much smaller than previous report for free A and B

excitons [142], reported Ins. This strongly suggests that in these samples, the A and B excitons

are mainly bound to an impurity state, which makes the DoX dominate the relaxation process

instead of free exciton recombination. This agrees well with the PL data (figure 6-9) in which the

DoX is three orders stronger than free A-X. In this case, A, is much smaller than A,, which

indicates that the radiative recombination can be neglected compared to nonradiative processes

in the exciton relaxation process.

In figure 6-14, we plot the TRDR spectrum of AX in c-plane bulk ZnO at different

temperatures up to 70K, where the laser wavelength is tuned to resonantly probe the A-X as the










temperature increases. The artifact observed in Eigure 6-12 does not show up here because the

pump and probe laser beam are orthogonally polarized. We also observe mono-exponential

decay of DR in this figure. The fitting results of the relaxation time are r, = 130 + 10ps which

do not change significantly with temperature up to 70K and imply that the A-X relaxation

process is dominated by a bound to impurity state instead of radiative recombination up to 70K,

since the binding energy between neutral donor and an exiton is around ~10meV [18], which

makes it difficult to break them at low temperature.

In semiconductor, immediately after the carrier are excited with coherent laser light (pump

beam), the carriers preserve the coherence generated with laser beam in a very short time (~ps)

[143], if the probe beam arrives during this carrier coherent status, strong interaction will be

expected between the coherent carriers and coherent light, which result in the sharp feature in

Fig. 12. In this case, the actual signal that we acquired is the convolution of probe pulse and

carrier decay, which are presumed to be Gaussian function and exponential decay function

respectively. The convolution result is given as:

A 02 t a t
S(t) = exp( )[1-2 erf .: 6-10.


Where z is the exponential decay time and Jdo is the FWHM of the Gaussian function.

Fig. 6-13 shows the fitting of the fast relaxation cure with the convolution function 6-10, we can

see that the pulse width is around 0.5ps and the coherence exponential decay time is around

1.4ps.

6.8.2 Relaxation Dynamics of A-X and B-X in ZnO Epilayer and Nanorod

In figure 6.-15, TRDR spectra of AX and BX in ZnO epilayer at 4.2K are plotted. It is

clearly resolved that the carriers populate on BX decay mono-exponentially. The fitting result of









BX relaxation time is r = 25+1 ps .however the A-X shows a stretched exponential decay

process, which is described by


I= ~~ ~h Aept+I,61

where z is the decay time and n<1 is stretched factor.

With this function, the fitting results of A-X relaxation in ZnO epilayer are n=0.9 and

z=50ps.These exciton relaxation times are much smaller than the bulk ZnO, which indicate that

the density of defect states in the ZnO epilayer sample are more than that in the bulk ZnO

sample. Also, by comparing the carrier relaxation time, we might expect that the defect state

dominates in epilayer sampler should be different from that in bulk sample since the relaxation

are quite different. These can be convinced in the PL spectrum in Eigure 6-10, in which we can

not see the free X emission, most Xs are bound to defect states and emit photons at 3355 meV in

stead of 3360 meV in bulk ZnO samples.

In Eigure 6-16, the TRDR of ZnO bulk nanorod is shown. The excitation and probe light

energy is 3416mev, which is supposed to be above the ZnO bandgap. We can see that the TRDR

cure of ZnO bulk nanorod sample decay stretched exponentially. This curve is fitted with 6-1 1.

The fitting results are z=17ps and n=0.65.

The stretched exponential relaxation is summation of distribution of independent

exponential decay relaxations and is indication that there is an inhomogeneous distribution of

recombination times. It is reported in many semiconductors material especially in nanostructures

[144-145]. Three mechanisms [146-147] are proposed to interpret the stretched exponential

decay.

The distribution in lifetime is a result of varying carrier localization such that carriers can

escape from one area of sample to other area and recombine nonradiatively.










The migration of excitons between distorted nanostructures is possible, which result in the

capture and delayed released of excitons.

Distribution of the lifetime in PL at a single wavelength could be explained by the

distribution of the nanocrystal shapes in a given area.

From the above explanations, we found that the stretched exponential is mainly caused by

the either trapped of carriers, carrier hopping between nanostructures or different size of

nanostructures.

We can see that the stretched exponential decay of exciton in ZnO epilayer and nanorods

indicate that the sample might have many defects states, which traps the carriers, the nanorod

sample might have different size effect and also the carriers in nanorod might migrate between

rods.









Table 6-1. Some parameters of ZnO bulk semiconductors
Point group 6mm(Csv) (Wurtzite)
Lattice constants at room temperature a=3.250, c-5.205 nm
Electron mass 0.28 me,
Hole mass 1.8 mel
Bandgap energy at room temperature 3.37 eV1
Exciton binding energy 60 meV1
Melting point 2250 K1
LO phonon 70 mevl
SReference[10]




















X


SZn atom on the top layer


SZn atom on the bottom layer

* atom


Figure 6-1.


Top view of the lattice structure of a wurtzite ZnO crystal. In the x-y plane, ZnO
has hexagonal symmetry along the z-axis. In z-axis direction, Zn atoms are on the
top and bottom layers, O atoms layer is between the two Zn atom layers. Also,
another O atoms layer (not shown) is on the top of top layer of Zn atoms. In the
(0001) direction, hexagonal symmetry is along the z-axis.
































Figure 6-2. The orientation of light polarization with respect to the ZnO unit cell.
The a polarization is defined as perpendicular to c-axis and 2n polarization is defined
as parallel to c-axis.





Figure 6-3.


Band structures and symmetry of each band of a ZnO semiconductor.
At the center of the Brillouin zone, the conduction band has r7 symmetry, and for
the valence bands listed as A, B and C from top to lowest, the symmetries are, T9
and r7 respectively.


Conduction Band


A(J= 3/2)


B(J=3/2)


C(J=1/2)


Valence Band




















(a) DTX


(c) AOX


electron


hole


Figure 6-4. Schematic of types of impurity bound exciton complexes. (a) an ionized bound
exciton (b) a neutral donor bound exciton (c) a neutral acceptor bound exciton


(b) DoX


Point defect










B//C
+3/2


I -3/2


BIC


(DO, X)


gh=1.25


ghi-0






ge=1.95


+1/2

-1/2


(DO)


+1/2


-1/2


ge=1.95 (AO, X)


ghl=O(AO) +/-3/2


(b)
Figure 6-5. Energy diagram of Zeeman splitting of neutral bound excitons in ZnO.
(a) donor-bound exciton, (b) acceptor-bound exciton


1























C -axi s


Fig.6-6. Voigt configuration of c-plane ZnO in magnetic field.Faraday configuration is shown
in Chapter 4.


Zn O


Laser






































3.45
Energy (eV)


Figure 6-7.


Reflection spectrum of a-plane bulk ZnO semiconductor for different linear optical
polarization at 4.2K. The upper curve is a polarization and the lower curve is an
polarization. The arrows point out the exciton energy position and the related
symmetry.











6000 ~jiX

.: I4000 25X]
3[000 ,,IW
2000 a l
/; ~~1000I15D




3350 355 360 335 337 337
Energ me5ErsW(O4


14 16 ~13 20 22 24 26 28 30

Magnetic Flold B(T)


S3360-
-




3358


2.4- g=1.95






1.2 . .
12 14 16 18 20 22 24 26 28 30
Mragneticr Field (B)


(c) (d)
The magneto-PL spectrum of a and c-plane bulk ZnO sample and Zeeman splitting
at 4.2K PL spectrum in (a) Faraday and (b) Voigt configurations, (c) The Zeeman
energy splitting in Voigt geometry as function of magnetic field, (d) Zeeman
splitting AE vs. magnetic field, black dot is experimental result and red and blue
line are fitting with g=1.95 and 2.0 respectively.


Figure 6-8.











100000


S10000


1000


100

3300






100000-



10000



-c 1000-


3350 3400
Energy (mev)


3450


100 L
3300


3350


Energy (mev)


(b)
Comparison of reflection and PL spectrum of c-plane bulk ZnO. (a) reflection
(black curve) and PL (red curve) at zero magnetic field, (b) reflection in the Faraday
geometry (black curve), Voigt geometry (red curve), and PL in the Faraday (green
curve) and Voigt (blue curve) configurations at 30 T.


Figure 6-9.


3400













innnon


1 I\A-X



I ~B-X
4 3285mev

Bound X-LO Phonon

100 I
3250 3300 3350 3400
Energy (mev)

(a)




100000- Bound X



AX
10000-


B X
0- 1000-



100
3250 3300 3350 3400 3450
Energy (mev)

(b)
Figure 6-10. Comparison of reflection and PL spectrum of c-plane epilayer ZnO at 4.2 K. (a)
reflection (black curve) and PL (red curve) at zero magnetic field, (b) reflection in
the Faraday geometry (black curve), Voigt geometry (red curve), and PL in the
Faraday (green curve) and Voigt (blue curve) configurations at 30 T.

























Dichroic
G-L 1/2 BSmirror
WP


Cr~yostat


Figure 6-11i. Pump-probe experimental setup for measuring TRDR of ZnO semiconductors. BS
is beam splitter, WP is waveplate, G-L is Glan-Laser polarizer, PD is photodiode


















IB

0.01




0 50 100 150 200

Time Delay (ps)

(a)









-6-4-2 02 46 8101
~1 I Delay Time (ps)
-10.01



-5 0 0 50 100 150 2v0

Delay Time (ps)

(b)
Figure 6-12. TRDR plots of a-plane bulk ZnO semiconductor at 4.2K (black dot) and
exponential decay fitting line.(a) AX probe at 3375 meV, decay time 130+10ps,
(b) BX, probe at 33 87 meV decay time 4511ps. Both of the inserts are TRDR
spectra show fast decay in short time (~1ps) range. The cure in (a) does not fit
well with exponential decay due to alignment problems of optics.




























-0.6 -0.3 0.0 0.3 0.6 0.9 1.2 1.5

Time Delay (ps)

Figure 6-13. Fast decay in TRDR of A-X in a-plane bulk ZnO and the fitting with convolution
of Gaussian function probe pulse and exponential decay response function.
Fitting parameters are pulsewidth=0.5ps and Tresponse=1.4ps.































20 40 60 80 100 120 140 160

Time Delay (ps)


Figure 6-14. Temperature dependent TRDR of A-X recombination in c-plane bulk ZnO. Probe
wavelength is tuned to the A-X resonant wavelength. The fitting results of decay
time z=130ps do not change significantly with the temperature increasing.










0.02

0.015


0.01




o 0.005


O~ 5L



0 20 40 60 80 100
Time Delay (ps)

(b)
Figure 6-15. TRDR plots of excitonic recombination in ZnO epilayer for different exciton
states. (a) A-X, probe tuned to 3375 meV (b) B-X, probe tuned to 3387 meV.
Fitting result is shown with red line.


Time Delay (ps)

(a)
















0.01.


T=10OK










1 E-3.
O 40 80 120 160 2*0

Time Delay (PS)


Figure 6-16. Experimental TRDR plot of ZnO nanorod sample at 10K and fitting result with a
stretched exponential decay. Black dots are experimental results and red curve is
fitting results with a stretched exponential function. Fitting parameter are
z=1711ps and n=0.6510.01.









CHAPTER 7
CONCLUSION AND FUTURE WORK

In order to study the carriers dynamics of III-V group semiconductor quantum wells at

high carrier density (~1012Cm-2) and high magnetic fields, we have developed an ultrafast optics

facility at the National High Magnetic Field Laboratory, including an ultrafast chirped pulse

amplifier, optical parametric amplifier, and a 17.5 Tesla superconducting magnet (SCM3) as

well as the necessary cryogenic system and optical probes for both SCM3 and the 31 T Bitter

magnet in cell 5. This unique facility provides us high power pulses (GW/cm2) in broad

wavelength range (200nm to 20pum) and high magnetic fields (up to 31 Tesla) to study the

quantum optics of e-h pair in semiconductor quantum wells. A detailed description of this

facility was shown in Chapter 2.

To understand the optical transmission and reflection spectrum of semiconductors, we

gave a detailed description of the optical response theory. In addition, the detailed theory of the

electronic states in semiconductor quantum well is given as well as the excitonic states and LL

splitting in high magnetic field was presented.

With these as a background, this dissertation has presented a systemic spectroscopic study

of magneto-optical properties of InxGal-xAs/GaAs multiple quantum well in the low and high

excitation regimes using CW light source high excitation domain with a high power ultrafast

light sources at magnetic field up to 30 T.

In low excitation regime, we can clearly resolve the interband LL transitions originating

from the same conduction and valence subbands in the absorption spectrum of InxGal-xAs/GaAs

multiple quantum wells at 4.2K to 30 T. Anticrossing phenomena and dark excitonic states are

shown between the traces of elh ns and el lns magneto excitonic states. Theoretical calculation

shows that this larger splitting (~9 meV) does not arise from valence band complexity.









In high excitation regime, we measured PL emission from InxGal-xAs/GaAs multiple

quantum wells excited with high power CPA pulses (~GW/cm2). We do not see Coulomb

interaction-induced anticrossing between LL levels originating from heavy holes and light holes.

Bandgap renormalization is clearly observed when we compared the Landau fan diagrams of

absorption spectrum in low excitation and PL spectrum in high power regime. Both of these

indicate that Coulomb interaction in e-h pair is screened at high carrier density (~1012/CM2) and

PL from high density e-h plasma dominates the out-of-plane PL emission at high field and high

excitation.

In the high power excitation spectrum of InxGal-xAs/GaAs multiple quantum well, we

observed strong and sharp features on the PL peaks, suggesting the study of amplified emission

processes in the InxGal-xAs/GaAs MQWs. With the ultrafast facility developed at NHMFL, we

were able to study the in-plane PL emission from InxGal-xAs/GaAs MQWs. We observed

abnormally strong emission. By measuring and analyzing the field dependent, power dependent

PL spectra and the single pulse excited PL spectra, we characteristized this sharp peak emission.

(I) the PL emission strength of sharp peak increased linearly above a certain magnetic field (13

T) or laser fluence (0.01 mJ/cm2) associated with an ASE process. (II) above a critical magnetic

field (~16 T) or laser fluence(~-0.03 mJ/cm2), the PL strength increases super linearly (~B1. or

F .), (III) for single pulse excitation above the fluence threshold, we collect the in-plane PL

emission for different propagation directions, and the single shot experiment shows

anticorrelated emission between the PL strength at different directions. However, for the single

pulse excitation experiment, we observed a complete correlation between in-plane PL at different

propagating directions, consistent with ASE emission. With an understanding of the cooperative

theory of light emission introduced in detailed in chapter 5, we found that the characteristics of









strong PL above magnetic field or fluence threshold from in-plane emission are consistent with

the cooperative emission process--superfluorescence, in which all the excited carrier are coherent

during the emission process and give a very short burst emission of coherent light.

This dissertation also presents comprehensive spectroscopic investigations on ZnO

semiconductors, including bulk, epilayer and nanorod samples. The A and B excitonic states are

clearly identified in the reflection spectra with optical selection rules. PL from donor or acceptor

bound excitons dominates the emission spectrum up to 70K in the bulk ZnO and ZnO epilayer.

To understand the excitonic states of ZnO in more detail, we measured the PL spectrum at high

magnetic field up to 30 Tesla. Zeeman splitting form donor bound excitons is clearly resolved

and analyzed with theoretical predication, we found that in Voigt geometry, the effective Lander

factor is g~2, which is close to theoretical predication.

Ultrafast time resolved pump-probe experiments are also carried to study the A-X, B-X

dynamics in bulk ZnO, ZnO epilayer as well as ZnO nanorod. Exponential decay is observed in

A-X (~130 ps) and B-X (~50 ps) in bulk material, which is corresponding to relaxation to DoX.

In epilayer and nanorod sample, we observed stretched exponential decay process, (n=0.9 and

z=50 ps for A-X for the epilayer, n=0.6, 2=17 ps for the nanorods), related with carrier hopping

transport and carrier localization.

For the future, we need to obtain the time resolved information of the cooperative

recombination process in high density e-h plasma in high magnetic field, including measuring

the SF pulse width, time delay for evolution of coherence between atoms. We proposed the

following experiments:

*Time resolved pump-probe experiment to measure the carrier dynamics in InxGal.

xAs/GaAs QW at high magnetic fields. This can be done with the CPA and OPA.










* Time resolved PL from in-plane emission in QW at high magnetic field, this can be done

with streak camera and provide us the time information of evolution of coherence.


* Upconversion PL measurement of SF from InxGal-xAs/GaAs QW in high magnetic field,

this can provide us the time information of the pulse width of SF.


As for the ZnO semiconductor, we propose to perform time resolved PL measurements

with a streak camera, which can provide more information of the radiative and nonradiative

dynamics of exciton and bound excitons.









APPENDIX A
SAMPLE MOUNT AND PHOTOLUMINESCENCE COLLECTION

A commercial Janis cryostat (shown in Fig.2-8) is modified for sending fs laser directly on

the sample cooled down to 10K inside the cryostat. On the tail of modified optical cryostat

shown in Fig.2-10, an optical window is mounted on the bottom of the cryostat outer tail. Fig. A-

1 shows the detailed configuration of the sample mount, optical fiber and PL collection used in

the experiments.

The sample mount, which is made of cooper, is bolted on the bottom of liquid helium tail

of the cryostat. An indium foil is used between the sample mount and the bottom of liquid

helium tail for better heat conduction. With this method, the sample can be cooled down to

around 10K.

The InxGal-xAs/GaAs MQW is positioned on the top of a sapphire plate, which is about

1mm thick. Special optical glue is used to firmly attach the sample on the sapphire plate. This

optical glue is transparent for visible and near infrared light, which is suitable for 800nm CPA

excitation light and the PL emission around 930nm. The optical glue is dried with strong UV

light heater. A right prism with size Immxlmm is also attached to the sapphire plate and one

edge of the InxGal-xAs/GaAs MQW. The sapphire plate with sample on it is positioned on the

cooper sample mount with GE varnish, special glue with good conductivity at low temperature.

A Cernox temperature sensor is attached to the sample mount right beneath the sapphire plate, so

that the temperature of sample can correctly measured. An electric heater is also position around

the sapphire plate for temperature control.

Two optical fibers are inserted into the small tubing inside the liquid helium and go

through the bottom of the helium tail, indium foil and sample mount, and reach the sapphire

plate. The sapphire is positioned well so that the two fibers are right on the top of the center of









sample and the top of right angle prism respectively. The fiber on the center is used to collecting

the PL emitted perpendicular to the quantum well plane while the fiber on the prism is used for

collecting the PL propagating inside the quantum plane, the in plane PL is coupled into the fiber

with the prism. Strong white light is induced to the fibers from the open end to Eind the best

positions of the other ends of optical fiber on the top of sapphire plate.






















11111111~1111~


~| Stainless steel tubing


Optical fiber
center collection


Liquid Helium tall


Indium fail -


SOptical fiber
edge collection





SSample mount

-H eater


Cernox1
sensor


Right angle prism


Figure A-1. Detailed schematic diagram of sample mount and PL collection used in the
experiment.









APPENDIX B
PIDGEON-BROWN MODEL

In a realistic calculation of electronic states in semiconductor in magnetic fields,

k p theory [71] is required to for good approximation of the bandstructure. For narrow gap

semiconductors such InGaAs or InAs, the coupling between the conduction and valence bands is

strong, so it is necessary to calculate the LLs with eight-band model. Pidgeon and Brown [94]

develop a model to calculate the LLs in magnetic field at k-0. This model is generalized to

include the wave vector (ks 0 ) in this chapter.

The wave function basis in Tab. 3-1 is still used in the calculation. In the presence of a

uniform magnetic field B along z-axis, the wave vector k in the effective mass Hamiltonian is

replaced by the operator

k= (p +-A), -1


where p = -ihV is momentum operator. In Landau gauge, B = V xA = B:

Two operators are defined as

a = (k, + ik, ), B-2 (a)

a = (kx iky ), B-2 (b)


where h is the magnetic length Ai = ,I-.


The operators defined in Eq. B-2 are creation and annihilation operators. The states they

create and annihilate are simple harmonic oscillator functions, and aa' = N are the order of





Note: The Pidgeon-Brown Model is taken with permission from Y. Sun, Theoretical Studies of
the Electronic Magneto-optical and Transport Properties of Diluted Magnetic Semiconductors,
Page 45-50, PhD dissertation, Univ. of Florida, Gainesville, FL2005









harmonic functions. Using these two operators to eliminate kx and k, in the Hamiltonian, a new

Landau Hamiltonian is reached


HI =rL L B-3

The La, Lb and Le are given by

E, +A i-a 7 -a --ai

-i-a -P-Q -M iM
L B-4


2Z Va i M2~ -i O -P-


E, +A i-a+ -i~n --ai -a

a -P-Q MiJM
La V M PO B-5



63 A




L = v 2B-6

i. -i~ Li L


The operators A, P, Q, L and M~ are


A72N +1
A 4( + k 2), B-7(a)
A 2N+1
P = ( + 2k ), B-7(b)
n2


L = -73,( ), B-7(d)











M = ( > ( a ). B-7(e)
m, 2
The parameter yl, y2, Y3 and Y4 are Luttinger parameters [80] and A is the spin-orbit

coupling. With Landau gauge translation symmetry in the x direction is broken while translation

symmetry along the y and z directions is maintained. Therefore, k,- and k, are good quantum

numbers and the envelop of the effective mass Hamiltonian HL can be written as





er~ky+k z) a ,.B-8
F

a6 ne n~+1




In Eq. B-8, n is the Landau quantum number associated with the Hamiltonian matrix, v

labels the eigenvectors, A=LxL,- is the cross sectional area of the sample in the x-y plane,

,,(5) are harmonic oscillator eigenfunctions evaluated at 5 = x A ~k,, and a ,~,~,(k, )is complex

expansion coefficients for the vth eigenstate, which depend explicitly on n and k. Note that the

wave functions themselves will be given by the envelop functions in Eq. B-8 with each

component multiplied by the corresponding k-0 Bloch basis states given in Table 3-1.

Substituting Fny from Eq. B-8 into the effective mass Schrodinger equation

with H given by Eq. B-3, we obtain a matrix eigenvalue equation

H,F,(,, = E,~,, (k, ) .~

That can be solved for each allowed value of the Landau quantum number, n, to obtain the

Landau levels E,~, (k, ). The components of the normalized eigenvectors F,~, are the expansion

coefficients a, .










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BIOGRAPHICAL SKETCH

Xiaoming Wang was born in Nov. 1971. He earned the Bachelor of Science degree at

Tianjin University, China, in 1994. After that he entered the graduate school of Tianjin

University and got his Master of Science degree in physics in 1997. Right after that, he started

his j ob as a research associate in the Institute of Physics, China Academy of Sciences. After three

year of being a research associate in the Institute of Physics, Chinese Sciences, he resigned his

j ob and came to University of Florida in 2000, to pursue a Ph.D in physics. He j oined Prof.

David Reitze's ultrafast group in summer 2001. He has been working for several different

research proj ects, some of which are related to this dissertation.





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1 ULTRAFAST OPTICAL SPECTROSCOPIC STUDY OF SEMICONDUCTORS IN HIGH MAGNETIC FIELDS By XIAOMING WANG A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2008

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2 2008 Xiaoming Wang

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3 To my wife and my daughter

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4 ACKNOWLEDGMENTS First of all, I would like to express my deep gratitude to my advisor, Professor David Reitze, for his supervision, in struction, encouragement, tremendous support and friendship during my Ph.D. He guided me into a beauti ful world of ultrafast optics. His profound knowledge of ultrafast optics, condensed matter physics and his teaching style always impress me and will help me all through my life. I wish to thank my supervisory committee, Pr of. Stanton, Prof. Tanner, Prof. Rinzler and Prof. Kleiman, for their instructi ons for my thesis and finding e rrors in my thesis manuscript. I would like to give my sincere thanks to the visible optics staff scient ists at the National High Magnetic Field Laboratory, Dr. Xing Wei and Dr. Stephen McGill, for their excellent technical support for our experiments. I learned pl enty of knowledge about spectrometers, fibers, cryogenics, magnets and LabView program from th em. Also I give my special thanks to Dr. Brandt, former director of DC facility at NHM FL, for his great administrative assistance. I appreciate the experimental and theoretical supervisions we received for our research projects from Prof. Stanton from University of Florida, Prof Kono from Rice University and Prof. Belyanin from Texas A&M University. Spec ial thanks should be given to my research collaborators, Dr. Young-dahl Cho and Jinho Lee. Our research projects would not be so successful without th eir contribution. This work is supported by National Science F oundation and In House Research Program at the National High Magnetic Field Laboratory. Finally I want to send my warmest thanks to my wife and my daughter, my parents and parents in law for their endless love and support. I could not complete my studies without their emotional and financial support.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ..........8 LIST OF FIGURES................................................................................................................ .........9 ABSTRACT....................................................................................................................... ............14 CHAPTER 1 INTRODUCTION AND OVERVIEW..................................................................................16 1.1 Semiconductors and Quantum Wells............................................................................17 1.2 Magneto-spectroscopy in High Magnetic Fields..........................................................18 1.3 Motivation for Performing Ultrafast Sp ectroscopy in High Magnetic Fields..............19 1.3.1 Quantum Optical Processes in Se miconductors--Superfluorescence................19 1.3.2 Studies of Technologically Interesting Materials..............................................20 2 HIGH FIELD MAGNETO-OPTICAL TEC HNIQUES AND FUNDAMENTALS OF MAGNETO-OPTICAL SPECTROSCOPY...........................................................................24 2.1 Introduction...................................................................................................................24 2.2 Basic Background of Optical Response of Solids.........................................................24 2.3 Magneto-spectroscopy of Semiconductors--Methods...................................................27 2.3.1 Transmission Spectroscopy...............................................................................27 2.3.2 Reflection Spectroscopy....................................................................................28 2.3.3 Photoluminescence (PL) Spectroscopy..............................................................29 2.4 Time-resolved Spectroscopy of Semiconductors..........................................................29 2.5 CW Optical Experimental Ca pabilities at the NHMFL................................................32 2.6 Development of Ultrafast Magneto-optical Spectroscopy at NHMFL.........................34 2.6.1 Introduction of Ultrafast Optics.........................................................................34 2.6.2 Magnet and Cryogenics for U ltrafast Optics at NHMFL..................................35 2.6.3 Ultrafast Light Sources......................................................................................36 2.6.3.1 Ti:Sapphire femtosecond oscillator..........................................................36 2.6.3.2 Chirped pulse amplifier............................................................................37 2.6.3.3 Optical parametric amplifier....................................................................38 2.6.3.4 Streak camera...........................................................................................39 3 ELECTRONIC STATES OF SEMICO NDUCTOR QUANTUM WELL IN MAGNETIC FIELD...............................................................................................................57 3.1 Introduction...................................................................................................................57 3.2 Band Structure of Wurzite and Zinc Blend Structure Bulk Semiconductors................57 3.3 Selection Rules..............................................................................................................60

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6 3.4 Quantum Well Confinement.........................................................................................61 3.5 Density of States in Bulk Semiconductor and Semiconductor Nanostructures............63 3.6 Magnetic Field Effect on 2D Electron Ho le Gas in Semiconductor Quantum Well....64 3.7 Excitons and Excitons in Magnetic Field......................................................................66 3.7.1 Excitons..............................................................................................................66 3.7.2 Magneto excitons.............................................................................................67 4 MAGNETO-PHOTOLUMINESCENCE IN INGAAS QWS IN HIGH MAGNETIC FIELDS......................................................................................................................... ..........78 4.1 Background...................................................................................................................78 4.2 Motivation for Investigating PL from InGaAs MQW in High Magnetic Fields Using High Power Laser Excitation..............................................................................81 4.3 Sample Structure and Experimental Setup....................................................................82 4.4 Experimental Results and Discussion...........................................................................82 4.4.1 Prior Study of InxGa1-xAs/GaAs QW Absorption Spectrum.............................82 4.4.2 PL Spectrum Excited with High Peak Power Ultrafast Laser in High Magnetic Field..................................................................................................84 4.5 Summary.......................................................................................................................87 5 INVESTIGATIONS OF COOPERATIV E EMISSION FROM HIGH-DENSITY ELECTRON-HOLE PLASMA IN HIGH MAGNETIC FIELDS.........................................98 5.1 Introduction to Superfluorescence (SF)........................................................................98 5.1.2 Spontaneous Emission and Amp lified Spontaneous Emission..........................99 5.1.3 Coherent Emission Process--Superradiance or Superfluorescence.................101 5.1.4 Theory of Coherent Emission Proces s--SR or SF in Dielectric Medium........106 5.2 Cooperative Recombination Processes in Semiconductor QWs in High Magnetic Fields......................................................................................................................... ..109 5.2.1 Characteristics of SF Emitted from InGaAs QW in High Magnetic Field......110 5.2.2 Single Shot Random Directio nality of PL Emission.......................................112 5.2.3 Time Delay between the Exc itation Pulse and Emission.................................113 5.2.4 Linewidth Effect with the Carrier Density.......................................................113 5.2.5 Emission intensity Effect with Carrier Density...............................................113 5.2.6 Threshold Behavior..........................................................................................114 5.2.7 Exponential Growth of Emission St rength with the Excited Area..................114 5.3 Experiments and Setup................................................................................................115 5.4 Experimental Results and Discussion.........................................................................117 5.4.1 Magnetic Field and Power Dependence of PL................................................117 5.4.2 Single Shot Experiment for Random Directionality of In Plane PL................119 5.4.3 Control of Cherence of In Plane PL from InGaAs QW in High Magnetic Field................................................................................................................120 5.4.4 Discussion........................................................................................................121 5.5 Summary.....................................................................................................................125 6 STUDY OF CARRIER DYNAMICS OF ZI NC OXIDE SEMICONDUCTORS WITH TIME RESOLVED PUMP-PROBE SPECTROSCOPY.....................................................140

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7 6.1 Introduction.................................................................................................................140 6.2 Background of Crystal Structure and Ba nd Structure of ZnO Semiconductors.........141 6.3 Valence Band Symmetry and Selection Rule s of Excitonic Optical Transition in ZnO Semiconductors...................................................................................................142 6.4 Impurity Bound Exciton Complex (I line ) in ZnO and Zeeman Splitting..................144 6.5 Samples and Experimental Setup fo r Reflection and PL Measurement.....................146 6.6 Results and Discussion................................................................................................147 6.7 Time Resolved Studies of Carrier Dyna mics in Bulk ZnO, ZnO Epilayers, and ZnO Nanorod..............................................................................................................149 6.8 Experimental Results and Discussion.........................................................................151 6.8.1 Relaxation Dynamics of A-X and B-X in Bulk ZnO.......................................151 6.8.2 Relaxation Dynamics of A-X and B-X in ZnO Epilayer and Nanorod...........152 7 CONCLUSION AND FUTURE WORK.............................................................................172 APPENDIX A SAMPLE MOUNT AND PHOTOLUMINESCENCE COLLECTION..............................176 B PIDGEON-BROWN MODEL.............................................................................................179 LIST OF REFERENCES.............................................................................................................182 BIOGRAPHICAL SKETCH.......................................................................................................190

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8 LIST OF TABLES Table page 1-1 Some band parameters for some III-V co mpound semiconductors and their alloys.........22 3-1 Periodic parts of Bloch functions in semiconductors........................................................70 3-2 Selection rules for interband transitions using the absolute values of the transition matrix elements................................................................................................................ ..71 5-1 Some experimental conditions for obse rvation of super fluorescence in HF gas............126 6-1 Some parameters of ZnO bulk semiconductors...............................................................155

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9 LIST OF FIGURES Figure page 1-1 Physical and energy structure of semiconductor multiple quantum well..........................23 2-1 Transmission spectrum of InGa As/GaAs MQW at 30 T and 4.2 K..................................40 2-2 Reflection spectrum of ZnO epilayer at 4.2K....................................................................41 2-3 e-h recombination process and photoluminescence spectrum in semicondcutros.............42 2-4 Simple illustration of optical pump-probe transient absorption or reflection experiment..................................................................................................................... .....43 2-5 Experimental setup for optical pumpprobe spectroscopy and TRDR spectrum of ZnO............................................................................................................................ ........44 2-6 Time resolved photoluminescence spectrum of InxGa1-xAs/AlGaAs MQW at 4.2K............ 2-7 Technical drawing of the 30 Tesla resistive magnet in cell 5 at NHMFL.........................46 2-8 Technical drawing of cr yostat and optical probe for CW optical spectroscopy at NHMFL.......................................................................................................................... ....47 2-9 Block diagram of the CW magneto op tical experiment setup at the NHMFL..................48 2-10 Schematic diagram of modified magneto opt ical cryostat for direct ultrafast optics........49 2-11 Technical drawing of the 17 Tesla superconducting magnet SC M3 in cell 3 at NHMFL.......................................................................................................................... ....50 2-12 Technical drawing of the special opti cal probe designed for superconducting magnet 3 in cell 3 at the NHMFL...................................................................................................51 2-13 Schematic diagram of Coherent Mi ra 900F femtosecond laser oscillator.........................52 2-14 Schematic diagram of Coherent Le gendF chirped pulse amplifier (CPA)......................53 2-15 Top view scheme of layout of the optical elements and beam path in TOPAS OPA........54 2-16 Operation principle of a streak camera..............................................................................55 2-17 Block diagram of ultrafast optics expe rimental setup in cell 3 and 5 at NHMFL.............56 3-1 Band structure of Zinc blend semiconductors...................................................................72 3-2 Band structure of wurzite structure semiconductors..........................................................73

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10 3-3 Schematic diagrams of band alignment and confinement subbands in type I semiconductor quantum well.............................................................................................74 3-4 Density of states in different dimensions...........................................................................75 3-5 Electronic energy states in a semic onductor quantum well in the presence of a magnetic field................................................................................................................. ....76 3-6 Calculation of free electron hole pair energy and magneto exciton energy of InxGa1xAs/GaAs QW as function of magnetic field.....................................................................77 4-1 Magneto abosorption spectrum and sche matic diagram of interband Landau level transitions.................................................................................................................... .......88 4-2 Magnetophotoluminescence experimental re sults of band gap change and effective mass change.................................................................................................................... ...89 4-3 Valence band mixing of heavy hole a nd light hole subbands in semiconductor quantum well................................................................................................................... ...90 4-4 Structure of In0.2Ga0.8As/GaAs multiple quantum well.....................................................91 4-5 Faraday configurati on in magnetic field............................................................................92 4-6 Energy levels of electron and hole quantum confinement states in InxGa1-xAs quantum wells.................................................................................................................. ..93 4-7 Magneto-photoluminescence spectrum of InxGa1-xAs quantum well at 10K....................94 4-8 Landau fan diagram of abso rption and PL spectrum of InxGa1-xAs quantum well in magnetic field up to 30 T...................................................................................................95 4-9 Magneto-PL and excitation density dependence of the integrated PL in InxGa1-xAs quantum wells at 20 T and 10 K........................................................................................96 4-10 Theoretical calculation and experimental results of PL in high magnetic field................97 5-1 Spontaneous emission and amplified spont aneous emission process of a two level atom system.................................................................................................................... .128 5-2 Four steps in the formation of collectiv e spontaneous emission--SF in N atom system.129 5-3 Schematic diagram of the configuration fo r collection of in plane PL from InGaAs multiple QW in high magnetic field................................................................................130 5-4 Experimental schematic showing the conf iguration for a single shot experiment on InxGa1-xAs QWs...............................................................................................................131

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11 5-6 Fitting method to determine line widths using a Lorentzian and Gaussian function for the sharp peak and broader lower-energy peak................................................................133 5-7 Excitation power dependent PL spectrum and fitting results of in plane emission.........134 5-8 Excitation spot size effect on the in plane PL emission...................................................135 5-9 Single shot directionality measuremen t of in plane PL emission in SF regime..............136 5-10 Single shot directionality measurement of in plane PL emission in ASE regime...........137 5-11 Schematic diagram of the configuration of control of emissi on directionality in InxGa1-xAs multiple QW..................................................................................................138 5-12 Control of coherence of in plane PL emission in InxGa1-xAs QW...................................139 6-1 Top view of the lattice struct ure of a wurtzite ZnO crystal.............................................156 6-2 The orientation of light polarizati on with respect to the ZnO unit cell...........................157 6-3 Band structures and symmetry of each band of a ZnO semiconductor...........................158 6-4 Schematic of types of im purity bound exciton complexes..............................................159 6-5 Energy diagram of Zeeman splitting of neutral bound excitons in ZnO.........................160 6-6 Schematic diagram of Voigt configurat ion of c-plane ZnO in magnetic field................161 6-7 Reflection spectrum of a-plane bulk Zn O semiconductor for different linear optical polarization at 4.2K..........................................................................................................162 6-8 The magneto-PL spectrum of a and c -plane bulk ZnO sample and Zeeman splitting at 4.2K........................................................................................................................ ......163 6-9 Comparison of reflection and PL spectrum of c-plane bulk ZnO....................................164 6-10 Comparison of reflection and PL spect rum of c-plane epilayer ZnO at 4.2 K................165 6-11 Schematic diagram of the pump-probe e xperimental setup for measuring TRDR of ZnO semiconductors........................................................................................................166 6-12 TRDR plots of a-plane bulk ZnO se miconductor at 4.2K and exponential decay fitting line................................................................................................................... ......167 6-13 Fast decay in TRDR of A-X in a-plane bulk ZnO and the fitting with convolution of Gaussian function and exponential decay function.........................................................168 6-14 Temperature dependent TRDR of AX recombination in c-plane bulk ZnO..................169

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12 6-15 TRDR plots of excitonic recombination in ZnO epilayer for different exciton states.....170 6-16 Experimental TRDR plot of ZnO na norod sample at 10K and fitting result...................171 A-1 Detailed schematic diagram of sample mount and PL collection used in the experiment..................................................................................................................... ...178

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13 LIST OF ABBREVIATIONS BEC Bound exciton complex CCD Charged coupled device CPA Chirped pulse amplifier CW Continuous wave DOS Density of states LL Landau level MQW Multiple quantum well NHMFL National High Magne tic Field Laboratory OPA Optical parametric amplifier PL Photoluminescence PMT Photomultiplier tube SCM Superconducting magnet SF Superfluorescence TRDR Time resolved differential reflectivity X Exciton

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14 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy ULTRAFAST OPTICAL SPECTROSCOPIC STUDY OF SEMICONDUCTORS IN HIGH MAGNETIC FIELDS By Xiaoming Wang May 2008 Chair: David H. Reitze Major: Physics We studied the magneto-excitonic states of tw o-dimensional (2D) electron and hole gas in InxGa1-xAs/GaAs multiple quantum wells (MQW) with continuous wave (CW) optical spectroscopic methods, including transmissi on and photoluminescence spectroscopy, in high magnetic field up to 30 Tesla. Interband Landau level ( LL ) transitions are clearly identified. The anticrossing behavior in the La ndau fan diagram of the transmission spectrum is interpreted as dark and bright exciton mixing due to Coulomb in teraction. With the unique facility of ultrafast optics at National High Magnetic Fi eld Laboratory, we are able to change the 2D electron hole gas into 0D and increase density of each quantum state as well as the actual sheet carrier density in the quantum well (up to 1012cm-2) dramatically. Under these c onditions, interactions between electron and hole pairs confined in 0D system pl ay a very important role in the electron hole recombination process. With high power pulsed la sers and cryogenic equipment, we studied the strong magneto photoluminescence emission from InxGa1-xAs/GaAs MQW in high magnetic field. By analyzing the power de pendent, field dependent and dire ction dependent PL spectrum, the abnormally strong PL emission from InxGa1-xAs/GaAs MQW in high magnetic field is found to be the result of cooperative recombination of high density magneto electron-hole plasmas.

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15 This abnormally strong photoluminescence from InxGa1-xAs/GaAs MQW in high magnetic field under CPA excitation is proved to be superfluorescence. We studied CW spectroscopic properties of Zn O semiconductors including reflectivity and photoluminescence at different crystal orientations A, B excitonic states in ZnO semiconductors are clearly identified. Also, with time resolved pump probe spect roscopy, we studied the carrier dynamics of excitonic states of A and B in bul k ZnO as well as ZnO epilayer and nanorods.

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16 CHAPTER 1 INTRODUCTION AND OVERVIEW During the past few decades, the trans port and optical prope rties of electron ( e ) hole ( h ) gas in two-dimensional (2D) semiconductor quant um well (QW) in magnetic field have been studied extensively in theory and experiments [1-5]. However most of the magneto-optical studies are based on continuous wave (CW) optics or low magnetic field. In this dissertation, we first investigate th e magneto-excitonic states of 2D electron and hole gas in InxGa1-xAs/GaAs multiple quantum wells (MQW ) with CW optical spectroscopic methods, including transmission and photolumin escence (PL) spectroscopy. With the unique facility that exists at National High Magne tic Field Laboratory ( 30 Tesla magnetic field combined with intense ultrashort pulse lasers), we are able to change the 2D electron hole gas into a quasi-0D system, and increase carrier density of states of each qua ntum state as well as actual sheet carrier density dramatically. Unde r these conditions, the excitonic effect is suppressed because the Coulomb in teraction between high-density e-h pairs is screened, while the interactions between e-h pairs confined in this quasi 0D system play a very important role in the recombination process. With high power pulsed lasers and cryogenic equipment, we studied the strong magnetoPL emission from InxGa1-xAs/GaAs MQW in high magnetic fiel ds. With analyzing the power dependent, field dependent and single shot di rection dependent PL spectrum, the abnormally strong PL emission is found to be result from a cooperative recombination process of high density magneto e-h plasmas, which is called superfluorescence (SF). The second part of this thesis focuses on th e CW and ultrafast opti cal spectroscopic study of ZnO semiconductors. Due to its unique band gap (~3.35 eV) and large exciton binding energy (~60mev) at room temperature [6-10], these are promising materials for optoelectronic

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17 applications, such as blue and ultraviolet emitters and detectors. By analyzing the CW spectra, the band structures, excitonic and impurity bound excitonic states are identified. By using pumpprobe spectroscopy, the dynamics of different ex citonic states are studied in bulk ZnO, ZnO epilayer and nanorods. 1.1 Semiconductors and Quantum Wells By using epitaxial growth such as molecular beam epitaxy (MBE) and metal organic chemical vapor deposition (MOCVD), modern science and technology have provided us the methods of manufacturing a ve ry thin epitaxial layer (~nm) of a semiconductor compound on another different semiconductor with interface of very high precision (atomic precision), thus allowing for quantum-engineered materials and structures. The optical properties of semiconductor QWs ha ve been extensively studied [11-15], and many physical phenomena have been investigated thoroughly, i.e. interband transitions, intersubband transitions. Figure1-1 shows physical and band structur e of III-V or II-V I group semiconductor multiple quantum wells, composed of periods of ABAB, A and B are two layers of different type of semiconductor compounds, i.e. InXGa1-xAs and GaAs. The bandgap of compound B (the well) lies within the bandgap of the compound A (the barrier). Th e thickness of barrier A is typically greater than 10 nm, so th at carriers will be confined in the QW layers. This particularly unique property of semiconductor heterojunction s provides us an ideal system for studying the interesting physics and applicati on of device in two dimensional electron gas system--carriers in QWs are confined in the z direction, the growth direction of QW, and still move freely in the quantum well plane, or x-y direction. The interface betw een barrier and well imposes confinement on carriers in QWs, which results in the formation of discrete quantum states in both conduction and valence band. In a semiconductor, if an electron in valence band is excited

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18 to conduction band as a free electron, a hole will be left in valence band. Through the Coulomb interaction, this electron hole pa ir can form a hydrogen atom (H) like quasi-atom system: an exciton (X). In a semiconductor QWs, due to the spatial confinement and discrete quantum state confinement, excitonic effects are more pr onounced than semiconductor bulks [16-20]. These discrete excitonic states of exciton provide a unique system to study quantum optical processes of carriers in semiconductor quantum wells. 1.2 Magneto-Spectroscopy in High Magnetic Fields In the presence of a high magne tic field, the cyclotron energyc of a charge carrier is greater than the ex citon binding energy Eb (for GaAs, c =4 Eb above 20T). Thus, we open a new regime to study semiconductor magneto-optics, where the magnetic field effect due to the formation of Landau levels ( LL s) will suppress the exciton effe ct. Also, in high magnetic field, electrons and holes populate on LL s, which provide us a system to study the mid infrared light driven intraband LL transitions. Many new physical processes can be explored in semiconductor quantum wells at high magnetic fields [21-25]. Another impact that applied high magnetic fields have on a semiconductor QW is an alteration of the carrier confinement. Free carrier s are confined in QW plane since the magnetic length lB is on the order of a few nm. At high magne tic fields, the density of states (DOS) of a two dimensional electron gas system will evolve into a zero dimensional system, like a quantum dot; the separation between LL s varies with the intensity of ma gnetic field. Magneto-excitons (or magneto-plasmas) confined in quasi-nanorods in semiconductor QWs at high magnetic field provides us with an atomic-like system with tunable internal energy levels to study quantum optics in solids.

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19 In early studies of magnetooptics in semiconductor quantum wells, light sources used in the experiments were usually continuous wave (C W) white light or CW lasers (see Chapter.2.5 for detail), which provided static spectroscopic information only. In the past twenty years, with the development of ultrafast laser te chnology and magnet technology, time resolved spectroscopic studies of magneto optical experime nts like time resolved Kerr rotation or time resolved Faraday rotation can be carried ou t in a split coil supe rconducting magnet [26-30]. However, time resolved dynamics of magneto-excitons populate on LLs in semiconductor QW has been carried out at fields less than 12 T [3133] and not yet been realized at higher magnetic fields. Furthermore, in high magnetic fields, sh eet carrier density in QW can also increased dramatically due to the 0D like DOS at each LL If the excitation power of the pulsed laser is very large, i.e., as that achievable with amplified ultafast laser systems (CPA) as the excitation light source, we can create a carrier density in excess of 1013/cm-2 in the QWs. In this case, the eh response in the QW will be dominated by plasma -like instead of exciton-like behavior. These high-density magneto-plasmas confined in QWs in teract with each other and correlate to each other before they start to recombine. This leads to many new and ex citing physical phenomena, as we discussed later. 1.3 Motivation for Performing Ultrafast Sp ectroscopy in High Magnetic Fields 1.3.1 Quantum Optical Pro cesses in Semiconductors--Superfluorescence In high magnetic field, e-h pairs are confined in a quasi 0D structure. Therefore, we can use this atom like system to study quantum optics in electron hole pair in hi gh magnetic field, i.e. strong electromagnetic field induced energy sp litting--AC Stark Effect [34] and cooperative recombination process--Superfluorescence [35]. In an atomic ensemble, if the atoms are in excited state, they will relax down to ground state through emission of photons. This process is called spontaneous emission if there is no

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20 interaction between atoms duri ng the emission. In the case wher e the decoheren ce time of the atom is significantly greater than the spontaneous emission time, due to the interaction between atoms, the atomic ensemble can evolve into to a coherent state and emit a burst of photons through a cooperative radiative process called superfluorescence. Th is type of emission, characterized by its short pulse width and high in tensity compared to spontaneous emission, has been observed in rarefied gas systems [36], however due to very short carrier decoherent time in solid, superflorencence has not been observed so far. 1.3.2 Studies of Technologically Interesting Materials In order to study quantum optics in semiconduc tor QW in high magnetic field, the intrinsic properties of semiconductor material are very crucial to observe quantum processes. These properties include band structure, electron and hole effective masse s, QW structure, and barrier and well compositions. Among all the III-V group and II-VI group semiconductor materials, III-V group compounds such as InxGa1-xAs/GaAs, InxGa1-xAs /InP, InxGa1-xAs /AlGaAs and GaAs/AlGaAs QW series are the best materials to study quantum optical phenomena of e-h pairs in semiconductor QWs. These materials have been thoroughly studi ed using magneto-optical spectroscopy and their band structures are well know n [37, 38]. First, their band ga ps energy are in the near infrared region, which is very suitable for exci tation with Ti: Sapphire ultrafast lasers; second, the electron subband and valence hole subband ar e separated reasonably well which cause less band complexity; third, the electron and hole eff ective mass in these materials are relatively small and the exciton binding energy are relativ ely large (~10 meV), which make it easy to observed higher LL s in high magnetic field. Some band stru cture constants of some III-V group semiconductors are listed in Table 1-1.

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21 In this dissertation, we selected InxGa1-xAs/GaAs MQW for the host material for 2D e-h gas. The behaviors of high density e-h pairs under high power excitation in high magnetic field are the main result in this dissertation.

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22 Table 1-1. Some band parameters for some III-V compound semiconductors and their alloys. Parameters GaAs InAs InP ac() 5.6516.0515.871 E g(mev) 15191417114231Ex g (mev) 198111443114801so(mev) 341139011081m*e( ) 0.06710.02610.07951m*e(X) 1.910.6410.0771m*hh(me) 0.4510.4110.641m*lh(me) 0.08210.0261 1 Reference [37] ac is the crystal lattice co nstant in c direction. E g and Ex g are the bandgaps at and X point. so is the spin orbit interaction, m*e( ) and m*e(X) are the electron effective mass at and x point. m*hh and m*lh are the effective mass of heavy hole and light hole.

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23 (a) (b) Figure 1-1. Physical and energy structure of se miconductor multiple quantum well.(a) Physical structure type I semiconductor multiple quantum well, (b) Energy structure of type I semiconductor multiple quantum well

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24 CHAPTER 2 HIGH FIELD MAGNETO-OPTICAL TEC HNIQUES AND FUNDAMENTALS OF MAGNETO-OPTICAL SPECTROSCOPY 2.1 Introduction In this chapter, we introduce the ba sics on optical res ponse theory, including optical complex dielectric constant and refractive index n We then give a background in the techniques used to study optical pr operties of semiconductors, discussed the experimental techniques of CW meas urements on semiconductors, including transmission, reflection and photoluminescence spectroscopy. To understand the carrier dynamics in se miconductors, pump-probe spectroscopy is employed. By understanding the how the dielectric constant and refractive index n change with carrier density N we can study the time resolved differential transmission and reflection spectroscopy. In addition, a detailed descri ption is provided for the existing CW spectroscopic experimental setup at the NHM FL that will be used for our measurements. Finally and most importantly, to extend our research re gime in high magnetic fields and ultrafast lasers, we have developed an ultrafast f acility at the NHMFL to study the ultrafast magneto optical phenomena in high magnetic fiel d. In this chapter, we give and overview of the ultrafast facility and describe the technical details. 2.2 Basic Background of Optical Response of Solids In a solid state system, including semiconduc tors, the optical response such as light transmission and reflection is determin ed by the complex dielectric constant Coupled with an underlying model for the physics that relates to the dielectric function, the knowledge of the dielectric function over a give n spectral range completely specifies the optical behavior of the mate rial. In Drudes model [39], is given by [40]

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25 1 4 ) ( ) ( ) (2 2 2 i m Ne ie, 2-1 where N is the electron density, e is the electron charge, me is mass of electron, is a phenomenological relaxation time constant corresponding to the mean time between carrier and ion collisions, and is dielectric constant at high frequency ( ). The refractive index n is [40] 2 2" 2 1 ) ( n, 2-2 And the intensity absorption coefficient is [40] ) ( cn 2-3 where is also the absorption coeffici ent in Beer Lamberts law [40] z I z I exp0. 2-4 The expression for optical reflection is given by 2 2 1 2 2 1 2) ( n n n n R 2-5 where n1 and n2 are the refractive index on both sides of a solid and the incident beam light is perpendicular to the solid surface. In the low frequency of optical frequency regime, corresponding to the infrared part of spectrum where1 we have [40] em ne i24 ) ( ) ( 2-6 and 2 1 n, 2-7

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26 for the index of refraction and 2 c 2-8 for the absorption coefficient. In high optical frequency regime where1 corresponding to ul traviolet part of spectrum, we have [40] 2 21 p, 2-9 where e pm Ne 2 24 is plasma frequency. For p we have [40] n 2-10 The relation between dielectric constant and optical susceptibility is [40] 4 1 2-11 is a complex parameter, given as i 2-12 Since the dielectric function and optical susceptibility have both real and imaginary components, both of them will contribute the optical response such as the transmission T and reflection R. Theref ore, the optical resonant frequencies correspondent to ( ) are not necessarily directly rela ted to absorption peaks or dips on the transmission and reflection spectrum. However, KramersKronig transformations [40] allow us to determine the real part of optical response function from the imaginary part at

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27 all frequency and vice versa, so that we are able to figure out the frequency of optical resonance in the spectra. The real part and imaginary part of optical susceptibility are related by [40] 0 2 2 0 2 2' Pr 2 Pr 2 d d, 2-13 and 0 0 2 2 2 2 0 2 2' ' lim Pr d d d, 2-14 where Pr refers to the principal part of the complex integral. 2.3 Magneto-spectroscopy of Semiconductors--Methods In magneto-spectroscopic studies of semiconductors, many experimental techniques have been developed. These sp ectroscopic methods include transmission and reflection spectroscopy, photoluminescence (PL) and photoluminescence excitation (PLE) spectroscopy, and optical detected re sonance spectroscopy (ODR). Here, we will restrict our discussion to th e methods that have been applied in this dissertation. 2.3.1 Transmission Spectroscopy Transmission spectroscopy [40-44] is very useful tool in the study of electronic states in quantum well (discussed later in Ch apter 3, 3.6). The firs t investigations of GaAs/AlGaAs quantum wells used this me thod. From Eq. 2-3, we can see that ( ) is related only with so that we can find the resonant frequency directly from transmission spectrum. In transmission spectroscopy, a white light beam is incident on the semiconductor sample, which is usually placed in a cryostat, and the transmitted white light is collected and sent to a spectromete r. The spectrum will be resolved with the

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28 spectrometer and the intensity of each wavelength is detected by either a CCD array or a photomultiplier. Using the CW optical setup at NHMFL, a typical transmission spectrum of GaAs/AlGaAs multiple quantum well in high magnetic field 30 Tesla and 4.2K is shown in Fig. 2-1. In this figure, we can clearly resolve several quantum states, which will be interpreted in detail in Chapter 4. The dips in spectrum correspond to specific interband transitions, which are the positions of excitonic states (see section 4.4). Using transmission spectroscopy, we can directly mark the energy positions of Gaussian shape absorption dips as excitonic states on the spectrum. However, care should be taken for the band gap of substrate and barrier material s that they are high enough from the well material band gap to avoid overwhelmed by the continuum states of the barrier and substrate materials. 2.3.2 Reflection Spectroscopy Reflection spectroscopy is also an importa nt method to study the optical properties of semiconductor materials [45-48]. In refl ection spectroscopy a white light beam is incident on a sample and the reflected light is collected and sent to a spectrometer for frequency resolution. Compared with transmission spectrosco py, this method offers a few advantages. It has a good signa l noise ratio and not affected by the substrate materials unless the optical depth of quantum well is large, and it is a good method to study the above band gap excitonic feat ures in semiconductors posse ssing very high absorption coefficient, since in transmission spectrum these features will be overwhelmed by the high absorption coefficient. Reflection spectro scopy has a significant disadvantage: the refractive index n shown in Eq. 2-2 has both and which have different contributions to reflection so that the loca tion of resonant electronic stat e position is not completely straightforward and further analysis is needed Fig. 2-2 is a reflec tion spectrum of a 400

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29 nm thick ZnO eplilayer at 4.2 K, the energy pos itions of electronic states are not clearly resolved However, for a very good approximation, we can identify the states at the arrow points shown on the figure as the en ergy positions of electronic states. 2.3.3 Photoluminescence (PL) Spectroscopy PL spectroscopy is also very important method to study excite states in semiconductors [49-53]. In transmission and reflection spectroscopy, information about the optical absorption processes is obtained. They cannot be used to provide information about the photon emission process. In PL spectroscopy, electrons in valence band are excited with photons whose energy is higher than the band gap of semiconductor sample, followed by relaxation down to the bottom of conduction band. This leads to recombination with holes on the top of va lence band, which undergo a similar energy relaxation, simultaneously producing a photon, which has the energy of the transition (See Fig. 2-3(a)). From the photon emission, we can use PL spectroscopy to understand the excited states in conduction and valen ce bands. Fig. 2-3(b) shows a typical PL spectrum measured with the ultrafast magneto -optical setup at NHMFL, we can observe clearly PL peaks in the spectrum. The detaile d physics of this spectrum will be discussed in Chapter 3, 4 and 5. 2.4 Time-resolved Spectroscopy of Semiconductors The CW optical spectroscopic techniques de scribed above provide a wide range of methods to study the optical properties of photoexcited carriers in semiconductors. However, these methods provide the informati on of static states in semiconductors only. In order to understand the dyna mical processes of photoexcited carriers, time resolved spectroscopic techniques need to be employe d. Since the 1970s, extensive studies of

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30 time resolved carrier dynamics in semiconducto r have been reported [54-58], which have opened a new research area for semiconductor optics. The most common time resolved spectros copic method used to investigate the carrier dynamics in semiconductors are pump-probe spectroscopy and time-resolved photoluminescence spectroscopy. In Fig. 2-4, a basic illustration of dege nerate (equal wavelength) ultrafast pump probe experiment is shown in transmission geometry. The laser pulses (in our case of duration ~100 fs) are split into two pulses ca lled the pump pulse and probe pulse, and pump pulse is much stronger than probe pul se. The pump and probe pulses are spatially overlapped on the sample with an optical focu sing lens. Pump pulses are absorbed by the sample and excite carriers, which change th e optical properties such as refractive index n (See equation 2-1, 2-2). Af ter a controlled time delay t the probe pulse reaches the sample, the transmission of this probe pulse wi ll be recorded. By changing the time delay t between pump and probe, we can record the intensity of tr ansmission of probe pulse at different time delays. The absorption coefficient ( ) is time dependent, it changes after pump pulses excitation and will go back to orig inal value. Therefore, the transmission of probe light also manifests the dependency on time delay t, because the relationship between T and ( ) is ) exp(0L I I T 2-15 Generally speaking, in optical pump-probe sp ectroscopy, the pump pulse excites certain optical process in a sample and the probe is us ed to map out the dynamics of this process.

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31 A typical pump-probe spectroscopy experimental setup is shown in Fig. 2-5. In this spectrum resolved pump-probe setup, either th e transmission or reflection of the probe is sent to a spectrometer before it reaches the PMT (Photo Multiplier Tube), so that change of probe light at different wavelength can be resolved and detected. The intensity of reflection or transmission of probe beam will be recorded at different time delay between pump and probe pulse by changing the re lative optical path of pump beam. The spectrometer is used to select specific wavelengths to probe. In many cases, the change of probe induced by pump pulses is normalized to see the magnitude of the effect. These tec hniques are called differential transmission spectroscopy (DTS) or different reflection spectroscopy (DRS), and the signals are given by 0 0 0 0 0 0R R R R R T T T T T 2-16 For DTS, because of Eq. 2-15, we have L L T T) ( 1 ) ) ( exp(0 2-17 However, for the DRS, the expression is quiet complicated because R is associated with both real and imaginary part of dielectric c onstant (see Eqs.. 2-1, 2-2 and 2-5). Thus, by measuring the time resolved DTS and DRS, we can infer the carrier dynamics in semiconductors. Fig. 2-5(b) shows a typica l degenerate time-resolved differential transmission (TRDR) spectru m of ZnO epilayer at 4.2K.

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32 Time-resolved differential transmission (T RDT) and reflection (TRDR) provide an indirect method to study th e carrier dynamics with ve ry good time resolution (~100 fs and shorter). However the mechanism of ca rrier recombination processes can not be inferred, i.e. the radiative and nonradiative carrier recombination processes cannot be distinguished from a pump-probe spectrosc opy since both of them will contribute to carrier recombination. To solve this probl em, alternative techniques are required to perform time-resolved study of the radi ative processes. In time-resolved photoluminescence, PL emitted from sample is sent to a streak camera, with which temporal information of PL emission is acqui red. The resolution of this method (~ps) is not as high as pump-probe spectroscopy. Th e combination of pump-probe spectroscopy and time resolved PL spectroscopy will give us a thorough understanding of photoexcited carrier dynamics in semiconductors. Fig. 2-6 shows a TRPL spectrum measured from InxGa1-xAs/AlGaAs MQW at 4.2K taken using a Hamamatsu streak camera. These time-resolved figures are typical data we use in this thesis and the deta iled physics will be discussed in the following chapters. 2.5 CW Optical Experimental Capabilities at the NHMFL Since the construction of the DC magnetic field facility at the National High Magnetic Field Laboratory (NHMFL), there has been high demand for research in magneto-optics, and many research projects have been accomplished with the welldeveloped CW magneto-optical techniques that have been established [59-68]. In this dissertation, many experiments were carried out to characterize InxGa1-xAs/GaAs MQW sample by using the CW magneto optical setup at NHMFL in Tallahassee.

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33 In order to reach high magnetic fields, we used a 31 Tesla resistive magnet in cell 5 at NHMFL. Fig.2-7 shows the schematic diagram of this magnet. This magnet is a resistive magnet consists of a few hundreds of thin copper disks (Bi tter disks). The Bitter disks are connected electronically and electric current can fl ow through Bitter disks in a spiral pattern. In Fig.2-7, we can see that th ere are four coils of Bitter disks in the magnet housing. There are huge flows of electric curr ent (~37KA) in the magnet coils when they are in operation at full field, at the same time, cold water flows continuously through holes punched on the Bitter disks to remove the huge amount of heat (~MW) generated by the electric current. In many magneto-optical experiments, lo w temperatures are usually required to measure transmission, reflection and photol uminescence. Specially designed cryostats and probes have been designed to work at li quid helium temperatures with these resistive magnets with bore size around 50mm. The techni cal drawing of a cryostat and probes are given in Fig. 2-8. This cryostat has a long ta il, so that the probe/sample can reach the position of highest magnetic field. In this cr yostat, liquid helium is stored in the center space and enclosed by liquid nitrogen or ni trogen shield and vacuum jacket, which significantly reduce heat leaking in to the helium reservoir. In Fig 2-8, an optical probe is inserted into the liquid helium reservoir of this cryostat, and the sample inside the probe is cooled down by back filling low-pressure helium exchange gas into probe. Light is delivered to the sample through an optical fibe r, and temperature of sample is measured with a Cernox temperature sensor and cont rolled with a heater mounted on sample mount.

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34 In Fig. 2-9, the layout of a typical CW magneto-optical experiment setup at NHMFL is shown in a block diagram. An optical probe is inserted in the cryostat, which is positioned on the top of a Bitter magnet. A Lakeshore temperature controller controls the temperature of the sample via a sensor and heater co-located next to sample. The input light and output signal light are deliver ed to sample and spectrometer respectively through two optical fibers. In the case of transmission, reflection measurements, CW white light sources (Tungsten or Xenon lamp s) are used for input illumination while lasers (He-Ne, He-Cd, Argon and Ti:Sapphire) are used as input excitation light for photoluminescence (PL) experiments. The transm ission, reflection and PL signal light are collected with the output optical fiber mounted next to the sample and analyzed by a 0.75 m single-grating spectrometer (McPherson, Model 2075) equipped with single channel photon counting electronics PMT as well as a multi-channel CCD de tector. All of the control units in this setup, including magnet controller, temperature controller, spectrometer controller, PMT and CCD controller are managed by an Apple computer through GPIB interfaces. 2.6 Development of Ultrafast Magnet o-optical Spectroscopy at NHMFL 2.6.1 Introduction of Ultrafast Optics With the existing CW magneto optical se tup at NHMFL, many experiments have been done successfully. However, there is still a drawback of this experimental setup time-resolved magneto-optical information can not be acquired due to large stretch effect of multimode optical fibers, which expand the pulse width of ultrafast laser pulse dramatically (from ~100fs to ~20ps) and result s in a significant loss of time resolution. In order to obtain time-resolved magneto-sp ectroscopy in high magnetic fields, a new

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35 facility needs to be developed, which incl udes a new magnet, cryostat, probe as well as new ultrafast light sources and detection methods. 2.6.2 Magnet and Cryogenics for Ultrafast Optics at NHMFL Note that in a standard pump-probe e xperiment, while the ex citation (pump) and probe pulses must be delivered to the sample through free space to preserve the temporal resolution, the collection of the light from the sample can be accomplished using standard fibers. To preserve the temporal duration of a fe mtosecond laser pulse be fore it reaches the sample, direct optical propagation in free space is required. We also needed to modify current cryostat so that it can be used on resistive magnet for ultrafast magneto optical experiments. A technical drawi ng of modified optical cryostat is shown in Fig. 2-10. We mount an optical window on the bottom of outer tail of the cryostat, open the bottom of nitrogen shield, weld a copper sample mount right on the bottom of helium tail so that samples can be cooled down with a cold sa mple mount. For the coll ection of light after excitation of the sample, optical fibers positi oned right on the top of sample are used to deliver transmission or PL to spectrometer or detector. With this configuration, the ultrafast laser pulse can r each the sample directly th rough resistive magnet bore and optical window, while the sample can still be as cold as 10K (for more details see appendix A). In addition to resistive magnet, a supe rconducting magnet was al so developed and commissioned by us to carry out magneto-optical experiments, especially for the ultrafast magneto-optics laboratory. We redesigned th e cryostat for a 17 Tesla superconducting magnet such that femtosecond laser pulses can be steered into the center magnet bore and

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36 excite sample directly at field center. Fig 2-11 shows the section view of this superconducting magnet. There is a stainless steel center bore welded on the cryostat and going through the center of magnet. This bore isolates the sample chamber and helium reservoir, which make it possible to do dire ct optics with this superconducting magnet. The cold stainless steel bore is sealed with an opti cal window on the bottom and a specially designed probe loading system on the top, shown in Fig. 2-12. With this probe loading system, we can change sample w ithout causing air leak into the center bore merged in liquid helium. The sample on pr obe is cooled down with backfilling lowpressure helium exchange gas in the center bore. 2.6.3 Ultrafast Light Sources In addition to the development of cryoge nics and magnet system, we also set up several femtosecond pulse laser systems for time resolved magneto-spectroscopy. These ultrafast laser systems incl ude a Ti:Sapphire femtosecond oscillator, a Ti: Sapphire chirped pulse amplifier (CPA) and an optical parametric amplifier (OPA). 2.6.3.1 Ti:Sapphire femtosecond oscillator Fig. 2-13 shows the schematic diagram of Coherent Mira 900 F femtosecond laser system. In this laser system, a prism pair compensates dispersion caused by broad bandwidth of laser emission. This passive mode locking ultrafast oscillator laser acquires self-mode locking with Kerr Lens effect, and th e shaker in the cavity works as a trigger to initiate the mode locking. The pulse width of this ultrafast laser oscillator is around 150fs and the energy per laser pulse is around 4nJ. Th is laser is tunable fr om 700 to 900 nm and runs at 76MHz repetition rate. We use this ultrafast laser to get second harmonic

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37 generation from BBO nonlinear crystal and ca rry out degenerate pump probe experiments on ZnO semiconductors as de scribed in Chapter 6. 2.6.3.2 Chirped pulse amplifier In many optical experiments, strong ultraf ast laser pulses (up to mJ per pulse) are needed for either nonlinear effect like self phase modulation (white light generation) and parametric amplification or for high carrier density generation in samples. Most of our experiments were done with the Clark-MXR 2001 CPA. Howeve r, because of reliability problems the Clark MXR laser was later replac ed by the Coherent la ser in early 2007. The current Coherent Legend-F chirped pulse amplifier (CPA) is set up in cell 3 at DC facility for research in ultrafast magne to optics. Fig. 2-14 shows the schematic diagram of this CPA femtosecond laser system This CPA itself consists of three basic components: a pulse stretcher, a regenerati ve amplifier cavity, and a pulse compressor (see Fig.2-14). There are two external lasers for this CPA system, a Coherent Vitesse oscillator (similar to the Mira described a bove), which generates a high repetition rate ultrafast seed pulse train for amplification and an Evolution, which is a Q switch laser used to pump Ti:Sapphire crystal inside regene rative amplifier cavity at a variable (but typically 1 kHz) repetition rate with a 10mJ pulse. This CPA system functions in the following manner. First, a 150 fs seed pulse tr ain is generated in Vitessee laser and sent into pulse stretcher. This seed pulse is stre tched to approximately 100 ps, so that it will not destroy the Ti:Sapphire crystal in regencavity as it get amplified. A Pockel cell (PC1 in Fig. 2-14) then picks off one pulse from the train within the regenerative amplifier cavity for amplification. The pulse undergoe s several roundtrips wi thin the cavity and through the Ti:Sapphire crysta l which is prepumped with the Evolution laser and

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38 experiences a total gain of approximately 106. Once the amplification of seed pulse reaches its maximum (around 2 mJ per pulse), it is switched out of the regencavity by a second Pockel cell (PC2 in Fi g. 2-14) within the cavity. Finally, the amplified pulse propagates through a grating compressor (see Fi g.2-14) to compress the pulsewidth back down to 150fs. At the output, we obtain 150fs laser pulses at a 1 kH z repetition rate and 2 mJ per pulse from this CPA system. As we di scuss in Chapter 5, this laser is used to study PL from high density of carriers in InxGa1-xAs/GaAs MQW in high magnetic field. 2.6.3.3 Optical parametric amplifier The Ti:Sapphire oscillator and CPA lase r can provide us with ultrafast pulse, however, their wavelength ranges are limited. Therefore, an optical parametric amplifier (OPA) is required to conver t light to different wavelengt hs while preserving the short duration of the pulses. Fig.2-15 shows the la yout of a Quantronix OPA laser. This is a five pass system in total. The first three pa sses of the pulse occur through a beta barium borate (BBO) nonlinear optical crystal for fr equency conversion, and a signal pulse (at frequency signal) and idler pulse (at frequency idler) are generated. In the forth and fifth passes through the BBO crystal, signal and idler pulse are parametrically amplified with a fraction of CPA pulse. The relation between f undamental CPA, signal and idler pulse is given by Idler signal CPA 2-17 After parametric amplification by CPA pulse, the signal and idler pulses are then used to generated ultrafast pulses at different wavelength through second harmonic generation (SHG), =2signal or 2idler, fourth harmonic generation (FHG), =4signal or 4idler, and different frequency mixing (DFG),

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39 Idler signal CPA 2-18 The five nonlinearly optical processes men tioned above cover wavelength range from 300 nm to 20 m. 2.6.3.4 Streak camera In many cases, time-resolved photoluminescence is a very important method to study the carrier dynamics since it provides a direct measurement of the radiative emission of photons as carriers recombine in semiconductors. A picosecond streak camera is the proper device to measure time resolved photoluminescence. Fig. 2-16 shows the operation principle of a streak camera. We are currently setting up a Hamamatsu Streak Camera at the NHMFL ultraf ast facility. In Fig.2-11 we can see that conceptually, a PL pulse generated after excitati on of a sample is steered into the slit and then focused on a photocathode, where it is conv erted into an electr on pulse of the same duration. The electron pulse is then accelerated and passe s through a very fast sweep electrode, which is synchronized with the PL pul se, so that electrons at slightly different time will be deflected at different angle by the AC high voltage and hit the CCD at different position. Using this method, the tem poral profile of a PL pulse is spatially mapped on CCD in a spatial prof ile. By placing a spectromete r at the front end of the streak camera, the PL can be spect rally and temporally resolved.

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40 13001350140014501500 e1hh2se2HH21se1lh1se1hh1sTransmission(a.u.)Energy (mev) Figure 2-1. Transmission spectrum of InGaAs/GaAs MQW at 30 T and 4.2 K.The energy position of each dip on transm ission curve is correspondent to a magneto exciton state. Magneto-excitonic states are labeled according to the convention presented in Chapter 3.

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41 3.353.403.45 reflectance (a.u.)Energy(ev) CX BX AX Figure 2-2. Reflection spect rum of ZnO epilayer at 4.2K.Excitonic states and their symmetry are labeled. In the reflection spectrum, the approximate position of an excitonic state is marked with an arrow, which is the middle point between a dip and the peak next to it on the low energy side. on the reflectance curve. This spectrum will be discussed further in Chapter 5.

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42 (a) (b) Figure 2-3. e-h recombination proc ess and photoluminescence spectrum in semiconductors. (a) Illustration of Photon induced photoluminescence in a direct bandgap semiconductor, (b) PL of InGaAs/GaAs MQW in high magnetic field 30Tesla excited with an intense femtosecond laser pulse.

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43 Sample pump pulse p r o b e p u l s e t t + t P r o b e T r a n s m i s s i o n P r o b e R e f l e c t i o n Figure 2-4. Simple illustration of optical pump-probe transient absorption or reflection experiment.Both pump and probe ar e from pulsed laser and spatially overlapped on the sample. The time delay between pump and probe is t. Either the transmission or reflection of probe light is detected. By changing the delay between pump and probe puls e, time resolved transmission or reflection spectrum can be obtained.

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44 Spectrometer PMT Probe Pump LOCK IN AMPLIFIER Chopper control Computer GPIB Delay state control f1-f2 Cryostat Sample (a) -50050100150200250 -0.05 -0.04 -0.03 -0.02 -0.01 0.00 Normalized /R/RTime Delay (ps) (b) Figure 2-5. Experimental setup for op tical pump-probe spectroscopy and TRDR spectrum of ZnO. (a) Pump probe experi mental setup for spectrum resolved time differential reflectivity. Pump a nd probe are modulated with frequency f1 and f2 respectively, a lock-in amplified is used to acquire the transient reflection signal; (b) Time resolved di fferential reflectivity of ZnO epilayer at 4.2K. Details will be discussed in Chapter 6.

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45 -2000200400600800 0 100 200 300 400 500 PL intensity (a.u.)Time Delay (ps) Figure 2-6. Time resolved photoluminescence spectrum of InxGa1-xAs/AlGaAs MQW at 4.2K taken with a Hamamatsu Streak camera. Time resolution is around 5ps.

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46 Figure 2-7. Technical drawing of the 30 Tesla resistive magnet in cell 5 at NHMFL. From National High Magnetic Field La boratory, www.magnet. fsu.edu, side view of 31T / 32mm Resistive Magnet with Gradient Coil (Cell 5), date last accessed September, 2007 magnet bore magnet housing Bitter disks

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47 vacuum jacket liquid nitrogen liquid helium nitrogen shield optical probe sample Cernox sensor and heater optical fibers electric wires rotator Figure 2-8. Cryostat and op tical probe for CW optical spectroscopy at NHMFL.The cryostat has vacuum jacket and liquid nitrogen space for thermal isolation. An optical probe is inserted in the liquid helium (LHe) of the cryostat, sample on the end of the probe is cool ed down with He exchange gas, the input light and output light are deliv ered through multimode optical fibers.

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48 Input Light source Single grating spectrometer 0.75m McPherson CCD PMT Temperature Controller Cryocon 62 Magnet Control Apple Computer Spectrometer Controller CCD Controller A/D Converter GPIB Interface cryostat Resistive Magnet Optical Probe Figure 2-9. CW magneto optical experime nt setup at the NHMFL. Input light is delivered to sample in optical probe through fiber, the sample is mounted on an optical probe, positione d at the field center and cooled down with LHe, the output light from sample is sent to a spectrometer and the spectrum is recorded with CCD or PMT. The magnet control and spectrum acquisition from spectrometer is computer ized with GPIB interface.

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49 vacuum jacket liquid nitrogen liquid helium nitrogen shield optical probe sample optical fibers Bitter magnet Cernox sensor and heater CPA/OPA Figure 2-10. Modified magneto optical cryostat for direct ultrafast optics. The optical cryostat is positioned on the top of a resistive magnet and the sample is right at the field center A sample mount is att ached directly on the LHe tail of the cryostat, so that the sample can be cooled down. An optical window is mounted on the bottom of the outer tail of the cryostat, through which the ultrafast laser can reach the sample without being stretched significantly. The PL or probe light is delivered to detector and spectrometer through optical fiber.

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50 vacuum jacket LN2 space LN2 space LHe reservor superconducting manget center bore superconducting manget optical window mount KF flange connected to load lock KF flange optical window LHe reservor He relife valve N2 exhaust port N2 shield vacuum jacket to vacuum pump Figure 2-11. Technical draw ing of the 17 Tesla superconducting magnet SCM3 in cell 3 at NHMFL. Stainless steel tubing is used as the center bore of this magnet, an optical widow is mounted on the bo ttom of the tubing, samples on probe are positioned in the center tubing. Ultraf ast laser is steered in to the bore and excites samples without being stretched much. Pulsed laser

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51 cubic chamber for wires and fiber 9-pin connector for electric wires fit through cap for fiber fit through flange connector SS tubing 3/4" Load lock G-10 rod to mount wire SIP G-10 ring fiber cernox sensor sample double oring seal chamber pump out port A pump out port B sample mount To vacuum pump valve A valve B connect to KF 50 on top of center tubing Figure 2-12. Technical dr awing of the special op tical probe designed for superconducting magnet 3 in cell 3 at the NHMFL. A load lock system is attached on the top part of this probe, the vacuum in the center bore of the magnet is not broken when loading a nd removing the probe from the cold magnet bore. Temperature of the sample is controlled with a Cernox sensor and electric heater. Ultraf ast laser can reach the samp le directly and the PL or probe light from sample is delivered outside with fibers. Laser pulse

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52 From 5W Verdi laser BP1 BP2 M2 M7 Ti:Sapphire M5 M6 L1 BRF Starter M3 M1 150fs 76MHz, 4nJ Output Coupler M4 Figure 2-13. Coherent Mira 900F femtosecond laser oscillator. BP1and BP2 is a Bruster prism pair, M1 and M7 are cavity mirrors BRF is birefringe filter, M5 M7 are spherical mirrors, M2, M3 and M6 are mirrors, L1 is a lens.

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53 Figure 2-14. Coherent Legend F chirped puls e amplifier (CPA). PC is pockell cell, wp is waveplate. 150fs pulse, 1KHz, 2mJ 100ns Stretcher

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54 BBO Crystal CPA CPA CPA Signal +idler Grating Figure. 2-15. Top view of the optical el ements and beam path in TOPAS OPA.

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55 t1 t2 V Time varying high voltage t2 t1 Incident light pulses Photocathorde Electrons Streak Image Streak Image Time Figure 2-16. Operation princi ple of a streak camera. Th e photocathorde converts light pulse t1 and t2 in to two electron pulses, the two electron pulses have different positions for streak images because the high voltage bias is time varying.

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56 Bitter Magnet Vitess Legend CPA Evolution TOPASS OPA Cryostat Optical fiber Optical fiber Spetrometer PMT Box car averager Computer Delay stage Delay stage parascope CCD Dichro mirror Dichro mirror SCM3 Figure 2-17. Ultrafast optics experime ntal setup in cell 3 and 5 at NHMFL. SCM 3

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57 CHAPTER 3 ELECTRONIC STATES OF SEMICONDUCTOR QUANTUM WELL IN MAGNETIC FIELD 3.1 Introduction This chapter provides a background in the physics and optics of quantum confinement induced by structural modificat ions (quantum wells) and stro ng magnetic fields. Optical and electrical transport properties of semiconductor materials are determined by their electronic states. A background in the fundamental band th eory of semiconductors is necessary to understand the magneto optical spectroscopy, specifically, of InxGa1-xAs/GaAs multiple quantum wells, a typical III-V group semiconductor materi al, and ZnO (bulk, epilayer and nanorod), typical II-VI group semiconductor material. Band structures of Wurzite symmetry (C6v) ZnO and Zincblende symmetry (Td) InxGa1-xAs semiconductors are introduced. In semiconductor quantum wells, carriers are co nfined in the two dimensions defined by the barriers, and the electronic states have new ch aracteristics with respect to bulk materials due to quantum confinement. The exciton effect, energy states due to quantum confinement and selection rules of optical transitions in quant um well are given in detail in this chapter. In a high magnetic field oriented perpendicular to the plane of the quantum wells, further confinement is introduced to a semiconductor qu antum well, and the basic theory of magneto optical process of semiconductor quantum well is given to understand the optical processes related with interband Landau level transitions. Also, the density state of 3D, 2D and 1D systems are given in this chapter. 3.2 Band Structure of Wurzite and Zinc Blend Structure Bulk Semiconductors In a crystalline solid with N atoms, the electronic states of the N electrons make up continuous energy bands separate d by finite width band gaps. In a crystal, the electron

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58 wavefuction and periodic potential of this crystal remain unchanged under translational symmetry R (l, m, n), which can be described by the three primitive vectors: a, b and c as nc mb la n m l R ) (, l m n are integers. Because of the translational symmetry, the electronic wave functions in a crystal can be described w ith Bloch function [40] ) ( 1 ) ( r u e N rk r k i k 3-1 is the index of an electron energy band, k is a reciprocal lattice vector, N is the total number of primitive cell unit in the crystal and u is a periodic function inside a primitive cell and has translational symmetry ) ( ) ( r u R r u 3-2 In equation 3-1, the Bloch function is normalized over the whol e crystal and in Eq. 3-2, ) ( r ukis a function normalized over the volu me of a unit cell. The value of k is limited to the Wigner-Seitz cell in reciprocal space, which is called Brillouin Zone. Semiconductors are also a kind of solid crysta l, which has a finite band gap between the highest and fully occupied valence band and a lo west partially occupied (doped) or totally unoccupied (undoped) conduction band. The ba nd gap values and band structure of semiconductors, which determine many optical a nd transport properties, are very important parameters. The band gaps of semiconductors va ry from near infrared (InAs 0.43eV) to ultraviolet (ZnO 3.40eV). Among most of the III-V group semiconductors such as GaAs and InAs, the typical structure is zinc-blende, while for the II-VI group semiconductors like GaN and ZnO, the most common structure is the Wurzite structure. In semiconductors, the Hamiltonian of an electron can be de scribed as [71]:

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59 Crystal SH H r V m k H 0 2 2) ( 2 3-3 where k is the momentum of electron, m* is electron effective mass, V(r) is periodic potential in semiconductor crystal, Hso is the spin and orbit interaction, and Hcrystal is the interaction between electron and crystal field in an unit cell. Compar ed to the first two terms, the later two are relatively small and can be treated as perturbation. As the prototypical direct gap semiconductor, th e first Brillouin zone and band structure of GaAs (fcc structure) are given in Fig. 3-1 (a). (We will be working with In0.2Ga0.8As in this disseration, but the descriptions given for GaAs are applicable since GaAs and InAs have same crystal structure.) At the center of the Brillouin zone, the point is labeled as point (0, 0, 0). X (1, 0, 0) on ky axis, and L (1/2, 1/2, 1/2) are also the fundamental points. The calculated electronic band structure of bulk GaAs is shown in Fig. 3-1 (b). The conduction band in GaAs has absolute minimum value at the -point and two local minima at the L-point and X-point, which are referred as L valley and X valley. Th e conduction band of GaAs does not split since it is a s-like nondegenerate band, while the valence band split in to three bands: heavy-hole, lighthole and split-off bands since they are p -like three folds degenera te [71]. The degeneracy between split-off (J=1/2) and heavy-hole and lighthole (J=3/2) is lifted due to the interaction ( Hso) between electron spin (s=/ 2) and angular momentum ( l = for p-like electron). However, at the -point, the degeneracies of light-hol e and heavy-hole subbands are not lifted because of the high cubic symmetry ( Td point group) of the GaAs cell (Hcrystal=0). In a Wurzite structure semiconductor such as GaN and ZnO, the firs t Brillouin zone and bandstructure are quite different from the zinc-b lende structure. Fig 3-2 (a) and (b) present the first Brillouin zone and band structure of a zi nc-blende structure GaN semiconductor. At the point, the valence band of Wurzite structure semiconductors split into three subbands (heavy

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60 hole, light hole, and split-o ff) due to the hexagonal ( C6v point group) symmetry of GaN crystal cell, which gives an additional perturbation part of Hcrystal 0 and lifts the degeneracy. In the optical transitions in semiconductors, a ph oton is either absorbed or emitted. This is based on electron transitions between the top of valence band and bottom of conduction band. The selection rule for this optical transition is k = 0, which expresses the momentum conservation of crystal. Compared to the crys tal momentum, the momentum of photon is very small and can be neglected. For direct bandgap semiconductors such as GaAs and ZnO, the valence band absolute maximum and the conduction band absolute minimum occur at -point, the center of Brillouin zone, where interband and intr aband (inter-subband) transitio ns are observed without phonon emission. The optical transitions from other va lley (X or L valley) in conduction band to -point of the valence band must be accompanied by the emission of a phonon to conserve the crystal momentum. 3.3 Selection Rules In Kane model [72], since in all the II-VI and III-V group semiconductors the chemical bond are formed with outer shell electrons nsnp the wave functions of hybridized s -like band and p -like bands can be represented usi ng 8 band edge Bloch functions (u0, u1,, u8) |S ,|X ,|Y ,|Z and |S ,|X |Y |Z However, after the spin orbit interaction Hso is considered, a new linear combination of these f unctions can be formed. In the new functions, J=L+S and Jz are good quantum numbers and H can be diagonalized. The new Bloch functions basis set [71] is given in Table 3-1. They are taken as a basis set in a Kane model calculation [72].

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61 The optical transitions between conduction ba nd and valence band due to electro dipole transitions in semiconductor are describe d by the transition matrix element [71] r d p Mi f if^ 3-4 where ^is the optical polari zation unit vector and p is the electron momentum operator. Using the Bloch functions (Eq. 3-2), Mifcan be expressed approximately as [71]: Mupuffdruufpfdriffifififi ^^, 3-5 where ufand uiare the wave functions for the initial and final state(see Eq.3-1), f N kr1 exp() is the envelop function and uufifi,, the transition matrix is mainly determined by first term in Eq.3-5. The absolute values of the transition matrix elements nu p S^ are listed in table 3-2, where S is the conduction band wavefunction and un is the valence band wavefunction, x, y, and z are the propagation direction of light, x, y and z are light polarization and i m SpX i m SpY i m Spze x e y e z. 3.4 Quantum Well Confinement In this thesis, we have focused our study on type I quantum well structure described in chapter 1. The Bloch wave function of an elect ron or hole confined in the quantum well with periodic potential V (z) is described as [41] ) ( ) ( r u z er k i 3-6

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62 here k is the electron wave vector in xy -plane and ()z is an envelop function along the z direction, in which the quantum well is grown. We can separate the wave function (Eq. 3-6) into xy and z directions. In the z direction, we have ) ( ) ( ) ( 22 2 2z E z z V dz d m in 3-7 The eigenvalues En of this equation 3-7 ar e the energies of different quantum confined subbands. A schematic diagram of the confinemen t subbands in a type I quantum well is shown in figure 3-3. For the states in the xy plane, if we use parabolic bands for kx and ky, the carrier energies in the quantum wells are given by: EE m kknxy2 222 (). 3-8 The Bloch wave function (Eq. 3-6) for a quantum state labeled by n can be expressed as r k i n n n ne z u f u ) ( here, k and r are the 2D electron wave vector and position vectors in the xy-plane. With the envelope functions ()z, we can derive the selec tion rules of the envelope function from equation 3-5, dz z z dr e f fm n k k i i ff i) ( ) (* ) ( 3-9 The first term shows that the optical transi tion is allowed when the electron momentum k is conserved i fk k The second term gives us the selection rule for transition between two different subbands [41]

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63 n-m=even. However, the transitions corresponding to n-m=0 are far stronger than n-m=2, 4, 6 [41]. The optical transitions processes correspondent to n-m=0 are shown in Fig. 3-3. 3.5 Density of States in Bulk Semico nductor and Semiconductor Nanostructures A consideration of the density of states is very important for unde rstanding the optical response of semiconductors. It expresses how many states are available in the system in the energy interval between and +d ; the maximum number of carri ers is reached when all the density of states is occupied up to Fermi level. This will become particularly important for understanding the superfluorescence experiments in Chapter 5. The density of states in a bulk semiconductor is given as [41] g mD3 2 0 2 3 2 1 21 2 2 () 3-10a In a 2D semiconductor quantum well, the carriers are confined within th e well width, so the density of states is described as [41]: g mD j j2 2 0()() j= 1, 2, 3. 3-10b Here, j is the index of qua ntum confined states and () j is the step function. For a 1D system, the density of states is given by [41]: g mD r jj jjxz xz1 2 1 21 2 1 (), 3-10c Here, jx and jz are index of quantum confinement states on z and x direction. If all the 3 dimensions are quantum-confined fo r a free carrier, we have a quasi 0D system, and the zero dimensional carrier de nsity of states is given by [41] gD j j02 () 3-10d

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64 Here, jis the energy of the jth quantum confinement state and j is the Dirac delta function. The density of states curves fo r 3D, 2D, 1D and 0D system ar e plotted in Fig.3-4. We can see that for 3D and 2D systems, the density of states is continuous, while in 1D and 0D, the continuums collapse and the density of state get discrete and turn into function. 3.6 Magnetic Field Effect on 2D Electron Hole Gas in Semico nductor Quantum Well In a type I semiconductor quantum well such as InxGaAs1-x/GaAs, electrons and holes are confined in a potential well defined by the xy-plane. In the presence of magnetic field along the z direction, an additional quantum confinement is applied to the electrons and holes in the xyplane. The Hamiltonian of an electron in a qua ntum well in the presen ce of magnetic field along z direction is given by [71] H m p eA c Vz 1 22()(), 3-11 where AxB(,,) 00 is the vector potential and V(z) is the quantum well confinement potential. We can separate the elec tron wave function into xy-plane component and z direction component, so the wavefunction can be written in the form ) ( ) ( ) (z f y x h z y x Using this wave function, the Schrdinger e quation can be separated in two independent equations: (I) In z-direction (QW growth direction), we have ) ( ) ( ) ( 22 2 2z f E z f z V dz d m in 3-12

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65 This is referred to type I semiconductor quant um well confinement and discussed earlier (see Eqs.3-7, 3-8 and 3-9). (II) In xyplane (quantum well plane), we can modify the Schrdinger equation. Setting ) ( ) () (x e y x hyiyk, Eq. 3-12 can be modified into [71] ) ( ) ( 2 2* 2 2 2 2 2 2x E x m x B e dx d mxy ,. 3-13 where xx k Bey'. This is a typical Schrdinger equa tion for harmonic oscillators and the solution is well known. The energy of this xy -plane motion is given by [71] ENxyc 1 2 N =0, 1, 2... where cBe mc is called cyclotron frequency. Th e quantum states corresponding to the harmonic oscillator energy states are known as Landau levels. The total energy including both z and xy in-plane contributions is EENnc 1 2 There are some important lengths and densities that define quantum wells in magnetic fields. The magnetic length lc is defined as eB c lc. The degeneracy of a Landau level is 2eB h, where the factor of 2 comes from electron (hol e) spin. Typical Landau levels evolve from electronic quantum confinement energy levels in a quantum well are shown in figure 3-5. The crossing or anti-crossing effect between 3rd Landau level evolves from E1 and the 1st Landau level evolves from E2 state is shown. The crossing or anti-crossing effect depends on the symmetry properties of wave function of the states and the perturbation at the intersecting point. For a particular magnetic field, th e number of electrons populating a LL is finite. The electron density on a filly filled Landau level at a magnetic field is given by [71]

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66 n eB he. The filling factor is defined as eB nh n ne Physically /2 at any magnetic field gives the number of fully occupied Landau levels. And again, the factor of comes about because each Landau level has two spin states. 3.7 Excitons and Excitons in Magnetic Field 3.7.1 Excitons As discussed in Chapter 1, an exciton is a pair of an electron and a hole due to the Coulomb interaction between them, and its energy states are very sim ilar to a hydrogen atom. Therefore, the exciton energy levels are expressed as 2 2 2 2 42n R n m e Eexcition n 3-14 where is the dielectric constant of semiconductor material, m* is the reduced effective mass of an exciton, n=1, 2, 3, and 2 2 4 *2 m e R [41] is called the effective Rydberg energy and 2 2 *e m aB is an effective exciton Bohr radius. Similar to the hydrogen system, for a given quantum number n, the degenerate state has fine st ructures due to angular momentum l=0, 1, 2, 3. The fine structure of this exciton is also labeled as 1s, 2s, 2p In semiconductor quantum wells, the exciton bi nding energy increases with respect to bulk semiconductors because the electrons and hole at the bottom of conduction band and holes at the top of valence band, which form the excitons, are confined in the same well and their wave function overlap is larger than in the corresponding bulk material Therefore, the exciton binding energy depends strongly on barrier height and the well width.

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67 Unlike the exciton binding energy for the 3D bulk case given in equation 3-14, in a quantum well with well width less than the exciton diameter 2aB*, the confinement has a significant effect on excitonsone layer of electrons and holes gas are confined in a two dimensional plane. In quantum wells with ex tremely narrow well widt hs, the exciton binding energy are given by [41] 2 2) 2 1 ( n R EDExcition. 3-15 So, in the 2D case, the ground state binding energy of an exciton is 4R*, which is four times that of the 3D bulk semiconductor [73-76]. 3.7.2 Magneto excitons In the presence of magnetic field, the exci tons in semiconductors are called magnetoexcitons. Due to the existing magnetic field, the el ectron and holes start to orbit with respect to each other, and the orbit shrinks if the magnetic field increase s. We can expect that the hydrogen-like exciton wave functions diminish in radius with increasing magnetic field. The Hamiltonian of an exciton in a quantum well in the presence of magnetic field perpendicular to the well layer can be depicted as: HHH e rreh eh 2. 3-16 The first two terms are the Hamiltonian of electron and hole in magnetic field, and the third term is the Coulomb interaction, which depends on th e separation between electron and hole in an exciton. The first two terms can be expressed as [71]: H m peArVreh eh eh eh, ,(())()1 22, 3-17

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68 where ArB1 2 () is the vector potential from magnetic field. Due to the presence of the potential e rreh2, we cannot separate the Hamiltonian in Eq.316 and the wave function into two parts for z direction and xy-plane to get an analytical solution. However, if perturbation theory is used to treat the exciton ground stat e in the presence of an external magnetic field, we can consider the effect of low magnetic field as small perturbation. The perturbati on caused by magnetic field ca n be described as [71]: 2 3 2 2 4 2 2 *4 2 1 ) (B m e c DR B Eground 3-18 where is a dimensionless effective magnetic field in the form of R c which is the ratio of cyclotron energy and excition binding energy, ccecheB mc() is the combination of electron and hole cyclotron energy and D is th e dimensionality parameter for the excitons. Equation 3-18 is often called diamagnetic shift of exciton and only valid for <1 [71]. In the case of high magnetic field limit, where the magnetic field effect is larger than exciton effect and >>1, the magneto-exciton is more similar to a free electron hole pair in magnetic field, and the binding energy Ry is considered only as small perturbation (See Eq. 316). Therefore, in high magnetic fields, the ener gy shift due to magnetic field is given by: EBgroundc()1 2. For a GaAs semiconductor quantum well, where R* is 5.83 meV [77], the value of is around 5 T. This is a significant point--if we wa nt to study the optical ma gneto-exctions in GaAs,

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69 it is necessary to use high magnetic fields in exce ss of 20 T, since the magnetic field effect is 4 times larger than the Coulomb effect. Figure3-6 shows the calculation results of fr ee electron hole transition energy and exciton energy of InxGaAs1-xGaAs (including the band gap Eg) in magnetic field. The solid line are excitonic, which includes the Coulomb interact ion between electron and hole pairs that populate at different Landau levels, while the dashed li ne are Landau energy levels correspondent to free electron and hole populate on different Landau levels. Using this theoretical basis, we turn now to a study of the magnet o-optical properties of excitons in In0.2Ga0.8As/GaAs quantum wells with the goa l of understanding emission from highly excited quantum wells in high magnetic fields.

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70 Table 3-1. Periodic parts of Bl och functions in semiconductors Quantum number Wavefunction u1 |s, 1 2, 1 2 i |S u2 |s, 1 2, 1 2 i |S u3 |p, 3 2, 3 2 1 2 |(X+iY) u4 |p, 3 2, 3 2 1 2 |(X+iY) u5 |p, 3 2, 1 2 1 6|(X+iY) 2 3|Z u6 |p, 3 2, 1 2 1 6|(X+iY) 2 3|Z u7 |p, 1 2, 1 2 1 3|(X+iY) + 1 3|Z u8 |p, 1 2, 1 2 1 3|(X-iY) + 1 3|Z

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71 Table 3-2. Selection rules for interband transitions using the absolute values of the transition matrix elements Propagation direction x y z Transition Z 2 2 Impossible hh e X 2 Forbidden hh e Y 2 6 Forbidden hh e Z 6 6 lh e X 6 2 3 lh e Y 6 2 3 lh e Z 3 3 Split-off e X 3 3 Split-off e Y 3 3 Split-off e

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72 (a) (b) Figure 3-1. Band structure of Zinc blend semi conductors. (a) Brillouin zone of zinc blend structure. (b) Band structur e of Zinc blend structure semiconductor in <100> and <111> direction. X and L valleys of conduction band are shown. Light hole and heavy hole are degenerate at point. From Electronic archive of New Semiconductor Materials, Characteristics and Properties, Ioffe Institute, Russia [78]

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73 (a) (b) Figure 3-2. Band structure of wurzite struct ure semiconductors. Brillouin zone of a wurzite structure. (b) Band structure of a wurzite structure semiconductor in kx and kz direction. A and M-l valleys of conduction ba ndare shown. Degeneracy between heavy hole and light hole at point is lifted.From to Electronic archive of New Semiconductor Materials, Characteristics a nd Properties, Ioffe Institute, Russia [79].

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74 Figure 3-3. Band alignment and confinement s ubbands in type I semiconductor quantum well. e1 and e2 are subbands in conduction ba nd, hh1, hh2 are the heavy hole subbands in valence band, lh1 and lh2 are light hole subbands in valence band. The solid lines between conduction and valence band ar e correspondent to the allowed optical transitions.

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75 D(3d 2d (a) dd 1'd'1d 1 g1d 1d 0d 0d (b) Figure 3-4. Density of states in different dimensions. (a) Density of states in 3D bulk semiconductor and 2D QW; (b) density of states in1D (dot line) semiconductor quantum wire and 0D (solid line ) semiconductor quantum dot (d).

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76 Figure 3-5. Electronic energy states in a semiconductor quant um well in the presence of a magnetic field. The dashed line corresponds to crossing behavior and solid line corresponds to anti-crossing.

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77 Figure 3-6. Calculation of free electron hole pair energy (d ash line) and magneto exciton energy(solid line) of InxGa1-xAs/GaAs QW as function of magnetic field. s, p, d. f are different magneto excitionic states. Solid lines are for the e-h pair with consideration of Coulomb ef fect and dash lines are for the e-h pair without considering Coulomb interaction. Re print with permission from T. Ando et al., Phys. Rev. B 38, 6015-6030, (1988), figure 7 on page 6022.

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78 CHAPTER 4 MAGNETO-PHOTOLUMINESCENCE IN ING AAS QWS IN HIGH MAGNETIC FIELDS 4.1 Background Optical phenomena arising from interband and intraband transitions in 2D electron-hole gases in III-V semiconductor quantum well have been studied intensivel y and extensively in theory and experiments during the past several decades owing to the intense interest in the physics of low dimension system and their potential appl ications [81]. In a magnetic field, the quantum-confined st ates in the conduction and valences band split into different Landau levels, resulting in electr ons and holes populating different Landau levels, thus, the interband Landau level transitions will dominate optical transitions in magnetic fields. By observing and analyzing inter-LL optical transitions, we can st udy the optical transitions of 2D electron hole gas such that detailed info rmation about the conduction and valence band structures, carrier effective mass and carrier inte ractions between different Landau levels (such as crossing and anti-crossing) can be acquired [82-84]. This work will serve as a background to the next chapter on the nature of light emissi on from dense magneto-plasmas in quantum wells. Using relatively weak light s ources such as tungsten and xenon lamps, we can measure the absorption spectrum of optical transitions from valence band Landau levels to conduction band Landau levels in semiconductor QWs in magnetic fields and determine the energy peaks of each inter-Landau level transition. In the absorption spectrum, these optical transitions are still predominantly excitonic, since the separation between two electron hole pairs is relatively larger than the exciton Bohr radius (daexciton), so that the Coulomb interaction between electron and hole in a exciton system are not screened. PL due to recombination of electrons on a conduction Landau level with holes on a valence band Landau level is necessary to study the Landau level physics of magn eto-excitons (at low

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79 densities) or magneto-plasmas (at high densities). In this case, CW excitation (for example, with a He-Ne laser) is not sufficient since it cannot cr eate a large number of carriers to populate in higher Landau levels; the only photon emission cha nnel is due to the transition lowest electron Landau level to highest hole Landau level. Therefor e, pulsed lasers such as Q-switched or mode locked lasers are needed to generate a suffic iently high carrier dens ity so that interband transitions due to higher Landau levels are ob served. During the excitation, the laser pulse transfers large amount of energy to the semiconduc tor in a very short tim e (~ ps), and carriers can reach high densities before their r ecombination, which deplete the higher LLs. III-V group semiconductor quantum wells, es pecially composed of GaAs or InxGa1-xAs, are widely used to study the physics of magneto-e xcitons [85]. This group of materials has a relatively small effective mass m* ~ 0.067m0 (m0 is the free electron mass), which makes it easy to observe transitions between higher Landau le vels, since the Landau le vel splitting between two consecutive levels is given by c m eB Ec 4-1 In addition, for InxGaAs1-x/GaAs quantum wells, the degeneracy of heavy hole and light hole is lifted at point due to the existence of strain in th e well. This is an effect of degenerate perturbation in quantum mechanics. The lattic e mismatch between well and barrier material cause a crystal lattice distortion and induce a new static electric field in the Hamiltonian of electrons on valence bands. This perturbation lif ts the degeneracy between heavy hole and light hole subband. Since the heavy hole and light hole are separa ted by ~100 meV, we can observe transitions between electron LLs and LLs originating from heavy hole and light hole subbands respectively.

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80 Before we start to investigate the inter-LL transitions, the labeling of the inter-Landau level transitions needs to be defined. A diagram of interband LL transitions is plot ted in Fig.4-1(b), which describes the optical proc esses of each peak in absorption spectrum. We use the hydrogenlike excitonic notation to represent the transiti ons, and the meaning of each term is given as following. en is an electron on the nth subband, hn is a hole on the nth subband, l or h means heavy hole or light hole subband and ns means th at both electron and hole are on the nth LLs originate from a subband. This notion well represents the hydrogen like e-h pair bond with Coulomb interaction. However, under high excitation density, we use 0-0, 1-1 and 2-2 to represent the e-h inter LL transitions (see Fig. 4-2(a)), since th e electron and holes density is high and Coulomb interaction between electron and hole in an e-h pair is screened so that the electron hole pair is plasmonic instead of excitonic [89, 86-88]. Ando and Bauer [90], and Yang and Sham [9192] have theoretically studied magnetoexcitons in 2D electron hole gas in GaAs qua ntum wells from low to high magnetic field. Valence band complexity, which due to the mixi ng between different subbands in valence band (shown in Fig.4-2(a)) is consider ed in their calculation of inter-LL transitions to account for diamagnetic shift at low field, linear dependence of magnetic field at high field and other experimental results. Using nanosecond pulsed laser excita tion at high powers, Butov, et al. have studied the photoluminescence of interband -LL transitions in InxGa1-xAs quantum well up to 12 T in details [93]. In his experiments, the photoexcited electr on-hole gas is considered as a magnetoplasma instead of magneto-excitonic at high laser excitation powers (carrier density up to 1013cm-2 in the quantum well). In addition to 0-0 tr ansitions, transitions between higher LLs are also observed in

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81 the PL spectrum, as shown in Fig. 4-2( a). In Fig. 4-2(a), the peaks of the LL transitions (n-n) shift to the low energy side with the increasing of carrier density. This is caused by carrierinduced bandgap renormalization (B GR), which is considered to be many body effects and can be interpreted using many body theory inst ead of single particle theory [93]. 4.2 Motivation for Investigating PL from InGaAs MQW in High Magnetic Fields Using High Power Laser Excitation While these prior magneto-photoluminescence ex periments have revealed several insights about the physics of high densitie s of carriers in Landau levels, th ey were performed in relatively low fields (less than 12 T) using either CW optical measurements or nanosecond pulsed laser excitation, with excitati on densities of few GW/cm2. A drawback of using nanosecond excitation for these experiments is inte r-LL carrier relaxation can occu r during the excitation pulse, resulting in an equilibrium distribution of filled LLs. In addition, inter-LL recombination can actually occur during pumping, re ducing the carrier density. In order to investigate these PL effects in QW in new regi mes with higher densities and larger LL separation (i.e. higher magnetic fields a nd high pump power excitation), new facilities are required. As discussed previously in Chapter 2, we have developed an ultrafast spectroscopy laboratory at the DC High Field Facility of th e National High Magnetic Fi eld Laboratory, with the capability of pr obing over the 200 nm m wavelength range with 150 fs temporal resolution in fields up to 31T. In high magnetic fields, the density of states of 2D electron hole gas will evolve into a 0D hydrogen like system owing to magnetic field conf inement (See Chapter 3). We can expect that all the electron and hole stat es will populate a very sm all energy range in a width E about the energy E of the LLs resulting in each energy level of this 0D system having a very high density

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82 of state (see Fig.3-4). New optical phenomena are e xpected in this high-density electron hole gas system at high magnetic field since the Coul omb interaction between e-h is screened. 4.3 Sample Structure and Experimental Setup InxGaAs1-x/GaAs with x=0.20 semiconductor QW samples were grown via molecular beam epitaxy (MBE) method on GaAs substrates. The samples consist of a GaAs buffer layer grown at 570C followed by 15 layers of 8 nm In0.2Ga0.8As quantum well separated by 15 nm thickness GaAs barriers, all were grown at s ubstrate temperature between 390 to 435. Samples were provided by Glenn Solomon from Stanford Un iversity. The sample structure is shown in figure 4-4. Using the CW optics setup and resistive magne t described in Chapter 2 at the NHMFL, the absorption spectra were measured at 4.2K up to 30 Tesla. The white light source used for absorption spectrum is tungsten lamp and excitation light source for the CW PL spectroscopy is a He-Ne laser at 632nm wavelength. Using the ul trafast optics facility and a 31T resistive magnet, the photoluminescence spectrum was measured for the same sample at T=10 K. The excitation light sources are the CPA and a tunable OPA as described in Chapter 2. The CPA laser operates at 775 nm and the OPA was tuned to 11 00 nm and 1300 nm respectively. We excite the sample with different power up to 25 GW/cm2. In both absorption and PL experiments, we chose the Faraday geometry shown in Fig. 4-5, in wh ich the magnetic field is perpendicular to the quantum well plane and the propagation of li ght is parallel to the magnetic field. 4.4 Experimental Results and Discussion 4.4.1 Prior Study of InxGa1-xAs/GaAs QW Absorption Spectrum As a prelude to our investigations, Jho a nd Kyrychenko [82] have previously studied InxGa1-xAs QW samples used in our high field experi ments in high magnetic fields to understand the complex mixing behavior. For reference, the energy levels of this InGaAs quantum well are

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83 shown in Fig.4-6. The magnetic field-dependent absorption spectrum of InGaAs quantum is in shown in Fig 4-1(a). At zero fi elds, three exciton levels, e1hh1, e1lh1 and e2hh2, are clearly resolved, and the shape of absorption curve is a step function, corres ponding to a 2D e-h gas density of state. Between the ex citon levels, continuum absorption is also observed. We can see that the splitting between h1 a nd l1 hole state is relatively large (~100 meV), induced by the strain on InxGa1-xAs QW, which is caused by the mismatch of crystal lattice between InAs and GaAs semiconductor. This energy separation re duces the wavefunction mixing between h1 and l1 hole states and permits unambiguous study of the e1h1 exciton, since e1hh1 and e1lh1 exciton states can be considered separately. With increasing magnetic field strength, the e1hh1 and e1lh1 excit on states split into magneto-exciton states e1hh11s, e1hh12s, e1hh13s a nd e1lh11s, using the description of the magneto-exciton states given above. The corresp onding inter-Landau level transitions are given in Fig.4-1(b). At higher magnetic fields, we can see from spectrum that the continuum states between exciton steps collapse and the absorption spectrum curve evolves into 0D-like density of states, indicating that e-h gas system has evol ved into a quasi 0D system (see Fig. 4-1). In the absorption spectrum, each excite magneto -.exciton state (2s,3s,4s) originating from the e1h1 state shows anti-crossing like splitting when it intersects with e1l11s state, indicated with arrows. Jho and Kyrychenko have previously modeled this anti-crossing effect [83]. They found that each excited state show s anti-crossing like sp litting when it meets a dark state. This splitting behavior is independent of polarization, and se nsitive only to the parity of the quantum confined states. They also attribute the origin of this effect (~9meV) to Coulomb interaction between e-h pair instead of hole valence band complexity. In Fig. 4-4, an example of valence band mixing is shown. In this figure, the disper sion curve of heavy hole subband crosses the light

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84 hole subband at certain k value, which causes the wavefunctions of heavy hole and light hole get mixed also. 4.4.2 PL Spectrum Excited with High Peak Power Ultrafast Laser in Hi gh Magnetic Field We now contrast the above spectrum with PL observed using ultrafast laser pulses. Fig. 47 shows magnetic field dependent PL spectrum from InxGa1-xAs QW excited with 775 nm, 150 fs laser pulses of 10 GW/cm2, which generates carrier density ~1012cm-2. At zero field, we observe e1h1 and e2h2 interband transitions, and with the increasing of magnetic field these two PL peaks split into inter-LL transitions (Landau fan). We observed PL from well defined interLL transitions up to e1h15s, but the an ti-crossing-like splitting between e1h1ns and e1l1ns in the absorption spectrum are not observed in this PL spectrum. As mentioned above, the anti-crossing effect is due to the Coulomb in teraction between electrons and hol es, therefore, the absent of mixing of LL states indicated that the Coulomb interacti on is screened at high e-h density so that the corresponding transitions between LL states in Fig.4-7 are not purely excitonic. For comparison, we plot the Landau fan diag ram comparing the absorption spectrum and PL spectrum under high power excitation in Fig. 4-8. The Landau fan diagram of PL is very different from the Landau fan diagram of absorpti on even at high magnetic field. First, for the same inter-LL transition, the energy position of each PL peak has red shift with that of the CW absorption peak, which we attr ibute to carrier density-induced bandgap renormalization [93]. This band gap renormalization is caused by the many body effect of carriers and this many-body effect gets stronger at high carrier density. S econd, at high magnetic fiel d, since the excitonic effect can be neglected, we have the following form for the energies: ) 1 ( n c m eB E Eg, 4-2

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85 where E is the energy position of peak of a LL at given magnetic field B, Eg is the band gap, m* is e-h pair effective mass and n indicates the nth LL. We can see that in equation 4-2, E is linearly proportional to B and 1/m* is the slope, fitting result shows m*=0.0672m0, m0 is the electron effective mass. From Fig.4-8, we can see that for a trace of given LL, the effective mass in the absorption spectrum should be higher than that in the PL line, which indicates that the m* is higher at low carrier density. Third, in the ca se of free e-h pairs with no excitonic coupling, such as in e-h plasma, the traces of all the LLs originate from same subband should converge at zero field since the Coulomb intera ction bind e and h is screened. This effect is consistent with the traces of LLs in PL spectrum. However, in absorption spectrum, the line of LLs peak positions do not converge at zero field because of the existing of e-h binding energy. Thus, the magneto-PL of InxGa1-xAs/GaAs QWs excited with high power ultrafast laser pulses is most likely plasmonic instead of excitonic. In Fig.4-9, we plot the magneto-PL excited with different excitation intensity for three wavelengths (a) 1300 nm, (b) 1100 nm and (c) 775 nm at 25 T. For each wavelength, we denote the lowest and highest excitation intensity in GW/cm2. The peak position are assigned from lower energy side 0-0 to higher energy side 1-1, 2-2 and respectiv ely. From the Fig.4-9, we can see that the excitation with 1.1 m and 1.3 m are below InGaAs QW bandgap so that the PL originates from carriers excite d via two-photon absorption into the GaAs barrier and capping layer as well as the continuum states of InxGa1-xAs QW. For 775 nm as well as 1.1 and 1.3 m excitation, PL emission occurs af ter excited carriers rela x down to the QW subbands. In Fig. 4-9, the peak energies of each LL remain at fixed positions and do not show any red shift at high pumping intensity. This indicates that the many part icle interaction effect is not resolved and the bandgap renormalization effect is suppressed at low excitation power.

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86 In Fig4-9 (a), (b) and (c), we can see that the character of energy peaks 1-1 and 2-2 are very different from 0-0 peak. At low excitation powers, broad and weak peaks from 1-1 and 2-2 are seen in (b) and (c). With increasing the exci tation laser intensity, a narrow peak starts to appear on the high-energy side of 1-1 and 2-2 peaks and become dominant at high excitation power. The linewidth of narrow peak of 1-1 is 2.3 meV, smaller than that of 0-0 peak (9 meV), implying a different emission origin for these two peaks. In addition, we do not observe these narrow peaks in the magneto-exciton absorption spectrum shown in Fig.4-1. We plot the 775 nm, 1.1 m and 1.3 m laser excitation power de pendence of PL intensity for 0-0 transitions, 1-1 transiti on, including broad and narrow peak s, in Fig4-9 (d) to (f). For 775nm excitation, the PL intensity from all th e three states rise up rapidly at low power (<2GW/cm2) and then saturates. At 1.1 m and 1.3 m excitations, the PL intensity from 0-0 transition and tail of 1-1 transi tion increases proportionally to I2 pump, since the excitation requires a two photon absorption which scales as the square of laser intensity. However, the narrow peak of 1-1 transition shows very different scali ng. In Fig.4-9 (d), the narrow peak of 1-1 LL transition shows no emission until threshold pump intensity (~13 GW/cm2), which might be an evidence of stimulated emission processes. To understand the many particle effect in th e high density of elec tron hole gas generated with femtosecond lasers, we plot the magnetic field dependent spontaneo us emission calculated with an 8 band in Pidgeon-Brown effective ma ss model [94](for details see appendix B) in Fig.4-10 (a). Fig. 4-10(b) is the correspondent experimental results. By comparing the two curves, we estimate that the actu al carrier density is between 1012/cm2 and 1013/cm2 in our experiments. However, there are several discre pancies between theoreti cal calculation and our experimental results.

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87 (I) The energy peaks of higher LL levels are shifted due to the single particle theory, in which the Coulomb interactions between electron hole and renormalization effects are neglected. (II). Spin induced splitting in magnetic field is not observed experiment ally due to the large inhomogeneous broadening of the PL peaks. (III) The theory does not predict the emergence and power scali ng of the narrow emission peaks at 1-1 LL transition, We suggest that the experimental curves ar e induced by new emission processes at higher lying LLs. More systematic studies are presented in the next chapter to elucidate the origin of these phenomena. 4.5 Summary With the underlying theory of LL physics, we have elucidated the conduction and valence band structure of InxGa1-xAs/GaAs QW. The anticrossing behavior between LLs originate from different subbands has been discus sed. Previous investigation shows that the anticrossing is due to Coulomb interaction between e-h excitonic pair. Furthermore, by comparing the CW experimental magneto-absorption spectrum and magneto-PL spectrum with ultrafast high power laser excitation, it is found that the interaction between e-h is plasmonic rather than excitonic. Also new sharp features emerge in the PL spectrum of interband LL transitions, which implies new optical process in the PL emission. That is the subject of Chapter 5.

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88 1350140014501500 0.2 0.4 0.6 0.8 1.0 e2h21s e1112s e1hh11s e1l11s 0 T 10 T 20 T 30 TAbsorptionEnergy (meV) (a) (b) Figure 4-1. Magneto abosorp tion spectrum and schematic diag ram of interband Landau level transitions. (a) Magneto absorption spectrum of InxGa1-xAs/GaAs quantum well in Faraday geometry at 4.2 K up to 30 T, ma gneto excitionic states are labeled; (b) Energy diagram of the optical transition in the magneto absorption spectrum of InxGa1-xAs/GaAs quantum well. Each transiti on corresponds to a peak in the absorption spectrum.

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89 (a) (b) Figure 4-2. Magnetophotoluminesc ence experimental results of band gap change and effective mass change. (a) Band gap renormalized at high carrier density, (b) Reduced effective mass renormalized at high carrier density in InxGa1-xAs semiconductor QW.Reprint with permission from L. Butov et al., Phys. Rev. B 46, 15156 15162 (1992), Figure 2 on page 15158 and Figure 8 on page 15161

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90 Figure 4-3. Valence band mixing of heavy hole and light hole subbands in semiconductor quantum well. Light hole subband cr osses with heavy hole subbands.

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91 GaAs Cap layer 15nm GaAs 15nm GaAs 8nm InGaAs Buffer GaAs Substrate 15 Periods Figure 4-4. Structure of In0.2Ga0.8As/GaAs multiple quantum well used in our experiments.

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92 Figure 4-5. Faraday configurati on in magnetic field. The light pr opagates in the direction of the magnetic field B and the electric field polarization E is perpendicular to the magnetic field.

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93 Figure 4-6. Energy levels of electron a nd hole quantum confinement states in InxGa1-xAs quantum wells. e1,e2, hh1, hh2 denote the electron and hole states due to quantum confinement. 1325meV

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94 12801320136014001440 e2hh2 3-3 2-2 1-1 0-0 e1hh110 T 20 T PL I n t e n s i t y ( a u )Energy (meV)0 T Figure 4-7. Magneto-photoluminescence spectrum of InxGa1-xAs quantum well at 10K.The excitation laser source is a 775 nm CPA la ser with 150 fs duration and excitation power of 10 GW/cm2.

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95 048121620242832 1300 1350 1400 1450 1500 5-5 4-4 3s 3-3 2s 2-2 1s 1-1 PL absorption Energy (mev)Magnetic Field (T) Figure 4-8. Landau fan diagram of absorption and PL spectrum of InxGa1-xAs quantum well in magnetic field up to 30 T. The solid squares are the energy positions of interband LL transitions from absorption and the so lid triangles are en ergy positions of interband-LL transitions from PL spectrum.

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96 Figure 4-9. Magneto-PL (a-c) a nd excitation density dependence (e-f) of the integrated PL signal in InxGa1-xAs quantum wells at 20 T and 10 K.The left side plots the PL spectra on a semilog scale excited at (a) 1300 nm, (b) 1100 nm, (c) 775 nm, the excitation density is marked with arrows. The right side displays the excitation density dependence at (d) 1300 nm, (e) 1100 nm and (f) 775 nm.

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97 130013201340136013801 4001420144014601480 0.01 0.1 (33) (22) (11) (00) (22) (11) (00) HH2ExperimentPL (arb units)Energy (meV)1E-3 0.01 0.1 1 25 GW/cm2 @ 1.1 mPL Signal (nm-3)Theorynpair = 1x1013 cm-2B = 25 Tesla T = 4.2 Ke1h2 Figure 4-10. Theoretical calcula tion and experimental results of PL in high magnetic field. Theoretical calculation of the PL sp ectrum based on an 8 band Pigeon Brown model (top panel, from Gary Sanders) and experimental results (lower panel) of magneto-PL emitted from InxGa1-xAs with high excitation density at 25Tesla and 4.2K.

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98 CHAPTER 5 INVESTIGATIONS OF COOPERATIVE EM ISSION FROM HIGH-DENSITY ELECTRONHOLE PLASMA IN HIGH MAGNETIC FIELDS 5.1 Introduction to Superfluorescence (SF) In this chapter, we consider the unique nature of cooperative electro-magnetic emission made possible using ultrafast laser excitation of quantum wells placed in high magnetic fields. This combination allows us to create atomic-lik e behavior between electrons and holes at carrier densities well above those which support excitons. As such, these simulated atoms can emit light cooperatively via superfluorescence. The nature of the emission of light from at oms and atom-like systems depends sensitively on the physical environment surrounding them, and can be tailored by controlling that environment [96-98]. At the most fundamental le vel, atom-photon interact ions can be modified by manipulation the number densit y, phase, and energies of atoms and photons involved in the interaction. A very common example is the laser, in which mirrors are used to provide coherent optical feedback to a populati on inverted atomic system, resu lting in the emission of photons with well-defined spatial and spectral c oherence properties. Less common but equally fundamental examples are the superemi ssion processes, superradiance (SR) and superfluorescence (SF), cooperative spont aneous emission from a system of N inverted two-level dipoles in a coherent superposition state. Experiments probing these phenomena in atomic systems have provided significant insight into the fundamental physics of light-matter interactions [99]. In our experiments, by manipulating the coherent intera ctions of electrons and holes in a semiconductor quantum well using intense ultrashort laser pulses and strong ma gnetic fields, we generate superfluorescence in a completely new and unexplored regime. Our e xperiments begin to approach the question of whether atom-photon interactions in semiconductors are truly quantum as they are in atoms.

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99 5.1.2 Spontaneous Emission and Am plified Spontaneous Emission The simple illustration of spontaneous emission process is shown in Fig.5-1 (a). For a two level atom system with a high energy excited state E2 and a low energy ground state E1, the atoms populating the E2 state might spontaneously transit to E1 state without any external electromagnetic field perturbati on. A photon is emitted with energy1 2E E where is the angular frequency of an emitted photon. We can de scribe this spontaneous emission as [120] N A dt dN21 5-1 in which N is the number of atom on excite states E2 and A21 is called spontaneous emission probability or Einstein A coefficient. The solu tion of this equation is an exponential decay function given by NNet021, 5-2 where N0 is the initial number of atom on E2 state and 21 is the life time of this transition. Comparing Eq. 5-1 with 5-2, we have21 121A. As we know, if atoms are far enough from each other and the inter actions between atoms are neglected, the spontaneous emission that occurs in one atom on excited state is also isolated from the spontaneous emission from another at om on excited state. Therefore, spontaneous emission has random directionality. Also as we see from equation 5-1, the intensity of spontaneous emission is proportional to N, the total number of atoms involved in the transition. The instinct properties of the atomic system determine the value of 21, which ranges from s for rarified gases to ns for semiconductors. [100-102] Fig.5-1(b) shows the transition process of amp lified emission. In a two-level atom system as described above, an atom populates the excited state E2. Before this atom relaxes down to the

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100 ground state E1 through spontaneous emission, it can be pert urbed by the electro-magnetic field of an incident photon, which is emitted from spontaneous emission with energyhEE 21. Under the perturbation, this at om might transit to ground state E1, emitting a photon with energyhEE 21. This photon emission process is ca lled amplified spontaneous emission (ASE). After this transition, one photonh is turned into two photons. ASE process can be described with the following equation [121] N B dt dN ) (21 5-3 where B21 is a stimulated emission probability, called Einstein B coefficient and ( ) is the distribution function of radiation density of photons at frequency The relationship between A21 and B21 is given by [121] A Bc21 21 3 22 5-4 One important optical property of ASE is th at the emitted photon is exactly same as the incident photon [121]. These two ph otons have the same optical fre quency, spatial phase, optical polarization, and direction of propagation, which results in the coherence between them. Through ASE process, weak spontaneous emissi on can be amplified coherently in active medium. However, ASE can occur for any photon create d from spontaneous emission, and in a medium with a sufficiently larg e density of excited states, many spontaneously emitted photons can be exponentially amplified in different regions, such that light from different spatial regions are incoherent since they have different phases, polarizations a nd propagation directions. If an optical cavity is used to select a specific mode of ASE, a lasing effect can be observed since all other ASE processes are suppressed except the preferentially selected ASE mode.

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101 In ASE process, in the low intensity regime, where IzIs() the amplification of emission intensity in the pr opagation direction z is written as IzIegz()()00, 5-5 in the high intensity saturated gain regime, where IzIs(), the emission intensity is described by IzIIgzs()() 00. 5-6 In equations 5-5 and 5-6, I() 0is the intensity of light propagating in the medium at z =0, Isis the saturation intensity (which depends on the medium and density of excited states), z is the light propagation direction, and gN0221 is called optical gain, where 21is a probability factor called the stimulated-emission crosssection and usually very small~10-20cm-2 [96]. From the two equations 5-5 and 5-6, we can see that in low intensity regime, the light intensity grows as an exponentially along the z direction; in high intensity regime, the intensity grows linearly along the z direction. The gain is said to saturate in high-intensity regime. 5.1.3 Coherent Emission Process-Superradiance or Superfluorescence In SE or ASE processes, the separation between two atoms on excite states are relatively large, so that the electro-magnetic field induced by one atom does not interact with the other atom, and the electric dipole of each transition is not aligned nor has the same phase in the oscillation, which results in incoherence between different SE processes or ASE originating from different spontaneous emission processes, also resulting in inc oherent emission. However, in a N -atom ensemble, if the atoms in excited states are brought closer and closer, so that the electro-magnetic field ra diated interact with many excited atoms (in macroscopic scale) simultaneously and all the atom ic electro dipoles osc illate in phase before they start uncorrelated spontaneous emission, a coherent macrosc opic dipole state can exist for a

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102 short time. A very short burst of emission will occur, radiating str ong coherent light. This superemission process is called superradiance (SR) or superfluorescence (SF), depending on the nature of the initial formation of the macros copic coherence. For SR, the coherence of atoms is from the external excitation source, i.e. polar ized laser pulse, and excited atoms preserve the coherence before they emit photons. For SF, the at oms on excited state are initially incoherent, the coherence develop in the N atoms due to the interaction between them. The SF emission is a macroscopic coherent effect in an ensemble of N atoms, in which all the N atoms radiate photons cooperatively and cohe rently. Fig.5-2 shows the processes of SF emission. Initially, an ensemble of N atoms populates the ground state. With photoexcitation from a laser pulse, the N atoms are excited and populate higher energy states. The N atoms preserve the coherence from the coherent laser pulses for a very short time and then lose the coherence before they start to tr ansit to ground state. In this si tuation, the elec tro dipoles of N atoms are not aligned in phase. However, if the density is high enough, th e electro dipoles could develop the coherence and get aligned and start to oscillate in phase spontaneously due to the interaction between them. A small number of electro dipoles of the N atoms could be aligned in phase spontaneously due to quantum fluctuation or thermal effect, and then this coherence of electro dipoles is develope d to all the atoms through a very high gain mode ( L >>1). The N atoms in the coherent state will emit coherent photons in a very s hort burst of pulse. SR was first predicted theoretically by Dicke in 1954 [35] and first observed experimentally by Skribanovitz et al [103] in hydrogen fluoride (HF) gas in 1973. Many experiments about SR and SF have been perfor med and reported in atom gas system [104-106]. In addition to experiments of SF, more theore tical work elucidating the nature of SF under

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103 different conditions has also been done with either quantum fiel d theory [107] or semiclassical theory [108]. In Dickes SR theory, the cooperative emi ssion of electro dipoles takes place under the following condition, 3~V 5-7 Where V is the volume that excited atoms are confined and is the emission light wavelength. From this condition, cooperative emission exis ts in a very small active medium volume. However, Bonifacio et al [107] and MacGillivrary and Feld [108] extended the SF theory to optically thick medium (on the order of mm or cm), either a pencil shape geometry, in which the Fresnel number ( A/L where A is the cross section and L is the length of active medium) is not larger than 1 or a disk shape, in which Fresnel number is much larger than 1. In the description of SF, there are five tim e scales are involved: the dephasing times T2 and T2 *, the photon decay time E, cooperative time c and SF radiation time (or duration) R, and coherent delay time d. E is the time of a photon transi t time in the active medium, T2 and T2 are the coherence relaxation time due to homoge neous and inhomogeneous broadening effect, c is the characteristic exchange time of elect ro dipole coupled to radiation field, R is the pulse duration of SF emission, and d is the delay time, during which the spontaneous emission evolves into coherent emission. The expressions of these time scales c, R and d are given by [108] 2 2 1 2 0 0 0 1 0 2 tan) 2 ln( 16 ) 2 ( ) ( ) / 8 ( N T ck g g N g L N A TR d k c eous spon R 5-8

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104 where Tsp is the spontaneous radiatio n time of an atom transits from high energy state to the lower energy state, N is the number density of atomic system, is the transition wavelength, gk0 is the coupling factor between electromagnetic fiel d and electric dipole, which is a key factor in the evolution of coherent emission, k0 is wave vector of central frequency of optical transition and is the dipole moment of atomic dipole. Anothe r critical factor in the cooperative coherent emission is the cooperative length Lc, within which all the dipole os cillates in phase, resulting in the coherent emission. The expression of Lc is given by [108] 02 / g c Lc, 5-9 where is the density of atoms. In Bonifacios theory, the condi tion for cooperative emission of N atoms ensemble is given by [108] 2 2, T Td R c 5-10 Under this condition, initiate d by quantum fluctuations or thermal radiation, a small number of atomic dipoles oscillates in phase and emit photons spontaneously, then through the coupling between atomic dipoles and electromagnetic field, the N atom oscillators ensemble develop into oscillatory phase matching state in delay time d and radiate a short burst of coherent emission with pulse width R. Eq. 5-10 stresses that the emission takes place before the N atoms oscillator become dephased at time T2, T2* and the N atom oscillators develop into coherent state before they start to recombine. Bonifacio also mentioned in his theory that the relationship between active medium length L and critical cooperative length Lc

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105 In the case L< c the photons travel inside the active medium when the SF emission takes place, SF is still observable, however the emission pattern is oscillatory pattern in stead of sech2 pattern [108]. In the case L > Lc, the SF emission starts to get weaker and disappear, the emission process is dominated by ASE [108]. As shown in Eq.5-10, several requirements and characteristics for a system need to be satisfied to make SF emissi on observable. SF pulse duration r and delay time between excitation and SF burst d are much shorter than th e spontaneous emission time eous sponTtan and inhomogeneous dephasing time T ( T Teous spon d r, ,tan ) so that the electric dipoles can maintain their phase relation and emit coherent light before spontaneous emission occurs. Based on these requirements, rarified gas atom systems are the most favorable to observe SF emission, since they have relatively long eous sponTtan and (~ s ), and the SF pulse width and delay time is on the order of nanoseconds. Table 5-1 shows some of the time constant in the SF experiment done in Rb gas. By controlling the pressure of the atomic gas, SF emission pattern can be clearly resolved [109, 110]. However, in a solid-state system, i.e. semiconductors, the dephasing time T2, T2* are extremely small (~1ps) [111], and the condi tions in 5-10 are very difficult to satisfy. Thus, up until this work, it has been impossibl e to observe SF emission in semiconductors.

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106 5.1.4 Theory of Coherent Emission Proce ss--SR or SF in Dielectric Medium In 1964, A. P. Kazantsev [112] reported the fi rst theoretical results of collective emission processes in a two level system of a dielectric medium, such as a semiconductor. He found that if the electromagnetic field interact s with two level systems resonantly, the field amplitude is modulated with a characteristic frequency which is the coupling be tween electric field and two level systems. The two prerequisites in Kazantsevs theory can expressed as 10 2 N E 5-12 1 5-13 where is the relaxation time of two level system, 0 N is the energy stored in N atom system. Also, three simplifications of the two level sy stem in Kazantsevs theory are made, (1) the dielectric medium is infinite and sufficiently rarefied, in which case the << 0 (2) the medium is a two level system and (3) there is no di ssipation in the two level system so that 1/ ~0, only the early time (t<< ) is considered. With the conditions shown above, the intensity of radiation is given by EtEt()~exp()2 0 2 0 2 2~Nd 5-14 where E0 is the initial valu e of electric field, d is dipole momentum, N is the density of activated atoms and 0 is the transition frequency. It can be seen that the intensity of field increases exponentially and dramatically if the collective modulation frequency is large enough. Zheleznyakov and Kocharovsky [113] applied the idea of cooperative frequency, which couples the electric magnetic field and optical polarization P in the medium, to the coherent

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107 process of polarization wave function in dielect ric medium, and the cooperative frequency is given by cdN832 0/, 5-15 Where N = N2-N1, which represents the maximum popula tion inversion dens ity in the two level system. Belyanin et al. [114-118] calculated the Maxwell-Bloch equations for resona nt interactions between active medium and radi ation field in semiconductors. In the mean field approximation, the slowly varying electromagnetic field E(k) macroscopic polarization wave Pk, and inversion density Nk can be described via a coupled set of equations: dE dtT dE dt EPE k2 2 0 21 4, 5-16a dP dtT dP dt P EKk k c2 2 0 2 22 42 5-16b dN dt NN T E dP dtkkk p k ()102. 5-16c Here, E is the electric field and Pk is the optical polarizati on oscillating at frequency 0. The subscript k refers to electron-hole pair with quasi-momentum k TE is the photon life time for a given field mode, T1 is the relaxation time of excited state, T2 is the dephasing time of dipoles, d is the transition dipole moment, n is the refractive index, and Nk pis the inversion density excited by pumping. From these three equations, we can see that E and P are coupled, with the cooperative frequency c (and thus the density) determining the coupling strength and resulting emission. The left hand side of 5-16 (a) and (b) for E and P are harmonic oscillators with damping factors

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108 TE, T2, and right hand sides are driving force on the oscillators. However, the increasing rate of E and P strongly depends on the value of c, which couples the E and P and dominates the increasing rate of E and P The driving force c on RHS of 5-16 (b) should be associated with excited atom density and electric di poles, and transition frequency in the E and P resonant interaction, as shown in Eq.515. If an initial value of c is sufficiently large, equation 5-16 exhibit instability with resp ect to the growth of small initial oscillations of the E and P Given that c ET2 1, 5-17 equations 5-16 can be solved approximately in two regime [111]. First is amplified spontaneous emissi on regime. In this case, we have cT2 12, 5-18 and the growth rate is given by "c ET T4 12. 5-19 In order to get amplified, then we should have "c ET T4 12>0. Second is SF regime. In this case, we have cT2 12, 5-20 and the maximum growth rate of emission intensity is given by "c2. 5-21

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109 The SF pulse width R and coherent length Lc can be estimated with the value of c, also the delay time D, which characterize the coherent generation can be given as [111] R c DL c n Logfactor EE~ () ~ log(/)maxmin2 1020 1 2. 5-22 From the cooperative frequency c, many parameters can be derived. The SF pulse duration scales as SF cN~~ 11 2, 5-23 and the peak intensity of SF scales as I N NSF SF~~ 3 2. 5-24 The line width of cooperative recombination, wh ich is determined by the band filling of particle states in QW or QD scales as 2 1~ ~ Nc 5-25 5.2 Cooperative Recombination Processes in Semiconductor QWs in High Magnetic Fields Naturally, in solid-state systems such as semi conductors, it is quite di fficult to observe SR or SF since T2 in solid-state system is very small (on the order of ps). The ensemble of dipole oscillators formed by electrons and holes cannot build up cohere nce before they undergo phase breaking, since the electron and holes are not localized and easily be involved in collisions such as electron-phonon, electron-electr on, and electron-hole collisions However, Belyanin pointed out that in quantized semiconductors, such as a semiconductor QW in high magnetic field or QD,

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110 the electron and hole are spatially confined. This confinement reduces th e collision probability and can dramatically increase the dephasing time T2. Meanwhile, the density of states of QW and QD increase dramatically compared to that of a 3D bulk semiconductor (see chapter 3, equation 3-10 and Fig.3-4). This effect implies that instea d of populating in the cont inuum states in a bulk semiconductor, electrons and holes mainly confine themselves around the quantized energy levels because the continuum states are depleted in QW and QD structure. In this case, the number of dipoles formed by electrons and holes increase significantly at QW energies level E1, E2, which satisfy the high density of atom s requirement of SF (see equation 5-20). In a high magnetic field, the electron-hole pairs in a InxGaAs1-x QW are effectively confined in a quasi-zero dimensional state, a nd manifests this 0D e ffect in the absorption spectrum and PL spectrum (see Fig. 4-4 and 4-7) The electron-hole pair only populate at discrete LL states, ensuring that the spreading of the el ectron-hole pair energi es is small, favoring SF generation. Moreover, the density of state of LL levels for InxGaAs1-x/GaAs QW is high (~1012/cm2 at 20T, see Chap. 4, equation 4-13), which al so give rise to the generation of cooperative phenomena. 5.2.1 Characteristics of SF Emitted from InGaAs QW in High Magnetic Field. As mentioned before, semiconductor nanostruc tures such as QWs or QDs are an ideal system to observe cooperative recombination of electron-hole pairs, therefore we chose InxGaAs1-x/GaAs multiple QWs as our emission medi um, using ultrafast excitation and high magnetic field in combination to observe SF. The st ructure of this sample has been discussed in 4-3 and Fig.4-2. According to the results shown above (Eqs. 5-17 to 5-21), the key term that determines the growth rate of emission intensity I which corresponds to the coope rative emission process is the cooperative frequency c.

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111 In a two-dimensional semiconductor quantum we ll structure, the cooperative frequency is modified into the following form [114], c QWdNc nL822 2. 5-26 Here LQW is quantum well of thickness, is emission wavelength, is the effective overlap factor of electromagnetic field with the quant um well in the direction perpendicular to well plane, n is the refractive index and d is the transition dipole. The maximum photo excited electron-hole density is N ~ Ne-h. Based on the theory presented above, we can estimate the parameters for SF emission in the InxGaAs1-x/GaAs used in these experiments. The photon decay time is c F LnE~~2x10-13 s-1, where L is the active medium length, F is the Fresnel number. In reality, 4x10-13 s-1 seems to be a better estimate because the excited medium can guide the SF emission into the activ e medium. This waveguide effect is generated after medium is excited, due to an enhancement in the refractive index medium in the active area from the magneto-plasma, In this case the electro magnetic field will couple more with optical polarization. The cooperative frequency at initial time is given by equation 5-26, where N is carrier density in the quant um well plane, and is around 1/3. The estimation of cooperative is 2 1210 ~cm Nc13s-1. In equation 5-20, in order to ma ke the condition for SF satisfied, T2 is ~ 10-13 s-1, and we need N > 511 cm-2, which can be realized at high magnetic field (~20Tesla) and ultrafas t pumping (see chapter 3, equation 3-14).

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112 Below, we present investigations of the magneto-PL spectrum obtained from high-density electron-hole plasmas in InxGaAs1-x /GaAs QW in high magnetic fields, in which propagation of PL is perpendicular and parallel to the QW plane. Perpendicula r to the QW plane, abnormally sharp and strong emission lines from 0-0 and 1-1 LL s are observed as discussed in chapter 4. As we have discussed above, there is possibility that this emissi on is from ASE or macroscopic cooperative recombination--SF. Since the electron-hol e pairs are mainly populating in the QW plane, the in-plane PL should be much stronger than the PL colle cted perpendicular to the plane because the spontaneous emission should be amp lified when propagating in the in-plane path. Thus, we have developed experiments in new conf igurations to measure the in plane PL from InxGaAs1-x /GaAs QW. In order to show definitive evidence of cooperative recombination in QWs in high magnetic fields, there are a number of experime ntal signatures that uniquely characterize SF emission. These are listed in Table 5-2. For comp arison, we also include the ASE characteristics in the Table 5-2, since PL emission in InxGaAs1-x /GaAs QWs at high magnetic fields could be due to either emission mechanism. From these si x characteristics, we can distinguish a pure SF process from ASE processes, a nd they are given as follows. 5.2.2 Single Shot Random Directionality of PL Emission In an SF emission process, the coherent coll ective emission builds up stochastically from spontaneous emission, which can be emitted in any direction, and a specific SF burst will follow the propagation direction that the first spontaneous emission takes. It is essential to note that since this is a probabilistic quantum electro-dyn amic process, each SF burst forms independently on each subsequent excitation laser pulse. By contrast, in ASE processes many spontaneous emissions could be amplified, therefore, in a single shot, the PL emission should equally distribute in all direction and no ra ndom directionality is expected.

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113 5.2.3 Time Delay between the Excitation Pulse and Emission As we seen in Eq. 5-21, the SF emission is give n after the excitation pu lse, the delay time between is d, during which the spontaneous emission develops into SF through an extremely high gain mode. This delay occurs because of the inherent build up time for the coherence form from the initially incoherent di pole population. In ASE, the emi ssion process start in a short time (on the order of nl / c < d, where c is the speed of light and l is the length of activated medium and n is the refractive index) im mediately after the excitation pulse disappears, therefore, no time d delay is expected to be observed. 5.2.4 Linewidth Effect with the Carrier Density In the formation of ASE, spontaneous emissi on is amplified when travels through medium, however, the amplified emission linew idth depends on the gain function G( ) which is given below, ) ) ( exp( ) ( ) (0L G I I 5-27 Where I0( ) is the initial intensity fu nction in frequency domain and L is active medium that light get amplified. Usually, G( ) has Gaussian or Lorentz shap e, which result in the center frequency in I( ) get amplified more than frequency o ff center. This gain narrowing effect reduces the emission linewidth in ASE process. In SF process, as mentioned above in Eq. 522, the linewidth of c ooperative emission is broadened at high densities ~Neh1/2, since more carriers are i nvolved in the cooperative emission. 5.2.5 Emission intensity Effect with Carrier Density In an ASE process, emission is amplified linearly with N so that the emission intensity should increase linearly with th e increasing of carrier density N In an SF process, according to

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114 equation 5-23 the emission is a short burst and gi ven coherently, superlin ear increasing of the emission intensity is expected when carrier density N is increased. In magnetic field, the carrier density N depends on the magnetic field strength B (see chap.3, equation 3-14), the linea r relation between them is N~B so a superlinear relation, I~B3/2, between emission intensity and magnetic field is expect ed in SF emission. 5.2.6 Threshold Behavior Both ASE and SF exhibit threshold behavior with respect to laser excitation intensity. However, in ASE, the threshold is at the point where optical gain G>0 while in SF, the threshold is the point where c oherence is built up among carriers. 5.2.7 Exponential Growth of Emission Strength with the Excited Area Both ASE and SF will be amplified in the form of ) exp( ~0L I I so that the emission strength increases exponentially with respect to the excited area. Therefore this doesnt distinguish between be ASE a nd SF, but does show that an exponential process is occurring. We expect to see cooperative emission from high carrier density el ectro-hole plasma in InxGaAs1-x /GaAs QW in high magnetic field, however, in order to fully fill the LL and make the carriers populate on LL before they start to recombin e (time scale ~100ps), a high power (GW/cm2) ultrafast CPA laser is needed to generate d enough carrier density in a very short time (~ps). It is also critical to not e that the initial excitation at 800 nm, is well above (240meV) the 00 LL levels that we probe (at 920nm). In fact we excite electrons carri er into GaAs barrier continuum states and InxGa1-xAs well continuum stats., Most of electrons carriers populating in barrier are dumped into the InxGa1-xAs QW layer and increase the carrier density in well layers. Carries in QW layers will relax down to 0-0, 1-1. LL levels and there are many collisions during the energy relaxation (and momentum relaxa tion) which completely destroys the initial

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115 coherence of carriers imposed by the laser. Thus we can are truly probing SF as opposed to SR. After energy relaxation to the QW LL s, the carriers, now tightly confined both in space and energy, develop into a coherent state with intera cting with the electroma gnetic field from initial spontaneous emission and give a burst of SF emi ssion. This process shows the key signature of SF instead of SR. 5.3 Experiments and Setup To understand the PL emission processes in InxGaAs1-x/GaAs QWs excited with high intensity short laser pulses at high magnetic fiel ds, several experiments have been carried out. Magnetic field and excitation pow er dependent in-plane PL Single shot experiment for random directionality of in-plane PL Control of coherence of the in plane PL from InxGa1-xAs QW in high magnetic field. In all the experiments, we use the ultrafast magneto-optics facility developed by us at the NHMFL (see chap2, Figs.2-2, 2-3, and 2-4.). All the experiments are done at liquid helium temperature with the Janis optical cryostat designed for a resistive magnet. The InxGaAs1-x/GaAs QW sample is mounted on the liquid He tail of cryos tat for direct optics, in which laser beam can travel in free space and then excite the sample without being chirped. For most of the experiments, the ultrafast CPA laser system is the excitation light source, which has been introduced in Chap.4, 4.3. The excitation laser is focused on the InxGa1-xAs QW sample with one 1 m focal length lens, and the spot size on sample is around 500 m The configuration of the in plane PL collecti on geometry is shown in Fig. 5-3. In order to collect the PL travels in the QW planes, a small right angle roof prisms is mounted on the edge of the QW sample, which can steer the in plane light into the optical multimode fiber mounted right on the top of the prism. The area of prism is 1.0x1.0mm2, and the fiber diameter is 600 m

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116 The collection angle for this prism is approximately 40 With this configuration, PL emission travels in the QW plane is effectively and effi ciently collected and delivered to a McPherson spectrometer for analysis. In addition, for co mparison with the in-plane PL, PL emission perpendicular to the QW planes is collected via a fiber on the back face of the sample. The magnet used for study of cooperative emissi on is Bitter resistive magnet located in cell 5 at NHMFL, a 25 Tesla (upgraded to 31 Tesla now) wide bore (50 mm) magnet (see Fig.2-1). Most of our spectra were collected by aver aging over multiple shots (1000 shots in most cases). However, to probe the directionality of th e emission, in which the PL propagation is different from pulse to pulse, single shot experiments need to be performed to resolve this phenomenon. Thus, we measured the PL from InxGaAs1-x/GaAs QWs excited by one single laser pulse. An electro-optical Pockel cell was employed in this experi ment. As shown in Fig. 5-4, the laser beam propagates through two crossed polarizer s and gets rejected at the second polarizer. However, there is fast transient high voltage bias nonlinear crystal positioned between the two polarizers, which operate as a tr ansient half wave plate when th e high voltage bias is on. Each time when the high voltage is on, the high voltage bi ased crystal changes th e polarization of laser beam by 90 degree and let it go through the second polarizer. With this device, we can control the number of laser pulses and the repetition rate of the pulses that are sent to the sample and collect PL from a single excitation pulse. Also, in order to compare the PL intensity at different in plane dire ctions, two small right angle prisms are mounted at cleaved edge s 90 apart of InGaAs/As QW, which will simultaneously collect the PL excited with one CPA pulse and steer into two fibers mounted on top of roof prism. The excitation geometry of single shot measurement is shown in Fig.5-8

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117 5.4 Experimental Results and Discussion 5.4.1 Magnetic Field and Power Dependence of PL We measured the field dependency in plane PL emission spectrum of InxGa1-xAs/GaAs QW excited with 150fs CPA laser pulse s at a constant laser fluence ( Flaser~ 0.62 mJ/cm2) up to 25 Tesla. Experimental result is shown in Figur e 5-5(a). For comparison, PL collected at the same conditions with the center fiber is also shown in Fig. 5-5(b). The sharp in the edge collection PL spectrum is a lot stronger than th e PL from center collect ion. Broad PL emissions due to spontaneous emission from inter band LL transition are observed up to 12 Tesla. This broad linewidth (~9 meV) is due to inhomoge neous broadening, which originates from the inhomogeneities and possibly defects in the multi ple QW layers. The magnetic field dependent PL features above 13 T change dramatically, and sharp peaks (around ~2 meV) are observed on high energy side of broad feature of each interband LL transition. These sharp peaks dominate the PL at high magnetic field. However, each inter LL transition PL peak consist of overlapping broad and sharp peaks, shown in Fig.5-6. The shar p peaks are believed to be ASE or SF and their linewidth is determined through homogeneous broadening, since the emission concentrates around a narrow frequency. We fit the field dependent PL strength of 0-0 LL transitions with a combination of Gaussian function (for inhom ogeneous broadening line width) and Lorentz function (for homogeneous broade ning line width) given below. Gaussian function 2 0) exp( ) (w A I 5-28 where 1.386 w is the FWHM (full width at half maximum) linewidth, 0 is the center frequency of PL transition. Lorentzian function

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118 ) ) ( ( ) (2 2 0w w B I 5-29 where w is the FWHM and 0 is the center frequency of PL transition. The fitting results of sharp peak emission strengt h (black dot) and linewidth (red dot) of PL from 0-0 LL transitions vs. the ma gnetic field strength are shown in Fig.5-5 (c). In Fig.5-7(a) at a fixed magnetic field of 20 T, the PL spectrum of interband LL transition vs. excitation laser fluence is plotted. It is observed that below certain laser fluence (0.01 mJ/cm-2), only broad PL peaks with linewidth (~9 meV) exis t, but with the increasing of lase r Fluence, a sharp peak starts to emerge on the high energy side of broad peak At the highest excitation laser fluences, the sharp peak dominates the PL emission spectrum. With the same fitting procedure as used for the magnetic field dependent PL spectrum, laser flue nce dependent emission strength and linewidth of sharp PL peak from interband 0-0 LL tran sition are obtained and shown in Fig 5-7(b). Identical field and laser fluence dependent PL spectra are seen when collecting from the center fiber above the pump spot, i.e., out of plane, although at a much lower signal level (~1/1000). Also, increasing or decreas ing the pump spot size result ed in the emergence of sharp PL features in the spectra at a given fluence. T hus, the observed behavior is not due to a spatially or spectrally inhomogeneous distribution of carriers. Comparing the fitting results in Fig. 5-5(b) and 5-7(b), we can see similar patterns in curves of magnetic field or laser fluence depende nt emission strength and linewidth. There are a few regimes in the two set of curv es. First, below 12 T (or 0.01 mJ/cm2), narrow emission is not observed. In the range 1 2 Tesla or (0.01.03 mJ/cm2), the narrow peak signal strength S grows linearly ( S~B or Flaser, see green lines)) with respect to both B and Flaser. Second, above 14 T (0.03 mJ/cm2), the emission strength S starts to show a supe rlinear increase (S ~ B3/2, see blue lines) with respect to B or Flaser. Above 0.2 mJ/cm2 (see Fig. 5-7(b)), the signal resumes a linear

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119 scaling. Also, the field and Flaser dependent PL linewidths curve (r ed circles) plotted in Figs. 55(b) and 5-7(b) reveal a rema rkable correlation with the fiel d and fluence dependent emission strength curve. In the linear regime, the linewidth decreases m onotonically both versus B and Flaser until the emission becomes superlinear at the threshold point ( B =12T and Flaser=0.01mJcm-2 ) where the PL linewidth begins to increase. At a 20 Tesla, setting the excitation spot di ameter at 0.5mm, 0.1m m and 3mm, we also measured on fluence dependent PL spectrum respectively. The fitting results of emission strength and linewidth at different excitation sp ot sizes are plotted inFig.5-8 (b) (c) and (d), narrow emission was observed, but both the integrated signal S and the linewidth exhibited qualitatively different scaling fo r each different spot size. The curve in Fig. 5-8(b) shows the increasing pattern with increasing laser fluence as shown before (See Chap. 5-4, II) however, the emitted signal S in (c) and (d) shows an almost linear relation with respect to the Flaser ( S ~ Flaser), and in both of (c) and (d), and the li newidth curves monotonically decreased with increasing fluence. 5.4.2 Single Shot Experiment for Random Directionality of In Plane PL With a optical Pockel cell, we are able to re duce the repetition rate of CPA laser to very low frequency (~20Hz) so that we can use the mechanical shutter (spe ed ~20 ms) on McPherson spectrometer to record the PL spectrum from a si ngle CPA laser pulse excitation. Also we collect the in plane PL with two optical fibers simu ltaneously (the fibers are mounted on QW edges perpendicular to each other (see Fig. 5-4)), then deliver them to spectrometer to resolve the PL spectrum propagating in different directions in QW This measurement is crucial for determining the correlation of the emission and single shot di rectionality of the in plane PL emission. Figure 5-4 presents the directionality measurements of the emission for a single pulse excitation. Figure 5-9 (a) illustrates a se ries of spectra upon single pulse ex citation at a given fluence in the

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120 superlinear emission regime ( Flaser 9.7 mJ/cm2, B =25 T) for a 0.5 mm diameter spot size. The spectra are collected through fibers on edge 1 (black) and edge 2 (red). We can see that the relative height between the red and black curve ch anges from shot to shot which indicates that the propagation direction of in plane PL could be different from pulse to pulse since the two optical fibers are mounted to co llect PL propagating in different directions. Since the two optical fibers have different collection efficiency, in Fig.5-9 (b) we di splayed the maximum peak height from each edge (normalized to 1.0) versus shot number for the pumping conditions shown in Fig. 5-10(a). The maximum observed emission strength in Fig. 5-9(b) fluctuates as much as 8 times the minimum value, far greater than the pump laser pulse fluctuation (~2%). This strong anticorrelation between signals received from different edges indicates a collimated but randomly changing emission direction from pul se to pulse, as expected for cooperative spontaneous emission. At a lower excitation fluence in linear increasing regime Flaser ~ 0.02 mJ / cm2 (obtained with a 3 mm spot), we also measured th e shot to shot PL spectra collect ed with the same configuration discussed above and show it in Fig 5-10(a). We observed qualitatively different emission strength behavior from high power excitation sh own in 5-10(a). In Fig.5-10(a), the emission strength of different shot from the same opti cal fiber do not fluctuate as much as high power excitation. In Fig.5-10(b) we can se e that the normalized (to 1) shot to shot PL emission strength at different collection direction are highly correlated instead of anti-correlated in high power excitation. Fig. 5-10(b) shows omnidirectional em ission on every shot, as expected for ASE or SE. 5.4.3 Control of Cherence of In Plane PL from InGaAs QW in High Magnetic Field As discussed in Chap. 5.3, the intensity of cooperative emission or ASE increases exponentially with respect to the active length of medium in the propa gating direction. We

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121 shaped the excitation laser pulse and probed the spatial and directi onal characteristics of the PL emission process (see Fig.5-11). Using a cylindrical lens to focus the excitation laser beam on the QW sample, we generate an elliptically sh aped spot (pencil geometry) for the excitation region. When the cylindrical lens is rotated, we change the active medium length of PL emission propagating towards the two right angle roof prisms. The emissi on strength collected from the prisms should change according to the rotation angle. We define the 0 degree angle at the point where in plane PL from edge one is at maximum. We measured the signal as a function of angle from 0 to 180 degree for Flaser ~ 0.02 mJ / cm2 and B ~ 25 T (shown in Fig. 5-12), from which we can see that the PL emission strength change dram atically with respect to the angle cylindrical lens. In the experiment, the maximum signal fr om edge one, which correspondent to activated length 1.5mm is at 90 degree, the minimum signal fr om edge one is at 0 degree, correspondent to activated length 0.5mm. The ratio of signal strength 20min max I Icorresponds to 20 ~ ) 5 0 / 5 1 exp(, which is consistent with exponential increasing of emission strength vs. activated medium length in ASE or SF.. 5.4.4 Discussion With the analysis of all the experimental result shown in Fig. 5-5, 5-7, 5-8 and 5-10, we found that for the interband 0-0 LL transition, the scaling of the emission strength S the linewidth evolution, and single shot emission directionality indicate the following evolution processes as excitation power Flaser and magnetic field strength B are increased: (i) In the lowdensity limit ( B< 12 T, Flaser < 5 J / cm2), excited e h pairs relax and radiate spontaneously through interband recombination. The emission is isotropic with an inhomogeneous Gaussian shape linewidth of ~9 meV. This broad spontane ous emission can be seen in both Fig.5-5(a) at low magnetic field and in Fig. 5-7(a) at low lase r fluence. (ii) At a critical fluence 0.01 mJ / cm2

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122 (at 20 T) and magnetic field B ~12 T (at Flaser ~ 0.6 mJ/cm2), a carrier population inversion is established with increasing magnetic field and excitation laser fluence, which increases the carrier density in QW (since N~Flaser and N~B see equation 3-14). In th is case, ASE develops, leading to the emission of amplified pulses. Fi g. 5-10 shows that ASE is simultaneously emitted in all directions in the plane. The reduction in linewidth with increasi ng fluence results from conventional gain narrowing discus sed in section 5-2-1, in whic h spectral components near the maximum of the gain spectrum are preferential ly amplified than components with greater detuning [see Figs. 5-5(a) be low 17 T and Fig.5-7(a) below 0 03mJ / cm2]. In this high-gain regime, the spectral width reduces to 2 meV (FWHM), still larger than 2 /T2. (iii) If we keep increasing the magnetic field and laser fluence, since the DOS and physical density in QW are sufficiently high at hi gh magnetic field (at B ~20T, N ~1012cm-2), the cooperative frequency c exceeds 2 /(T2T2*)1 / 2, the build-up time of cohe rence between transition di poles are shorter than the decoherence time. The e h pairs establish a macroscopic dipol e after a short delay time and emit an SF pulse through cooperative recombinat ion (or a sequence of pulses, depending on the pump fluence and the size of the pumped area). According to the theoretical expression of in cooperative emission regime, the linewidth of emission increase with increasing of laser fluence due to reduced pulse duration of cooperative emission, until eventually saturation (due to the filling of all available states) halts the further decrease in pulse dura tion (shown in Fig.5-7(b), above 0.2mJcm-2). The transition from ASE to cooperative emission at 0.03 mJ / cm2 at 20 Tesla is shown in Fig. 5-7(b), we can see that the linewidth of emission starts to incr ease significantly, which is consistent with increasing with increasing of carrier density (predicted in Eq. 5-29).

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123 In ASE, the spontaneous emission is amplif ied during propagation in certain direction. However, since there are many spontaneous emissi on photons propagating in different directions with subsequent amplification, we observe that in a single shot measurement, ASE emission distribute in all directions. Signi ficantly, we find that unlike ASE, which should be emitted in all directions with the same intensity [see Fig. 5-10( b)], in this super linear regime the initial quantum fluctuations grow to a macroscopic le vel to establish cohere nce and lead to strong directional fluctuations from shot to shot [see Fig. 5-9(b)] This is consistent with the random direction distribution discu ssed in Chap5, 5.2.1 a. The linear scaling of linewidth vs Flaser above 0.1 mJ / cm2 is a combined result of absorption sa turation of the pump and saturation of SF emission. As discussed in Chapter 5, the intensity of cooperative emission increasing super linearly with respect to increasing of carrier density ( I ~ N3/2). Since the carrier density is proportional to Flaser or B we should expect observe I~B3/2 or I~F3/2 laser in the experiments. However, since the data was collected in a time-int egrated fashion with spectromet er and CCD, we cannot directly probe the peak SF intensity scaling mentioned be fore because the SF emission is on the order of hundreds femtoseconds. However, there are two lin es of evidence indica ting that the observed superlinear scaling is related to the formation of multiple SF pulses from the 0-0 LL transition. The superlinear increase for the 0-0 LL emissi on is accompanied by an emission decrease from higher LL s, indicating a fast depletion of the 0-0 level through SF followed by a rapid relaxation of e h pairs from higher LL s and subsequent reemission. Also, in the single pulse measurements shown in Fig. 5-9, data shows that the PL emissi ons collected from two fibers on different edges of QW sample are either correlated or anticorre lated in roughly equal proportion. This result indicates that fast re laxation from higher LL s refills the 0-0 LL resulting in a second pulse of SF

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124 emission in a random direction. On average, the two SF pulses in one excitation pulse are collected in two different edge takes 50% shots, and for the ot her 50% shots, the two SF pulse from one excitation go to the fiber on only one edge. This is in qualitative agreement with observations, in which 50% shots are co rrelated and 50% ar e anticorrelated. One could argue about weather the observed emission characteri stics are consistent with pure ASE (lasing), but this can be ruled ou t by examining the excitation power dependent experiments at 20 T at different excitation spot sizes. In Fig. 5-8( b), (c) and (d) three spot sizes 0.5 mm, 0.1 mm and 5 mm are selected for the ex periments. We can see that, only in the S vs. Flaser curve with excitation with 0.5mm spot size, lin ear and super linear in creasing behavior (the signature of cooperative emission) emerge. Also a gain region of 0.5 mm is consistent with the theoretical predication of coherent length) / ( ~SE SF SF cI I Ln c L which is found to be a few hundred micrometers. However, in the S ~ Flaser curve with 5mm excitation spot size, we only observe linear increasing behavior this is a typical ASE process, also the linewidth of the PL emission keeps decreasing with increasing of Flaser,, which is the gain narrowing effect in ASE. In the curve with excitation spot 0.1mm, we can see that the li newidth decreases up to certain Flaser,(~0.6mJcm-2), then it stop decreasing. Also we can see that the emission strength S is neither linearly nor superlinearly increasing with Flaser, increasing. The PL emission with 0.1 mm excitation spot might be a combination of ASE a nd SF or early stage in SF. In the case that the excitation spot size is either much larger or much smaller than the coherent length, and none optical cooperative emissi on signature is observed. We can conclude that collimated, randomly directed emission and superlinear scaling are observed only when the pumped spot is 0.5 mm, appr oximately equal to the theoretically

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125 predicted coherence length for SF emission in QWs They are not observed for 0.1 and 3 mm spot sizes. Finally, contrary to popular opinion in th e quantum optics community, pure SF does not require a rod like geometry. As shown in ref. [ 119], cooperative recombina tion is not constrained by the geometry of the excitation region, omnidi rectional superfluorescent emission has been observed in cesium. Moreover, the disk-like geomet ry of the pumped active region allows us to observe the key evidence for SF, namely, str ong shot-to-shot fluctuations in the emission direction. Previous experiments almost exclusiv ely employed a rod-like geometry, in which the only direct signature of SF is the macroscopic fluctuations of the delay time of the SF pulse and pulse duration. In a semiconductor system the SF pulse durati on and delay time for cooperative emission would be manifested on the ps and sub-ps scale and we need to employ ultrafast spectroscopic method such us pump probe spectroscopy, time resolved upconversion PL spectroscopy and time resolved PL spectroscopy with a streak cam era to observe these time parameters. Those experiments are underway at present. 5.5 Summary In this chapter we have reported on a se ries of experiments to generate SF in semiconductor quantum wells. Excited with high peak power CPA laser, we observed extraordinarily strong in-p lane PL emission from InxGa1-xAs/GaAs multiple quantum wells at high magnetic field. With increasing carrier dens ity, there are three regimes in emission from the interband 0-0 LL transition, spontaneous emission, amplified spontaneous and cooperative superfluorescent emission. In the SF regimes, all the experimental observations are in consistent with the optical signa tures of cooperative emission process.

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126 Table 5-1. Some experimental conditions for observation of super fluorescence in HF gas. The time unit is nanoseconds, L is th e length of activated gas, and d is the size of laser beam. Active length (cm) d ( m) T2* E R D L 5.0 432 50.170.156-2035 3.6 366 320.070.155-35180 2.0 273 50.350.126-2545 Reprint with permission from M. Gibbs et al ., Phys. Rev. Lett. 39 (1977), page 549.

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127 Table 5-2. Characteristics of SF emitted from InGaAs QW in high magnetic field Characteristics Superfluorescence(SF) Amplified Spontaneous Emission(ASE) Shot to shot random directionality Yes No Pulse delayed by d (~10ps) Yes No Emission linewidth increase with carrier density N Yes No Emission strength increase with excitation density Superlinear (~I1.5) Linear (~I) Threshold behavior Yes Yes Exponential growth with area (~exp(gL)) Yes Yes

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128 (a) (b) Figure 5-1. Spontaneous emission and amplifie d spontaneous emission process of a two level atom system.(a) Spontaneous emission (SE); (b) Amplified spontaneous emission (ASE).

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129 (a) (b) (c) (d) Figure 5-2. Four steps in the formation of collective spontaneous emission--SF in Natom system. (a) N atoms are excited by light absorption;(b) After excitation, the dipoles of the N two level atom randomly di stribute in all dire ction; (c) Electric dipoles are aligned and phase matched; (d) All the electric dipoles emit simultaneously a burst of coherent light pulse.

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130 Figure 5-3. Configuration for collection of in plane PL from InGaAs multiple QW in high magnetic field.One right angle prism is pos itioned at the edge of QW sample to collect in plane PL.

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131 Figure 5-4. Configuration for a single shot experiment on InxGa1-xAs Multiple QWs.

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132 (a) (b) (c) Figure 5-5. Magnetic field dependent PL spect rum and fitting results of in plane emission. (a) Field dependent PL emission spectru m from edge collection; (b) Field dependent PL emission spectrum from cente r collection and (c) Fitting results of emission strength and linewidth.

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133 Exp. Lorentzian Gaussian Figure 5-6. Fitting method to determine line wi dths using a Lorentzian and Gaussian function for the sharp peak and broader lower-ener gy peak.The broad peak (blue line) is Gaussian shape originates from spontaneous emission, while the sharp peak (pink line) is Lorentz shape originates ASE or SF.

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134 (a) (b) Figure 5-7. Excitation power dependent PL spec trum and fitting results of in plane emission. (a) excitation power dependent PL em ission spectrum at 20 Tesla and (b) fitting results of emission strength and linewidth.

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135 Figure 5-8. Excitation spot size effect on the in plane PL emission.Emission strength and linewidth of the narrow peak from the 0-0 LL versus (a) B and (b), (c), (d) Flaser for different pump spot size at 20 Tesla. Both B and F are on log scale.

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136 Emission Strength (a.u.) Edge 1 Edge 2#1 #6 1.31.4 Energy (eV) #16 #11 1.31.4 (a) 010203040 Edge 1 Edge 2Emission Strength (a.u.) Shot Number(00) (b) Figure 5-9. Single shot random directionality measurement of in plane PL emission excited with one CPA pulse in SF regime.(a) F our representative emission spectra from edge 1 (black) and edge 2 (red) fibers, ex cited from single laser pulse and measured simultaneously. (b) Normalized emission strength from the 0th LL versus shot number in the SF regime.

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137 Emission Strength (a.u.) Edge 1 Edge 2#1 #6 1.31.4 Energy (eV) #16 #11 1.31.4 (a) 010203040 Emission Strength (a.u.) Edge 1 Edge 2Shot Number (b) Figure 5-10. Single shot random directionali ty measurement of in plane PL emission excited with one CPA pulse in ASE regime.(a) Four representative emission spectra from edge 1 (black) a nd edge 2 (red) fibers, excited from single laser pulse and measured simu ltaneously (b) Normalized emission strength from the 0th LL versus shot number in the ASE regime.

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138 Figure 5-11. Configuration of cont rol of emission directionality in InxGa1-xAs multiple QW with cylindrical lens.

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139 Figure 5-12. Control of coherenc e of in plane PL emission in InxGa1-xAs QW. Edge emission strength of 0-0 LL transition from two or thogonally aligned fibers vs. the rotation angle is the angular separati on between the logner beam axis and the direction of the edge 2 fiber as shown in the Fig. 5-12..Emission strength of the 00 LL is plotted for edge 1(black) and edge 2 (red) as a function of angle.

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140 CHAPTER 6 CARRIER DYNAMICS OF ZINC OXIDE SEMI CONDUCTORS WITH TIME RESOLVED PUMP-PROBE SPECTROSCOPY 6.1 Introduction The II-VI group wide band gap semiconductor all oys such as ZnO, ZnMgO are recognized as important materials for potential applications in optoelectronic devices in the ultraviolet spectral range as well as for in tegrated optics substrates. Sin ce the exciton binding energy of ZnO is 60mev [122-126], which is very hi gh compared to GaN (~30mev) [127] or GaAs(~8mev)[128], the radiative el ectron hole recombination proce ss in ZnO is even visible at room temperature[129]. Due to these unique pr operties, ZnO semiconductor materials are of interest in applications such as UV light emitting diodes (LEDs) and laser diode (LDs) [130]. Also, ZnO crystal is excellent substrate materi al for growing another important wide band gap semiconductor [131-132], GaN, since the lattice mismatch is rela tive small. For ZnO we have =b=3.249oA and c=5.206oA, while for GaN, we have a=b=3.189oA and c=5.185oAThe dynamics of carriers in ZnO semiconductor, which are critical for high speed electro optical device design, have recently been inve stigated by ultrafast time-resolved pump-probe spectroscopic method or time resolved photolum inescent spectroscopy [133-134] with above band gap excitation. In our study, we have performed a comprehensive set of measurements on bulk ZnO, ZnO epilayers and nanorods. We measured the reflecti vity and PL spectra of bulk ZnO, ZnO epilayer and nanorod from 4.2 K to 70K. In order to under stand the excitonic states in ZnO materials, magneto reflection and PL spectra are also meas ured at 4.2K. Compared with previous studies [135], we identify and label th e excitonic state on each spec trum. Via spectrally resolved degenerate pump-probe spectrosc opy, we measured the time reso lvd differential reflectivity

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141 (TRDR) of the A and B excitonic states in bulk ZnO, ZnO epilayer and nanorod. We find the life time of the A exciton (A-X) is approximately 130ps and while the B excit on (B-X) is ~ 45ps at for bulk ZnO at 10 K. We also measured the te mperature-dependent TRDR of A-X in bulk ZnO up to 70K, we find that the life time of A-X is still around 100ps, which indicates that relaxation processes do not change signifi cantly at higher temperatures. This is associated with the properties of neutral donor bound X (D0X). The life time of A-X (50ps) and B-X(20ps) in ZnO epilayer are very different from bulk ZnO, wh ich is caused by different neutral donor bound X (D0X) states in epilaer. The relaxation process of ZnO nanorod is fitted with stretch exponential decay curve, indicating different relaxation dyna mics of Xs from bulk ZnO and ZnO epilayer. The coherent process in a very short time ra nge (~2ps) on the TRDR of A-X in bulk ZnO is analyzed with convolution of probe pulse with Gaussian function shap e and carriers response with exponential decay curve. 6.2 Background of Crystal Structure and Band Structure of ZnO Semiconductors ZnO crystallizes stably in a wurtzite structure with C6v point group symmet ry. This typical semiconductor lattice structure is shown in Fig. 61. In the x-y plane, th e atoms in a unit cell form a hexagon, and the zinc atoms form hexa gons and oxygen atoms form hexagons stack along the z-axis, called (0001) direction. In the x-y plane, since ZnO possesses he xagonal symmetry, many physical and optical constants are isotropic, while along the z-direction they are di fferent. However, we can use a, b and c unit vectors to label the unit cell of ZnO, where c is along z-axis and a, b are in x-y plane. In the study of optical properties of ZnO semi conductors, the polarizat ion of absorption or emission light are very critical to probe since th ey are associated with the selection rules of transition and band structure symmetry. We define linear polarization parallel to the c axis of

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142 ZnO and linear polarization perpendicular to the c-axis. The geometry and definitions of polarization with respect to ZnO un it vectors are plotted in fig. 6-2. As mentioned in chapter 3, a Hamiltonian with C6v symmetry will couple the s states and form lowest conduction band and px, py and pz states into three valenc e bands. The band structure of ZnO semiconductors is shown in Fig 6-3. At the center of Brillouin zone, the conduction band is s -like, which has 7 symmetry, while the p -like conduction band splits in to three doubly degenerate bands due to spin-obit ( so) and crystal-field interaction ( cr). In the valence bands, the top valence A band has 9 symmetry while the B and C bands have 7 symmetry. The excitonic states formed with electron in conduction band and holes in A, B and C valence bands are called A-X and B-X respectively. In Fig. 6-3, the total angular momentum ( J=L+S L is orbit momentum and S is spin momentum) of each points are shown. The A, B and C valence band states at point can be expressed as: 2 1 3 1 2 1 3 1 2 1 2 1 : 2 1 3 2 2 1 6 1 2 1 2 3 : 2 1 2 1 2 3 2 3 : Z iY X C Z iY X B iY X A 6-1 We can see that each valence band at point are degenerate, each band will split in to doublet states (spin up+ and spin down-) in magnetic field. 6.3 Valence Band Symmetry and Selection Rule s of Excitonic Opti cal Transition in ZnO Semiconductors The optical properties of bulk ZnO have been studied for over 40 years, and for the most part are well understood. However, there remain s ambiguity and controversy in the assignment of symmetries of the A, B and C valence band states. In Thomas and Rodinas assignment[136137], the symmetry of A, B and C valence bands are 7, 9 and 7 since they considered that Pz

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143 component is mixed into the A band, whic h results the revers e of the order of 7 and 9 in typical II-VI group semiconductors. In contrast, after caref ully studying of the absorption, reflection and PL spectra as well as the Zeeman splitting of excitonic states of ZnO semiconductor [138], Reynolds have concluded that the order of t op two valence bands in ZnO do not reverse. Therefore, in Reynoldss assignment of the orde r of valence bands in ZnO semiconductor, A, B and C bands have 9, 7 and 7 symmetry respectively. In this case, A band is pure Px and Py and the only optical transition from A band to c onduction band optical transition is expected to be polarization (c k // and c E k is the direction of light propagation, c is c-axis). For the B band, the optical transition could be either polarization (c k // and c E ) or polarization (c k and c E//). Based on group theory [18], the symmetry and se lective rules of optical transition between conduction band and A, B and C valence bands in ZnO semiconductor are given as follows: A-X: 5 6 7 9 6.2(a) B-X: 2 1 5 7 7 6.3(b) C-X: 2 1 5 7 7 6.2( c) where 5 is allowed in polarization and 1 is allowed in polarization. The optical transition 6 and 2 are prohibited and 1 is very weak [139]. In order to resolve the controversy of valence band ordering, a magnetic field was employed to observe Zeeman splitting of different optical transitions, since the Zeeman splitting for 7 9 transition and 7 7 transitions are very different-6 is a doublet and splits into two in magnetic field while 1 is a singlet and does not sp lit in a magnetic field. Reynolds clarified the symmetry of the t op valence band by studying the split ting behavior of PL emission

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144 line from A-X in magnetic filed at configuration [ 139]. In this thesis, we will consider the order of valence band according to the Reynolds assignment. 6.4 Impurity Bound Exciton Complex (I line) in ZnO and Zeeman Splitting In bulk semiconductor materials there are many t ypes of defects and lo calized states. Some of these states can bind excitons, resu lting in a bound excito n complex (BEC). Conceptualizations of an exciton bound to an ionized donor (D+X), a neutral donor (D0X) and a neutral acceptor (A0X) are plotted in Fi g.6-4. The binding energy E of these bound excitons usually increases a ccording to [40] X A X D X DE E E0 0 6-3 These BECs have many emission lines in the PL spectrum of bulk ZnO, termed I lines. Also, when the free excitons or BEC optical transi tions couple with longitu dinal optical (LO) phonon, the phonon replica can be observed in the PL spectrum at energy position LOm E E ', 6-4 where E is the positions of phonon replica, E is the energy of optic al free exciton or BEC transition which is coupled with LO phonons, m is an integer, and LO is energy of LO phonon. However, these phonon replica emission peaks are usually much weaker than the BEC emissions or free X emissions. In a magnetic field, a quantum state with spin will split into two states, spin up and spin down. The energy splitting between the two states are called Zeeman splitting. However, in the case of free excitons or BEC, both electrons and holes can be involved in Zeeman splitting, which makes the interpretation of energy splittin g of ZnO semiconductor in magnetic field more complicated than free electrons. Zeeman splitting in ZnO can be express as

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145 B g Eexc 6-5(a) where is Bohr magnon, B is magnetic field strength and gexc factor is Lande factor and can be written as: h e excg g g 6-5 (b) For an electron, the g factor is isotropic, while for a hole the g factor is anisotropic ( g// and g), and typically g is nearly zero [136]. In a bove expression, // means the c -axis of ZnO is parallel to the magnetic field B and means the c -axis is perpendicular to the magnetic field. In the case of BEC, the Zeeman splitting is qualitatively different than free excition Zeeman splitting since the spli tting of ground states of D0 and A0 has to be considered in addition to the splitting of electron and hol e in an exciton. Rodina and Reynolds [139] have studied the splitting of BEC in ZnO and the results are shown in Fig. 6-5. As shown in figure 6-5, the excited state of D0X consists of a donor defect, two electrons and one hole, with the two electrons spins antipa rallel. The Zeeman splitting of the excited state is determined by the anisotropic hole effective g factor, while the Zeem an splitting ground state D0 is given by the effective g factor of electron ge. Therefore the splitting of optical transition of D0X in the Faraday geometry ( B // c and k // c ) (see Fig.6-6) is given by B g g Eh e ) (// 6-6(a) and the splitting in Voigt geometry ( B c and k // c ) (see Fig.6-6(b) )is B g Ee 6-6(b) Also the Zeeman splitting should be linear in magnetic field. In the case of the acceptor bound exciton A0X, the Zeeman splitting has similar form.

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146 6.5 Samples and Experimental Setup for Reflection and PL Measurement The ZnO samples we used for magneto optical spectroscopic studies are bulk ZnO (grown by MTI Crystal Co.), ZnO epilayers (grown by Davi d Nortons group at University of Florida), and ZnO nanorod grown in GIST in South Ko rea). The size of bulk ZnO is 5x5x0.5mm and the orientations of the crystals are c -plane ( c -axis perpendicular to the plane) or a -plane ( a -axis perpendicular to the plane and c -axis in the plane) configurations. The bulk ZnO crystal was grown with hydrothermal method. The 400nm thick ZnO epilayer samples were grown on a c plane sapphire substrate via the MBE method a nd the self-assembly Zn O nanorod sample with rod diameter 8nm is grown with laser deposi tion. All the ZnO samples were nominally undoped. We measured the reflection spectrum of all the ZnO samples with polarized light to identify the excitonic states. We used a Deutri um lamp with the output polarized using a GlanLaser polarizer. In the reflection spectrum measurements, ZnO samples were put in a cold finger style optical cryostat, in whic h the samples can be cooled down to 4.2K with liquid helium. In magneto-optical spectrum measurements, we used the cw magneto-optical facility at NHMFL shown in Fig.2-2, 2-3. The ZnO was mounted inside the he lium tail of a Janis cryostat and cooled down with helium exchange gas. The light was delivered to ZnO sample through multimode optical fiber, and the reflection and PL emission were collected with another multimode optical fiber. Here, we used a UV Xenon lamp for measuring the reflection spectrum and a He-Cd laser (325nm wavelength) for exciti ng the sample to measure the PL spectrum. Both the reflection light and PL emission were delivered to a 0.75m McPherson spectrometer and the spectrum was recorded with a charge-c oupled device (CCD). In the temperature dependent measurement, the sample temperat ure was measured and controlled by a Cernox sensor, a Cryocon temperature controller and a heater with 50 W maximum power output.

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147 6.6 Results and Discussion In figure 6-7, the reflection spectrum of a-plane bulk ZnO at 4.2K obtained using and polarized light. The excitonic opt ical transitions obey the trans ition rules listed in equation. 6-2, where A-X ( 9), B-X ( 7) and C-X ( 7) are activated in polarized light and C-X ( 7) is activated only in polarized light. However we cannot spec ify the exact energy positions of free excitons peaks since the complexity in reflection spectrum (see Chapter 2). In figure 6-8(a), the magneto-PL spectrum of c -plane bulk ZnO is plotted for the Faraday configuration ( B // c k // c, E c ). We can see that the PL emission feature is a sharp peak sitting on the top a broader and weaker peak, which cau sed by inhomogeneous broadening. There is no significant magnetic splitting obs erved, although the sharp PL peak becomes broader (possibly due the onset of splitting) and the PL intensity becomes lower with the increasing of magnetic field strength. Figure 6-8(b) shows the PL spectru m of the same sample at Voigt configuration ( B c k // c, E c ). It is clearly evident that the sharp PL peak split linearly into two peaks with the increasing magnetic field. The energy position vs. magne tic field of the peaks is plotted in figure 6-8(c). This is Zeeman splitting and will be disc uss further in the following section, however, since we use multi-mode fiber to delivered light no polarization information can be obtained from the two PL peaks and the sp in states can be resolved. In order to understand the PL emission spectrum, we plot the reflection and PL emission at zero field in figure 6-9(a). We can assign the PL emission peak at 3377 meV to the recombination of free A-X, indicated by an arro w in the figure. The other PL peaks at lower energies are assigned as emission from im purity bound A-X, the strongest bound exciton PL peak is at 3360 meV and has been re ported to be neutra l donor bound exciton (D0X) [140].

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148 In figure 6-9(b), the reflection and PL emissi on spectrum of the c-plane bulk ZnO in both Faraday and Voigt configurations at 30 Tesla are plotted. From this data, we can conclude that the A-X and its bound state do not split in Faraday geometry while they split into two peaks in Voigt geometry. At 30 T, the splitting of PL peaks from A-X donor bound state is ~3.4 meV. The magnetic splitting of A-X and D0X can be interpreted with the splitting process shown in figure 6-5 and equation 6-6 as following. In the Faraday geometry, according to Eq. 6-6, the magnetic Zeeman splitting of A-X and D0X is determined by Lande factor gexc, which is gegh=0.7[16], therefore the Zeeman splitting at 30 Tesla is around 1.2 meV, which is smaller than the resolution of spectrometer and thus can not be observed with our spectrometer. However, in Voigt geometry the Lande factor gexc=ge, since gh=0, therefore the Zeeman splitting at 30 T is ~3.38 meV, which is in agreement of our observation 3.08 meV. In Fig.68(d), we plot the experiment al and calculated results of E vs. B the results are in good agreement if we take into consideration that the resolution of spectrometer is around 1meV. This agreement strongly proves that the dominant PL emission peak comes from neutral bound exciton. In the case of the ZnO epilayer sample, we plot the reflection and PL spectrum at zero fields in figure 6-10(a), we can clearly resolve the A-X and B-X in the reflection curve. In the PL spectrum we observe a strong emission at 3355 meV, which is also from bound exciton transition, however the PL peak is asymmetric and has a long tail at the low energy side, and in addition the PL linewidth is much broader (5~6 meV) than the bulk ZnO (2 meV). All of these observations imply that the optical quality of this ZnO epilayer is not as good as bulk ZnO, with more defect states present which cause more inhomogeneous broadeni ng and carrier trapping below the bandgap, and result in the PL linewidth broadening and an asymmetric line shape. At

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149 3285 meV, we observe a PL emission peak due to LO phonon coupled with bound exciton transition, since the LO phonon energy is 70 meV in ZnO. Due to the fact that the PL emission linewidth is larger than the predicted Zeeman splitting, we cannot resolve and observe the PL peak splitting in neither Faraday geometry nor Voigt geometry in this ZnO epilayer sample as shown in Fig.6-10(b). 6.7 Time Resolved Studies of Carrier Dynami cs in Bulk ZnO, ZnO Epilayers, and ZnO Nanorod As introduced in chapter 2, time resolved spectroscopy is a very important tool for understanding the dynamics of carri ers and excitons in semiconducto rs, critical for applications in electrooptical device. From Chapter 2, the changes to the dielectric fuction are given by [141] i L i i Lm e t N t2 0 2) ( ) ( 6-7 Where L is the laser frequency, ) ( t Ni is the carrier density in the ith energy band and mi is the carrier mass of the ith band. Since ZnO is a wide bandgap semiconductor, the high-frequency limit ( Lt >>1) is satisfied, ther efore the differential reflectivity is proportional to the change in carrier density in each energy band divided by the mass of the band, summed overall bands, which is shown in equation 6-8, i i im N R R ) ( ~. 6-8 This shows clearly that the diffe rential reflectivity measurements effectively probe the changes in carrier density in different ZnO energy bands. In the recombination of an electron and hole pair, both radiative and nonradiative recombination processes are usua lly involved, and the rate equati on can be expressed as follow

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150 ve nonradiati radiativeA A dt dN N 2 11 6-9 where N is the carrier density, radiative and ve nonradiati are radiative and nonradiative relaxation times, 2A2A is corresponding efficiency. In radiativ e recombination, photons are emitted as the carriers recombine to conserve energy, while in nonradiative processes, electrons and holes recombine through emission of acoustic phonons. As we have seen that bulk and epilayer ZnO exhibit different reflect ivity and photo-excited emission characteristics due to th e presence of defect states, we now turn to investigations of how those differences impact dynamical carrier processes. We measured the time resolved differential reflectivity (TRDR) spectrum of Zn O semiconductors, includi ng bulk with different orientation, c -plane epilayer and nanorod samples with 8 nm rod diameters. Since the absorption coefficient of ZnO is very high, it is very difficult to get good transmission signal from thick samples, we use reflection geometry to get TRDR signal. The experimental setup for measuring the TRDR of ZnO semiconductors is shown in figure 6-11. We used ultrafast laser pulses 150fs in duration at a wavelength of 730 nm from a Coherent Mira 900-F laser system with 76 MHz re petition rate. The laser beam was focused onto a nonlinear -barium-borite (BBO) crystal to freque ncy double the pulses into the near UV around 365nm via second harmonic generation (SHG). The UV laser pulses were then split into pump and probe beams using a sapphire plate. Both the pump and probe beam propagated through waveplates and Glan-Laser polarizers to make them parallel or perpendicularly polarized before they were focused down to 50 m on the ZnO samples, mounted in an optical cryostat. Liquid helium flows into the cryostat during th e measurements, by which we can cool down the ZnO samples to down to 4.2K and reduce the th ermal broadening effect and phonon effects. The

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151 pump beam was time delayed with respect to pr obe beam using a Newport stage controlled by computer. To obtain the best si gnal-to-noise ratio, the pump a nd probe beams were chopped with a differential frequency f1 = 2KHz and f2 = 1.57KHz, and the probe reflectivity signal was detected using photodiode via a lock-in am plifier demodulating the signal at f1-f2. 6.8 Experimental Results and Discussion 6.8.1 Relaxation Dynamics of A-X and B-X in Bulk ZnO In figure 6-12, the TRDR at 10K are plotted for A-X and B-X in a -plane bulk ZnO semiconductor, both the probe beam and pump beam set to polarization (perpendicular to caxes), in which A-X and B-X are optically activ ate. The DR curve decays exponentially. We fit the two curves exponentially with equati on 6-9 and obtain the following results, psAX10 130 andpsBX1 45 The sharp peaks in figure 6-12(a) and (b) at t =0 ps most likely arises from a coherent artifact due to the collinearity of the pump and probe polarization. More discussion about this fast relaxation process will be given in the following. However, the relaxation time is much smaller than previous report for free A and B excitons [142], reported 1ns. This strongly suggests that in these samples, the A and B excitons are mainly bound to an impurity state, which makes the D0X dominate the relaxation process instead of free exciton recombination. This agrees well with the PL data (f igure 6-9) in which the D0X is three orders stronger than free A-X. In this case, 1Ais much smaller than2A, which indicates that the radiative recombination can be neglected compared to nonradiative processes in the exciton relaxation process. In figure 6-14, we plot the TRDR spectrum of AX in c-plane bulk ZnO at different temperatures up to 70K, where the laser wavelength is tuned to resonantly probe the A-X as the

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152 temperature increases. The artifact observed in figure 6-12 does not show up here because the pump and probe laser beam are orthogonally polarized. We also obs erve mono-exponential decay of DR in this figure. The fitting results of the relaxation time arepsAX10 130 which do not change significantly with temperature up to 70K and imply that the A-X relaxation process is dominated by a bound to impurity state instead of radiative re combination up to 70K, since the binding energy between neutral donor and an exiton is around ~10meV [18], which makes it difficult to break them at low temperature. In semiconductor, immediately af ter the carrier are excited with coherent laser light (pump beam), the carriers preserve the coherence genera ted with laser beam in a very short time (~ps) [143], if the probe beam arrives during this carr ier coherent status, strong interaction will be expected between the coherent carriers and cohere nt light, which result in the sharp feature in Fig. 12. In this case, the actual signal that we acquired is the convoluti on of probe pulse and carrier decay, which are presumed to be Ga ussian function and exponential decay function respectively. The convolution result is given as: 2 2 1 )[ 2 exp( 2 ) (2 2t erf t A t S 6-10 Where is the exponential decay time and 2 is the FWHM of th e Gaussian function. Fig. 6-13 shows the fitting of th e fast relaxation cure with th e convolution function 6-10, we can see that the pulse width is around 0.5ps and the coherence exponential decay time is around 1.4ps. 6.8.2 Relaxation Dynamics of A-X and B-X in ZnO Epilayer and Nanorod In figure 6.-15, TRDR spectra of AX and BX in ZnO epilayer at 4.2K are plotted. It is clearly resolved that the carriers populate on BX decay mono-exponentially. The fitting result of

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153 BX relaxation time is BXps251.however the A-X shows a stretched exponential decay process, which is described by 0exp I t A In 6-11 where is the decay time and n<1 is stretched factor. With this function, the fitting results of A-X relaxation in ZnO epilayer are n=0.9 and =50ps.These exciton relaxation times are much sm aller than the bulk ZnO, which indicate that the density of defect states in the ZnO epilaye r sample are more than that in the bulk ZnO sample. Also, by comparing the carrier relaxation time, we might expect that the defect state dominates in epilayer sampler should be different from that in bulk sample since the relaxation are quite different. These can be convinced in the PL spectrum in figure 6-10, in which we can not see the free X emission, most Xs are bound to defect states and emit photons at 3355 meV in stead of 3360 meV in bulk ZnO samples. In figure 6-16, the TRDR of ZnO bulk nanor od is shown. The excitation and probe light energy is 3416mev, which is supposed to be ab ove the ZnO bandgap. We can see that the TRDR cure of ZnO bulk nanorod sample decay stretche d exponentially. This curve is fitted with 6-11. The fitting results are =17ps and n=0.65. The stretched exponential relaxation is su mmation of distribution of independent exponential decay relaxations and is indication that there is an inhomogeneous distribution of recombination times. It is reported in many semic onductors material especially in nanostructures [144-145]. Three mechanisms [146-147] are prop osed to interpret th e stretched exponential decay. The distribution in lifetime is a result of vary ing carrier localization such that carriers can escape from one area of sample to ot her area and recombine nonradiatively.

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154 The migration of excitons between distorted na nostructures is possible, which result in the capture and delayed released of excitons. Distribution of the lifetime in PL at a single wavelength could be explained by the distribution of the nanocrystal shapes in a given area. From the above explanations, we found that th e stretched exponential is mainly caused by the either trapped of carriers, carrier hopping between nanostructures or different size of nanostructures. We can see that the stretched exponential d ecay of exciton in ZnO epilayer and nanorods indicate that the sample might have many def ects states, which traps the carriers, the nanorod sample might have different size effect and al so the carriers in nanor od might migrate between rods.

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155 Table 6-1. Some parameters of ZnO bulk semiconductors Point group 6mm(C6v) (Wurtzite) Lattice constants at room te mperature a=3.250, c=5.205 nm1 Electron mass 0.28 m1e Hole mass 1.8 me1 Bandgap energy at room temperature 3.37 eV1 Exciton binding energy 60 meV1 Melting point 2250 K1 LO phonon 70 mev1 1 Reference[10]

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156 Zn atom on the top layer Zn atom on the bottom layer O atom y x z Figure 6-1. Top view of the la ttice structure of a wurtzite ZnO crystal. In the x-y plane, ZnO has hexagonal symmetry along the z-axis. In z-axis direction, Zn atoms are on the top and bottom layers, O atoms layer is between the two Zn atom layers. Also, another O atoms layer (not shown) is on th e top of top layer of Zn atoms. In the (0001) direction, hexagonal sy mmetry is along the z-axis.

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157 Figure 6-2. The orientati on of light polarization with respect to the ZnO unit cell. The polarization is defined as perpendicular to c-axis and polarization is defined as parallel to c-axis.

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158 Figure 6-3. Band structures and symmetr y of each band of a ZnO semiconductor. At the center of the Brillouin zone, the conduction band has 7 symmetry, and for the valence bands listed as A, B and C from top to lowest, the symmetries are, 9 and 7 respectively. 9 7 7

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159 (a) D+X (b) D0X (c) A0X Point defect electron hole Figure 6-4. Schematic of types of impurity bound exciton complexes. (a) an ionized bound exciton (b) a neutral donor bound excit on (c) a neutral acceptor bound exciton

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160 (a) (b) Figure 6-5. Energy diagram of Zeeman splitting of neutral bound excitons in ZnO. (a) donor-bound exciton, (b) acceptor-bound exciton gh =0 (D0, X) (D0) ge=1.95 B C B//C +1/2 -1/2 +3/2 -3/2 gh=1.25 +1/2 -1/2 +3/2 -3/2 gh =0 ge=1.95 (A0, X) (A0)

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161 Fig.6-6. Voigt configuration of c-plane ZnO in magnetic field.Faraday configuration is shown in Chapter 4.

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162 Figure 6-7. Reflection spectrum of a-plane bu lk ZnO semiconductor for different linear optical polarization at 4.2K. The upper curve is polarization and th e lower curve is polarization. The arrows point out the exciton ener gy position and the related symmetry.

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163 (a) (b) (c) (d) Figure 6-8. The magneto-PL spectrum of a and c -plane bulk ZnO sample and Zeeman splitting at 4.2K PL spectrum in (a) Faraday and (b) Voigt configurations, (c) The Zeeman energy splitting in Voigt geometry as f unction of magnetic field, (d) Zeeman splitting E vs. magnetic field, black dot is ex perimental result and red and blue line are fitting with g=1.95 and 2.0 respectively.

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164 3300335034003450 100 1000 10000 100000 ReflectivityPL FX3360mev 3377 mev D0X Energy (mev)PL IntensityAX (a) 330033503400 100 1000 10000 100000 Energy (mev)PL Intensity FX D0X AX (b) Figure 6-9. Comparison of re flection and PL spectrum of c-pl ane bulk ZnO. (a) reflection (black curve) and PL (red curve) at zero magnetic field, (b) reflection in the Faraday geometry (black curve), Voigt geometry (r ed curve), and PL in the Faraday (green curve) and Voigt (blue curve) configurations at 30 T.

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165 3250330033503400 100 1000 10000 100000 3285mevPL Intensity A-X B-X3355mev Bound X-LO PhononEnergy (mev)D 0 X (a) 32503300335034003450100 1000 10000 100000 PL Intensity BX AX Bound XEnergy (mev) (b) Figure 6-10. Comparison of reflection and PL sp ectrum of c-plane epilayer ZnO at 4.2 K. (a) reflection (black curve) and PL (red curve) at zero magnetic field, (b) reflection in the Faraday geometry (black curve), Voig t geometry (red curve), and PL in the Faraday (green curve) and Voigt (blue curve) configurations at 30 T.

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166 Figure 6-11. Pump-probe expe rimental setup for measuring TR DR of ZnO semiconductors. BS is beam splitter, WP is waveplate, G-L is Glan-Laser polarizer, PD is photodiode Dichroic mirror

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167 (a) (b) Figure 6-12. TRDR plots of a-plane bulk ZnO semiconductor at 4.2K (black dot) and exponential decay fitting line.(a) AX probe at 3375 meV, decay time 130ps, (b) BX, probe at 3387 meV decay time 45ps. Both of the inserts are TRDR spectra show fast decay in short time (~1ps ) range. The cure in (a) does not fit well with exponential decay due to alignment problems of optics.

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168 -0.6-0.30.00.30.60.91.21.5 TRDR-DR/R)Time Delay (ps) Figure 6-13. Fast decay in TRDR of A-X in a-plane bulk ZnO and the fitting with convolution of Gaussian function probe pulse and exponential decay response function. Fitting parameters are pulsewidth=0.5ps and response=1.4ps.

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169 020406080100120140160 10K 20K 30K 50K 70K Log(-R/R)Time Delay (ps) Figure 6-14. Temperature dependent TRDR of A-X recombination in c-plane bulk ZnO. Probe wavelength is tuned to the A-X resonant wavelength. The fitting results of decay time =130ps do not change significantly with the temperat ure increasing.

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170 -50050100150 0.005 0.01 0.015 0.02 Log(R/R)Time Delay (ps) (a) 020406080100 Log(-R/R)Time Delay (ps) (b) Figure 6-15. TRDR plots of excitonic recomb ination in ZnO epilayer for different exciton states. (a) A-X, probe tuned to 3375 me V (b) B-X, probe tuned to 3387 meV. Fitting result is shown with red line.

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171 04080120160200 1E-3 0.01 T=10K Log(R/R)Time Delay (PS) Figure 6-16. Experimental TRDR plot of Zn O nanorod sample at 10K and fitting result with a stretched exponential decay. Black dots are experimental results and red curve is fitting results with a stre tched exponential function. Fitting parameter are =17ps and n=0.65.01.

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172 CHAPTER 7 CONCLUSION AND FUTURE WORK In order to study the carriers dynamics of III-V group semiconductor quantum wells at high carrier density (~1012cm-2) and high magnetic fields, we have developed an ultrafast optics facility at the National High Magnetic Field Labo ratory, including an ultrafast chirped pulse amplifier, optical parametric amplifier, a nd a 17.5 Tesla superconducting magnet (SCM3) as well as the necessary cryogenic system and optical probes for both SCM3 and the 31 T Bitter magnet in cell 5. This unique facili ty provides us high power pulses (GW/cm2) in broad wavelength range (200nm to 20 m ) and high magnetic fields (up to 31 Tesla) to study the quantum optics of e-h pair in semiconductor quantum wells A detailed description of this facility was shown in Chapter 2. To understand the optical transmission and reflection spectrum of semiconductors, we gave a detailed description of th e optical response theory. In additi on, the detailed theory of the electronic states in semiconductor quantum well is given as well as the excitonic states and LL splitting in high magnetic field was presented. With these as a background, this dissertati on has presented a systemic spectroscopic study of magneto-optical properties of InxGa1-xAs/GaAs multiple quantum well in the low and high excitation regimes using CW light source high excitation domain with a high power ultrafast light sources at magnetic field up to 30 T. In low excitation regime, we can clearly reso lve the interband LL transitions originating from the same conduction and valence subba nds in the absorption spectrum of InxGa1-xAs/GaAs multiple quantum wells at 4.2K to 30 T. Anticrossing phenomena and dark excitonic states are shown between the traces of e1h1ns and e1l1ns magneto excitonic states Theoretical calculation shows that this larger splitting (~9 meV) doe s not arise from valence band complexity.

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173 In high excitation regime, we measured PL emission from InxGa1-xAs/GaAs multiple quantum wells excited with high power CPA pulses (~GW/cm2). We do not see Coulomb interaction-induced anticrossing between LL levels originating from heavy holes and light holes. Bandgap renormalization is clearly observed when we compared the Landau fan diagrams of absorption spectrum in low excitation and PL sp ectrum in high power regime. Both of these indicate that Coulomb interaction in e-h pair is screened at high carrier density (~1012/cm2) and PL from high density e-h plasma dominates the out-of-plane PL emission at high field and high excitation. In the high power excitation spectrum of InxGa1-xAs/GaAs multiple quantum well, we observed strong and sharp features on the PL peak s, suggesting the study of amplified emission processes in the InxGa1-xAs/GaAs MQWs. With the ultrafast facility developed at NHMFL, we were able to study the in-p lane PL emission from InxGa1-xAs/GaAs MQWs. We observed abnormally strong emission. By measuring and an alyzing the field depend ent, power dependent PL spectra and the single pulse ex cited PL spectra, we characteris tized this sharp peak emission. (I) the PL emission strength of sharp peak increa sed linearly above a certain magnetic field (13 T) or laser fluence (0.01 mJ/cm2) associated with an ASE proce ss. (II) above a critical magnetic field (~16 T) or laser fluence( ~0.03 mJ/cm2 ), the PL strength increases super linearly (~ B1.5 or F1.5), (III) for single pulse excitation above the fl uence threshold, we co llect the in-plane PL emission for different propagation directions and the single shot experiment shows anticorrelated emission between the PL strength at different directions. However, for the single pulse excitation experiment, we observed a complete correlation between in-p lane PL at different propagating directions, consistent with ASE emission. With an understanding of the cooperative theory of light emission introduced in detailed in chapter 5, we found that the characteristics of

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174 strong PL above magnetic field or fluence threshol d from in-plane emission are consistent with the cooperative emission process --superfluorescence, in which all the excited carrier are coherent during the emission process and give a very short burst emission of coherent light. This dissertation also presents comprehe nsive spectroscopic investigations on ZnO semiconductors, including bulk, epilayer and nanor od samples. The A and B excitonic states are clearly identified in the reflection spectra with optical selection rules. PL from donor or acceptor bound excitons dominates the emission spectrum up to 70K in the bulk ZnO and ZnO epilayer. To understand the excitonic states of ZnO in more detail, we measured the PL spectrum at high magnetic field up to 30 Tesla. Zeeman splitting form donor bound excitons is clearly resolved and analyzed with theoretical predication, we f ound that in Voigt geomet ry, the effective Lander factor is g ~2, which is close to theoretical predication. Ultrafast time resolved pump-p robe experiments are also ca rried to study the A-X, B-X dynamics in bulk ZnO, ZnO epilayer as well as ZnO nanorod. Exponential decay is observed in A-X (~130 ps) and B-X (~50 ps) in bulk material which is correspondin g to relaxation to D0X. In epilayer and nanorod sample, we observed stretched exponentia l decay process, (n=0.9 and =50 ps for A-X for the epilayer, n=0.6, =17 ps for the nanorods), related with carrier hopping transport and carrier localization. For the future, we need to obtain the time resolved information of the cooperative recombination process in high density e-h plasma in high magnetic fi eld, including measuring the SF pulse width, time delay for evolution of coherence between atoms. We proposed the following experiments: Time resolved pump-probe experiment to measure the carrier dynamics in InxGa1xAs/GaAs QW at high magnetic fields. This can be done with the CPA and OPA.

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175 Time resolved PL from in-plane emission in QW at high magnetic field, this can be done with streak camera and provide us the tim e information of evolution of coherence. Upconversion PL measurement of SF from InxGa1-xAs/GaAs QW in high magnetic field, this can provide us the time information of the pulse width of SF. As for the ZnO semiconductor, we propose to perform time resolved PL measurements with a streak camera, which can provide more information of the radiative and nonradiative dynamics of exciton and bound excitons.

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176 APPENDIX A SAMPLE MOUNT AND PHOTOLUMINESCENCE COLLECTION A commercial Janis cryostat (s hown in Fig.2-8) is modified for sending fs laser directly on the sample cooled down to 10K inside the cryosta t. On the tail of modified optical cryostat shown in Fig.2-10, an optical window is mounted on the bottom of the cryostat outer tail. Fig. A1 shows the detailed configuration of the sample mount, optical fiber and PL collection used in the experiments. The sample mount, which is made of cooper, is bolted on the bottom of liquid helium tail of the cryostat. An indium foil is used betw een the sample mount and the bottom of liquid helium tail for better heat conduction. With this method, the sample can be cooled down to around 10K. The InxGa1-xAs/GaAs MQW is positioned on the top of a sapphire plate, which is about 1mm thick. Special optical glue is used to firm ly attach the sample on the sapphire plate. This optical glue is transparent for visible and near infr ared light, which is suitable for 800nm CPA excitation light and the PL em ission around 930nm. The optical glue is dried with strong UV light heater. A right prism with size 1mmx1mm is also attached to the sapphire plate and one edge of the InxGa1-xAs/GaAs MQW. The sapphire plate with sample on it is positioned on the cooper sample mount with GE varnish, special glue with good conductivit y at low temperature. A Cernox temperature sensor is at tached to the sample mount righ t beneath the sapphire plate, so that the temperature of sample can correctly m easured. An electric heater is also position around the sapphire plate for temperature control. Two optical fibers are inserted into the small tubing inside the liquid helium and go through the bottom of the helium tail, indium fo il and sample mount, and reach the sapphire plate. The sapphire is positioned well so that the two fibers are right on th e top of the center of

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177 sample and the top of right angle prism respectively. The fiber on the center is used to collecting the PL emitted perpendicular to the quantum well pl ane while the fiber on the prism is used for collecting the PL propagating inside the quantum plane, the in plan e PL is coupled into the fiber with the prism. Strong white light is induced to the fibers from the open end to find the best positions of the other ends of optical fiber on the top of sapphire plate.

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178 Optical fiber edge collection Optical fiber center collection Liquid Helium tail LHe LHe Indium foil Cernox temperature sensor Heater Heater Sapphire plate Right angle prism InxGa1-xAs/GaAs QW Stainless steel tubing Sample mount Figure A-1. Detailed schematic diagram of sample mount and PL collection used in the experiment.

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179 APPENDIX B PIDGEON-BROWN MODEL1 In a realistic calculation of electronic st ates in semiconductor in magnetic fields, pktheory [71] is required to for good approxi mation of the bandstructure. For narrow gap semiconductors such InGaAs or InAs, the couplin g between the conduction and valence bands is strong, so it is necessa ry to calculate the LL s with eight-band model. Pidgeon and Brown [94] develop a model to calculate the LL s in magnetic field at k =0. This model is generalized to include the wave vector (0 k) in this chapter. The wave function basis in Tab. 3-1 is still us ed in the calculation. In the presence of a uniform magnetic field B along z-axis, the wave vector k in the effective mass Hamiltonian is replaced by the operator ) ( 1A p kc e -1 where ipis momentum operator. In Landau gauge, ^z B A B Two operators are defined as ) ( 2y xik k a B-2 (a) ) ( 2y xik k a B-2 (b) where is the magnetic length eB c The operators defined in Eq. B2 are creation and annihilation operators. The states they create and annihilate are simple harmonic oscillator functions, and N aaare the order of Note: The Pidgeon-Brown Model is taken with perm ission from Y. Sun, Theoretical Studies of the Electronic Magneto-optical and Transport Properties of Diluted Magnetic Semiconductors, Page 45-50, PhD dissertation, Univ of Florida, Gainesville, FL2005

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180 harmonic functions. Using these two operators to eliminate kx and ky in the Hamiltonian, a new Landau Hamiltonian is reached b c c a LL L L L H, B-3 The La, Lb and Lc are given by P Q i M i a V Q i Q P M a V i M i M Q P a V i a V a V i a V i A E Lg a2 2 3 2 2 3 1 2 3 2 3 1 B-4 P Q i M i a V i Q i Q P M a V M i M Q P a V a V i a V i a V i A E Lg a2 2 3 2 2 3 1 2 3 2 3 1 B-5 0 2 3 2 1 3 1 2 3 0 3 2 2 1 0 0 3 1 3 2 0 0 L i L i Vk L i L Vk i L i L Vk i Vk Lz z z z c. B-6 The operators A P Q L and M are ) 1 2 ( 22 2 4 0 2 zk N m A B-7(a) ) 1 2 ( 22 2 1 0 2 zk N m P B-7(b) ) 2 1 2 ( 22 2 2 0 2 zk N m Q B-7(c) ) 6 (3 0 2 a k i m Lz B-7(d)

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181 ) 3 )( 2 (2 2 3 2 0 2a m M B-7(e) The parameter 1, 2, 3 and 4 are Luttinger parameters [80] and is the spin-orbit coupling. With Landau gauge translation symmetry in the x direction is broken while translation symmetry along the y and z directions is maintained. Therefore, ky and kz are good quantum numbers and the envelop of the effective mass Hamiltonian HL can be written as 1 8 1 7 1 6 5 4 3 2 2 1 1 ) ( n n n n n n n n n n n n n n n n z k y k i na a a a a a a a A e Fz y B-8 In Eq. B-8, n is the Landau quantum number associated with the Hamiltonian matrix, labels the eigenvectors, A= LxLy is the cross sectional area of the sample in the x-y plane, ) ( nare harmonic oscillator eige nfunctions evaluated at yk x2 and ) (, 1z nk ais complex expansion coefficients for the th eigenstate, which depend explicitly on n and k. Note that the wave functions themselves will be given by th e envelop functions in Eq. B-8 with each component multiplied by the corresponding k =0 Bloch basis states given in Table 3-1. Substituting Fn from Eq. B-8 into the effective mass Schrodinger equation with H given by Eq. B-3, we obtain a matrix eigenvalue equation ,) (n z n n nF k E F H That can be solved for each allowe d value of the Landau quantum number, n to obtain the Landau levels ) (,z nk E. The components of the normalized eigenvectors ,nF are the expansion coefficientsia

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190 BIOGRAPHICAL SKETCH Xiaoming Wang was born in Nov. 1971. He ear ned the Bachelor of Science degree at Tianjin University, China, in 1994. After that he entered the graduate school of Tianjin University and got his Master of Science degree in physics in 1997. Right after that, he started his job as a research associate in the Institute of Physics, China Academy of Sciences. After three year of being a research associat e in the Institute of Physics, Chinese Sciences, he resigned his job and came to University of Florida in 2000, to pursue a Ph.D in phys ics. He joined Prof. David Reitzes ultrafast group in summer 2001. He has been working for several different research projects, some of which are related to this dissertation.