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Development of new III-V semiconductor quantum well infrared photodetectors for mid-and long-wavelength infrared detection

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Title:
Development of new III-V semiconductor quantum well infrared photodetectors for mid-and long-wavelength infrared detection
Creator:
Wang, Yanhua, 1955- ( Dissertant )
Li, Sheng S. ( Thesis advisor )
Neugroschel, Arnost ( Reviewer )
Bosman, Gys ( Reviewer )
Srivastava, Ramakant ( Reviewer )
Anderson, Timothy J. ( Reviewer )
Phillips, Winfred M. ( Degree grantor )
Holbrook, Karen A. ( Degree grantor )
Place of Publication:
Gainesville, Fla.
Publisher:
University of Florida
Publication Date:
Copyright Date:
1994
Language:
English
Physical Description:
vii, 146 leaves : ill. ; 29 cm.

Subjects

Subjects / Keywords:
Bandwidth ( jstor )
Barrier layers ( jstor )
Conduction ( jstor )
Dark current ( jstor )
Electric potential ( jstor )
Electrons ( jstor )
Photometers ( jstor )
Quantum wells ( jstor )
Superlattices ( jstor )
Wavelengths ( jstor )
Dissertations, Academic -- Electrical Engineering -- UF
Electrical Engineering thesis Ph. D
Infrared detectors ( lcsh )
Optoelectronic devices ( lcsh )
Quantum wells ( lcsh )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Abstract:
In this dissertation three types of III-V semiconductor quantum well infrared photodetectors (QWIPs) have been developed for 3-5 um mid-wavelength infrared (MWIR) and 8-14 um long-wavelength infrared (LWIR) detection. they are (1) GaAs/AlGaAs, GaAs/InGaP bound to continuum (BTC) QWIPs and InGaAs/InAlAs bound to miniband (BTM) QWIP, (2) nomral-incidence type II indirect bandgap AlAs/AlGaAs QWIP, and (3) normal incidence p-type strained layer InGaAS/InAlAs and InGaAs/GaAs QWIPs. These QWIP structures were grown by the molecular beam epitaxy (MBE) technique, with the exception of the GaAs/InGaP QWIP, which was grown by the metal-organic chemical vapor deposition (MOCVD) technique. Detectivity ranging from 10^9 to 10^12 cm-\/Hz/W was obtained for these QWIPs at T=77 K. The BTC and BTM QWIPs exhibited both photoconductive (PC) an photvoltain (PV) dual-mode (DM) detection characteristics. the peak wavelengths for the GaAs/AlGaAs QWIP were found to be at 7.7um and 12 um. The peak wavelengths for the GaAs/InGaP QWIP were found to be at 6.0um and 8.2 um. the voltage tunable InGaAs/InAlAs QWIP showed a peak wavelength of 10 um with dual-mode operation. a normal-incidence type II indirect bandgap AlAs/AlGaAs QWIP grown on (110)GaAS substrate was developed, which shows a multicolor detection feature with peak response wavelengths occurred at 2.2, 2.7, 3.5, 4.8, 6.5, and 12.5 um. Extremely large photo-conductivity gains of 630 and 3200 at peak wavelengths of 3.5 and 2.2 um were obtained at Vb=3 and 6 V, respectively, while a broad spectral photoresponse with peak wavelength at 12.5 um was observed. A normal-incidence p-type tensile strained-layer InGaAs/InAlAs QWIP grown on InP substrate with an ultralow dark current density (about six orders of magnitude smaller than the standard GaAs/AlGaAs QWIP) was developed in this work. this QWIP has achieved background limited performance (BLIP) for T</= 100 K, which is the highest BLIP temperature ever reported for a QWIP. The detectivity for this QWIP was found to be Dblip=5.9x10^10cm-\/Hz/W at peak wavelength of 8.1 um, Vb=2 V,a nd T= 77 K. finally, a normal incidence p-type compressive strained layer InGaAs/GaAs QWIP grown on GaAs substrate was also demonstrated for the first time in this work, which showed a two-color detection feature with wavelengths at 5.5 um and 8.9 um.
Thesis:
Thesis (Ph. D.)--University of Florida, 1994.
Bibliography:
Includes bibliographical references (leaves 139-145).
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Yanhua Wang.

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University of Florida
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University of Florida
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Copyright Yanhua Wang. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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AKJ5195 ( NOTIS )

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DEVELOPMENT OF NEW III-V SEMICONDUCTOR
QUANTUM WELL INFRARED PHOTODETECTORS FOR MID- AND LONG-WAVELENGTH INFRARED DETECTION












By

YANHUA 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


1994















ACKNOWLED GEMENTS


I would like to express my sincere appreciation to the chairman of my committee, Professor Sheng S. Li, for his guidance, encouragement, and support during the course of this research. I would also like to thank Professors A. Neiigroschel, G. Bosman, R. Srivastava, and T. Anderson for serving on my supervisory committee.

I am grateful to Dr. P. C. Yang for many beneficial discussions and much help in programmed control of the optical measurement system. I am also grateful to many friends and colleagues, including Drs. L. S. Yu, Y. C. Wang and F. Gao, along with D. Wang, J. C. Chiang, J. Chu, and C. S. Lee, for their helpful discussions and valuable assistance in the device fabrication and measurements.

Special thanks are extended to Dr. Pin Ho of Martin Marietta for the MBE growth of the Ill-V QWIP structures and to Dr. K. C. Chou for the growth of the GaAs/InGaP QWIP using MOCVD.

I am greatly indebted to my parents, wife, and daughter for their love, support and patience during the course of this study.

Finally, the financial support of ARPA is gratefully acknowledged.
















TABLE OF CONTENTS


Page

ACKNOWLEDGEMENTS . ii

ABSTRACT . vi

CHAPTERS

I INTRODUCTION.1I

2 QUANTUM WELL AND SUPERLATTICE STRUCTURES .12

2.1. Introduction. 12 2.2. Methods for Calculating Electronic States . 12 2.3. Superlattice and Miniband . 16
2.3.1. Dispersion Relations .17 2.3.2. Transmission Probability IT - Tj. 19
2.4. Carrier Transports . 21
2.4.1. Continuum State Conduction . 21 2.4.2. Miniband Conduction . 21 2.4.3. Hopping Conduction . 23
2.5. Corrections on Subband Energy States. 24
2.5.1. Electron-Electron Interaction . 24 2.5.2. Depolarization Effects . 25 2.5.3. Other Effects . 25

3 PRINCIPLES OF QWIP OPERATION AND FIGURES OF MERIT .30

3.1. Introduction. 30 3.2. Intersubband Transition. 30 3.3. PC and PV Detection Modes . 33 3.4. Figures of Merit. 34
3.4.1. Dark Current Id. 34 3.4.2. Spectral Responsivity R . 36 3.4.3. Collection Efficiencyq . 36 3.4.4. Detectivity D*, . 37









3.4.5. Background Limited Performance (BLIP). 38

4 A DUAL-MODE PC AND PV GaAs/AlGaAs QUANTUM WELL
INFRARED PHOTODETECTOR (DM-QWIP) WITH TWO-COLOR
DETECTION . 41

4.1. Introduction. 41 4.2. Design Consideration . 41 4.3. Experiments. 43 4.4. Conclusions . 46

5 A VOLTAGE-TUNABLE InGaAs/InAlAs QUANTUM WELL
INFRARED PHOTODETECTOR (VT-QWIP) . 54

5.1. Introduction. 54 5.2. Design Consideration . 54 5.3. Experiments. 56 5.4. Results and Discussion. 58 5.5. Conclusions . 59

6 A TWO-COLOR PHOTOVOLTAIC GaAs/InGaP QUANTUM
WELL INFRARED PHOTODETECTOR (PV-QWIP). 66

6.1. Introduction. 66 6.2. Design Consideration . 67 6.3. Experiments. 69 6.4. Conclusions . 71

7 A NORMAL INCIDENCE TYPE-Il QUANTUM WELL
INFRARED PHOTODETECTOR USING AN INDIRECT
BANDGAP AlAs/Al0.5Ga0.5As GROWN ON (110) GaAs
SUBSTRATE FOR THE MID- AND LONG-WAVELENGTH
MULTICOLOR DETECTION . 76

7.1. Introduction. 76 7.2. Theory . 77 7.3. Coupling between F- and X-bands. 80 7.4. Experiments. 81 7.5. Conclusions . 85

8 P-TYPE STRAINED-LAYER QUANTUM WELL INFRARED
PHOTODETECTORS WITH BLIP AT T < 100 K. 97

8.1. Introduction. 97









8.2. Theory . 98 8.3. A Tensile Strained-layer InGaAs/InAlAs QWIP . 102
8.3.1. Inversion between Heavy- and Light-hole States .103 8.3.2. Experiments. 103 8.3.3. Conclusions . 105
8.4. A Compressive Strained-layer InGaAs/GaAs QWIP .106
8.4.1. Interaction between Type-I and Type-Il QW States .106 8.4.2. Experiments. 108 8.4.3. Conclusions . 110

9 SUMMARY AND CONCLUSIONS. 124

APPENDICES

A ENERGY DISPERSION EQUATION FOR SUPERLATTICE .132

B OPTICAL MATRIX FOR STRAINED-LAYER SUPERLATTICE . 137

REFERENCES . 139

BIOGRAPHICAL SKETCH. 146














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

DEVELOPMENT OF NEW III-V SEMICONDUCTOR
QUANTUM WELL INFRARED PHOTODETECTORS FOR MID- AND LONG-WAVELENGTH INFRARED DETECTION By

Yanhua Wang

August 1994

Chairman: Sheng-San Li
Major Department: Electrical Engineering
In this dissertation, three types of III-V semiconductor quantum well infrared photodetectors (QWIPs) have been developed for 3-5 pum mid-wavelength infrared (MWIR) and 8-14 pm long-wavelength infrared (LWIR) detection. They are (1) GaAs/AlGaAs, GaAs/InGaP bound-to-continuum (BTC) QWIPs and InGaAs/InA1As bound-to-miniband (BTM) QWIP, (2) normal-incidence type-II indirect bandgap A1As/AlGaAs QWIP, and (3) normal-incidence p-type strained-layer InGaAs/InA1As and InGaAs/GaAs QWIPs. These QWIP structures were grown by the molecular beam epitaxy (MBE) technique, with the exception of the GaAs/InGaP QWIP, which was grown by the metal-organic chemical vapor deposition (MOCVD) technique. Detectivity ranging from 10' to 1012 cm-x/i-Hz/W was obtained for these QWIPs at T = 77 K.
The BTC and BTM QWIPs exhibited both photoconductive (PC) and photovoltaic (PV) dual-mode (DM) detection characteristics. The peak wavelengths for the GaAs/A1GaAs QWIP were found to be at 7.7 pm and 12 pm. The peak wavelengths









for the GaAs/InGaP QWIP were found to be at 6.0 ,m and 8.2 ym. The voltagetunable InGaAs/InAlAs QWIP showed a peak wavelength of 10 Pum with dual-mode operation.
A normal-incidence type-II indirect bandgap AlAs/AlGaAs QWIP grown on (110) GaAs substrate was developed, which shows a multicolor detection feature with peak response wavelengths occurred at 2.2, 2.7, 3.5, 4.8, 6.5, and 12.5 tim. Extremely large photoconductivity gains of 630 and 3,200 at peak wavelengths of 3.5 and 2.2 Fm were obtained at Vb = 3 and 6 V, respectively, while a broad spectral photoresponse with peak wavelength at 12.5 ftm was observed.
A normal-incidence p-type tensile strained-layer InGaAs/InAlAs QWIP grown on InP substrate with an ultralow dark current density (about six orders of magnitude smaller than the standard GaAs/AlGaAs QWIP) was developed in this work. This QWIP has achieved background limited performance (BLIP) for T < 100 K, which is the highest BLIP temperature ever reported for a QWIP. The detectivity for this QWIP was found to be DBLIP = 5.9x1010 cm-v/-Hz/W at peak wavelength of 8.1 jm, Vb = 2 V, and T = 77 K. Finally, a normal-incidence p-type compressive strained-layer InGaAs/GaAs QWIP grown on GaAs substrate was also demonstrated for the first time in this work, which showed a two-color detection feature with peak wavelengths at 5.5 pm and 8.9 pm.















CHAPTER 1
INTRODUCTION

Infrared photo detectors are transducers that can convert invisible JR radiation into a measurable electrical signal, and their arrays can be used as imaging sensors in military, industrial, medical treatment, and scientific research applications. Infrared radiation was discovered in 1800 [1], and it covers wavelengths ranging from 0.75 pim to 1000 ,im as shown in Fig. 1.1. In the entire infrared radiation spectrum, wavelengths ranging from 1 pim to 20 pim were found to be very important in the image applications. In atmospheric window applications, there are three main detection bands: (1) 1-3 pim short-wavelength infrared (SWIR), (2) 3-5 Prm mid-wavelength infrared (MWIR), and (3) 8-14 pim long-wavelength infrared (LWIR) (see Fig. 1.2). The 1-3 ysm band has been found to be very attractive in fiber optical communications. The 8-14 pum band is preferred for high performance thermal imaging sensors because of its great sensitivity to ambient temperature objects and its better transmission through the atmosphere, while the 3-5 pim band is more appropriate for hotter object detection or if sensitivity is less important than contrast.

Infrared detectors can be classified into two broad types, namely thermal detectors and photon (quantum) detectors. Thermal detectors such as bolometers and pyroelectric detectors are made from temperature-sensitive materials. When JR radiation is absorbed, the temperature of a thermal detector increases, which in turn produces a measurable electrical signal. Due to its response to thermal power, the thermal detector usually suffers from a low detectivity and a fairly slow response time, but it can be operated at ambient temperature. Photodetectors are fabricated from semiconductors whose electrical conductivity can be modulated by photon-induced transitions that excite carriers from bound states into mobile states. The detectors









respond only to incident photons with energy equal to or greater than the difference between transition states. Photodetectors can be operated at two detection modes: photoconductive (PC) and photovoltaic (PC) modes. In some practical applications, the PV mode operation may be more preferred than the PC mode detection due to its low noise level, low power dissipation, and large array size. The primary photodetectors used for thermal imaging in past decades are summarized in Table 1.1. In LWIR detectors, the most important detectors are fabricated from ternary compounds, HgCdTe (MCT). However, due to the volatility, high dislocation density, small wafer size, different temperature expansion between the MCT and silicon readout circuits, and processing difficulties in the MCT, progress has been very slow for LWIR image sensor applications.

Recent advances in epitaxial layer growth techniques such as Molecular Beam Epitaxy (MBE) and Metalorganic Chemical Vapor Deposition (MOCVD) enable the growth of semiconductor heterolayers with atomically sharp interfaces. With the advent of these epitaxial growth techniques, significant progress has been made in multiquantum well and superlattice optoelectronic devices. The atmospheric window infrared detection of the 3-5 /m MWIR and the 8-14 pm LWIR bands can be realized by using the quantum well and superlattice heterostructures.

Studies of heterojunction superlattices and their transport properties were first reported by Esaki and Tsu [2, 3]. Due to coupling effects between adjacent quantum wells, the resonant tunneling behavior between the different states of adjacent wells along the superlattice growth axis was observed in AlAs/GaAs system by Esaki and Chang [4]. The quantization of the energy states in the quantum wells was experimentally verified through the optical measurement by Dingle et al. [5]. In the quantum well and superlattice structures, the carriers are confined in the quantized states of the quantum wells, and they can transport either in the parallel within the wells or in the perpendicular along the superlattice growth axis. The parallel transport with









wavevectors k, and ky can give rise to two-dimensional electron gap (2-DEG) properties such as high electron mobility transistors (HEMTs), whereas in the perpendicular transport carriers can move along the superlattice growth axis with the wavevector k,, resulting in a much larger mobility difference between confined bound states and upper excited conduction states due to blocking potential barriers on the two sides of the well.
In quantum well infrared photodetectors (QWIPs), the conducting carriers transport along superlattice axis so as to suppress the dark current associated with the populated ground state and to enhance the photocurrent collection through the upper excites states. The excited states can be either the continuum states or the miniband states. In the continuum state conduction, the excited carriers can become the hot carriers with higher mobility at applied bias voltage, while in the miniband state conduction, the excited carriers can transport resonantly through the global miniband states. However, there are two different conduction processes in the miniband states:

(1) hopping conduction and (2) coherent miniband conduction. When the barrier layers of a superlattice are thick (i.e., isolated quantum wells) or a strong electric field is applied to the superlattice, the energy states become localized (i.e., Kane states) [6], and the carrier transport is dominated by the hopping conduction through the quantum wells. On the other hand, if the barrier layers of a superlattice are thin enough or applied bias is relatively low, wavefunction overlapping appears near adjacent wells and the miniband (Bloch states) conduction [7] is expected to be the dominant conduction process. In the miniband conduction scheme, the superlattice effective mass filtering effect [8] was observed, and a giant photocurrent gain was achieved in the interband transition. The following unique features were observed in the miniband conduction: (1) reduction of heterointerface recombination in optoelectronic devices,
(2) elimination of deep-levels-related photoconductive phenomena, (3) realization of coherent tunneling through miniband conduction, and (4) large oscillator strength.









In general, based on the energy bandgap alignments, the heterointerface multiquantum well/superlattice structures may be divided into four types: type I, type II staggered, type I misaligned, and type III (see Fig. 1.3). Type I alignment occurs when the bandgap of one semiconductor lies completely within the gap of the other, in which both electrons and holes are confined within the same narrower gap layers, for example, GaAs/AlGaAs, InGaAs/InAlAs, GaAs/InGaP, and GaSb/A1Sb. Type II staggered alignment results when two materials overlap but one does not completely enclose the other, and electrons and holes are confined in the different semiconductor layers such as ZnSe/ZnTe and CdSe/ZnTe materials. Type II misalignment arises if the band gaps of the two materials do not overlap at all in energy such as InAs/GaSb material. Type III alignment appears in heterojunctions containing a semimetallic compound such as HgTe/CdTe material. In these four types of heterointerfaces, it has been widely believed that high quality epitaxial layers could only be grown on the lattice matched substrates. However, the high quality epilayers could also be grown in slightly lattice-mismatched material systems if the individual epilayer thickness is within the critical thickness. In these lattice mismatched quantum well and superlattice structures, either tensile strain or compressive strain may be intentionally introduced [9]. Due to the strain effects, dislocation lines from the lattice mismatch can be locally confined within the layers, hence the mismatch is fully accommodated by the elastic strain.

In 1985, West and Eglash [10] first observed an extremely large dipole infrared intersubband absorption strength from a GaAs quantum well structure; they called this intersubband transition a quantum well envelope state transition (QWEST). This new dipole intersubband transition is ascribed to the "momentum vector reorientation" between the envelope states, and the Bloch states remain nearly constant. In contrast, the dipole transition from conduction to valence bands occurs between the Bloch states, and the envelope states remain constant. Based on the new intersub-









band transitions, Levine et al. [11] demonstrated the first GaAs/AlGaAs quantum well infrared photodetector (QWIP) based on bound-to-bound (BTB) intersubband transition for 8-14 pm LWIR detection. Since then, the rapid progress in QWIP performance has been made based on bound-to-continuum [12, 13], bound-to-miniband [14] intersubband transition schemes. Figure 1.4 shows the energy bandgaps and lattice constants of some III-V and II-IV compound materials used for the QWIP fabrication. The detectivity of the GaAs/AlGaAs LWIR QWIP for operating at photoconductive mode has been improved dramatically to the point where large 128 x 128 staring focal plane arrays have now been demonstrated [15, 16]. In addition, the imaging sensor arrays using GaAs/AlGaAs LWIR QWIPs for operating on the photovoltaic
(PV) mode have also been reported [17]. Table 1.2 lists the performance status of the GaAs/AlGaAs QWIP at T = 77 K. The QWIPs for the 3-5 pm MWIR detection using the intersubband transitions have also been investigated using InGaAs/InA1As and AlGaAs/GaAs material systems [18, 19]. However, QWIP arrays used for the atmospheric spectral window of both MWIR and LWIR bands have not been demonstrated yet. The image sensors at both the MWIR and the LWIR bands offer practical applications in tracking-and-searching and forward-looking infrared (FLIR) systems. The development of III-V semiconductor QWIPs for MWIR and LWIR detection is the main motivation of this dissertation.

















Table 1.1. Primary photon detectors for mid- and long-wavelength
infrared detection.


Material

InSb


PbSe


PbTe PtSi

Pb.17Sn.s3Te Hg0.799Cdo.201Te


Mode PC PC,PV

PC PC PC

Schottky

PV PC,PV


Operating T (K) 195

77 195

77 77 77 77 77


A,

(pm)
6.0 5.7 5.1 6.6 5.4

5.1 11 13


Array Size


640 x840






1024x1024


128 x 128















Table 1.2. Performance status of the GaAs/AlGaAs QWIPs at T
= 77K.


Ap
(ptm) 10.8 8.0 10 8.9 7.7 7.5


Dc I
cm-/-Hz/W


4 x1010 2x109
1.6 x1010 5.8 x 109


References

[11]

[12] [13]
[14]

[15,16]

[17]


Single or Array Single Single Single Single 128 x 128
4 x4


Year 1987

1990 1990 1991 1991 1992


mode PC PC PC PC PC PV












Wavelength


r-rays


X-rays
.

UV
.

Visible

IR


Microwave Radiowaves


o.1 A 1A

loA looA .



lp lOp loop 01 cm

1 cm. 10 cm lm
10 m
lOm 100 m

1 km 10 km 100 km


Wavelength, p


0.6 0.8
1

1.5
2

3
4


6
8 10 15



30


- < Cr
�. . . . �.



- Near IR





Mid IR




- Far IR




Extreme IR


Figure 1.1. Chart of electromagnetic spectrum.





















100 80 60

40 20

0


1 3 5 7 9
Wavelength (rim)


11 13


Figure 1.2. Atmospheric transmission through 1 km path.























EgI Eg2 Eg2

. . . . . . . .
-v.E

(a) Type-I (b) Type-Il Staggered





Eg2


.I Egi

. .



(c) Type-Il Misaligned (d) Type-Ill







Figure 1.3. Possible types of band alignments at semiconductor interfaces. Solid lines denote the conduction band E, and
dashed lines indicate the valence band E,
















3.0


2.5


2.0 G


1.5


1.0 "" 0.5


0.0
5.4


6.0 6.2 6.4 6.6


Lattice Constant (A)






Figure 1.4. Energy bandgap versus lattice constant for some Ill-V
and II-VI compound semiconductor materials.


5.6 5.8














CHAPTER 2
QUANTUM WELL AND SUPERLATTICE STRUCTURES

2.1. Introduction

The introduction of quantum well (QW) and superlattice structure makes it possible to design and fabricate various novel quantum devices. Long wavelength infrared (LWIR) photodetectors using the superlattice and quantum well structures have been extensively investigated based on bound-to-bound [11, 20], bound-toquasicontinuum [21], bound-to-miniband [14], bound-to-continuum [12, 22], and miniband-to-miniband [23, 24] intersubband transition mechanisms. In order to understand the optical and electrical properties of quantum well and superlattice structures, it is necessary to study them from both macroscopic and microscopic theories.

2.2. Methods for Calculating Electronic States

A crystal is made up of a large number of interacting particles, positive nuclei surrounded by negative electrons. The nuclei form a rigid lattice that is completely frozen at low temperatures. As the temperature is raised, nuclei vibrate about their mean positions, as described by phonons. Consequently, the theoretical treatment of the energy levels and wavefunctions in solids cannot be attempted without a number of simplifying approximations. We can write the total Hamiltonian of the system in the form
Ht = T +TN + Ve + YN + VNN, (2.1)

where T, and TN are the kinetic energy of electrons and nuclei, respectively, and V,, VN, and VNN are the electron-electron, electron-nuclei, and nuclei-nuclei interactions,









respectively. Since the strongest force between particles in a solid is due to coulomb interaction, the kinetic (T) and potential (V) energy terms can be expressed as Th2 v2 (2.2)

= Ze2 (2.3)
V47rIrr- rl'

where Z = 1 is for the electron, otherwise for the nuclei charges.
The system Schradinger equation can be written as

Ht'I(R,r) = E'1V(R,r). (2.4)

The system wavefunction I(R, r) can be expressed as the product of the nuclei wavefunction X(R) and the electron wavefunction O(R, r), ItF(R,r) = x(R)4'(R,r) (2.5)

where R represents the space and spin coordinates of the nuclei and r denotes the coordinates for the electrons. This eigenvalue problem can be further simplified for electronic states by using some basic approximations.

Due to the extremely different masses between the electrons and the nuclei, the eigenvalue problem can be split into two separate, though interdependent, eigenvalue problems for electrons and nuclei by using the adiabatic approximation [25], which assumes that electrons will adiabatically follow the lattice (or nuclei) vibration. The eigenvalues for electrons and nuclei can be solved from [T + V: + VeN] On(R, r) = E,(R)4'.(R,r); (2.6)

[TN + VNN + E.(R)]x(R) = E.X(R), (2.7)

where subscript n denotes a quantum number of the coordinates for the electrons. Even though we have the electron eigenvalue expression, this still represents a very complicated many-body problem. However, most of the systems such as the superlattice can be described by using the one-electron approximation, which assumes that









the motion of a single electron experiences some average force due to vibrating lattice and all other particles. These one-electron wavefunctions satisfy the self-consistent Hartree-Fock equations [26]. The solution of the Hartree-Fock equation is still a very difficult mathematical problem. For this reason, the band approximation is often employed, i.e., one solves the Schridinger equation with an assumed crystal potential V(r) [27]. The time-independent one electron Schridinger equation and the potential are given by
[h 2V2 + V(r) �(k,r) = E.(k)'0.(k,r), (2.8)

V(r) = VL(r) + VE(r) + Vs(r), (2.9)

where VL represents the perfect lattice periodic potential, VE is the superlattice periodic potential, and Vs is the random scattering potential. Figure 2.1 schematically shows the three components of V(r). The wavefunction of the electron is 0"(k, r) and the eigenvalue of the electron in the k-space for n-th band is E,(k). For example, near the bottom of the conduction band, the eigenvalues of electrons in a superlattice can be described by
E.(k) = E.(k.) + 2-- (k� ky), (2.10)

where E,(k,) is the energy dispersion relation along the superlattice axis (longitudinal) and other terms are the energy dispersion relations within the superlattice plane (transverse).

There are two different but equivalent procedures for obtaining the energy states and wavefunctions with the band approximation, which assumes that potential is invariant for all symmetry operations. These two procedures are (1) expand the crystal states on a complete set of Bloch type function and then determine the expansion coefficients by requiring the states to satisfy the appropriate Schr6dinger equation, such as the tight binding method, the orthogonal plane wave (OPW) method, or the pseudopotential method, and (2) expand the states on a complete set of functions that are solutions of the Schridinger equation within a unit cell and then determine









the expansion coefficients by the appropriate boundary conditions, such as the cellular method, the augmented plane wave (APW) method, or the Green's function method. As a practical matter one has to choose, from physical considerations, the method whose set of basis function sufficiently represents the exact eigenfunction within the band approximation. Besides the two basic analytical procedures above, semi-empirical approaches and interpolation schemes (i.e., k.p theory) are also very powerful tools in determining effective masses and densities of states (DOS) near high symmetry points in k space such as k = 0 of Brillouin zone center. Based on the k.p method, calculations of the band structure of a superlattice have been carried out by using the Kronig-Penney model and the modifications of the boundary condition [28]. The nonparabolicity effects in the band structures have been taken into account by using the Kane model [6].

By considering only the periodic potential VL(r) in V(r) (ignoring VE and Vs), the solution of the Schrfdinger equation is the Bloch type wavefunction,

on,k(r) = Un,k(r)exp(ik . r), (2.11)

where U,,k(r) is a periodic function with the same periodicity as VL and n denotes the band index. By considering slow varying potential VE and random scattering potential Vs and using calculated dispersion relation E(k), the eigenvalues and eigenfunctions can be solved by using the effective mass envelope function approach. The effective mass envelope equation for n-th band can be written as [E,(-iV) + VE + Vs]o5(r) = Eqn(r), (2.12)

where qn(r) is the envelope function and E is the eigenvalues that satisfy the effective mass equation. If the multiband model is incorporated in the effective mass equation, summation over band index n is required.

If the superlattice growth is along z-direction (x- and y-directions within super-









lattice plane), then the Bloch function becomes

U,k(r) =U,k(Z)exp(ik.x + ikly) (2.13)

and the envelope function 0,n(r) becomes a function of coordinate z, that is, 0,'(z).

2.3. Superlattice and Miniband


In conventional quantum wells, carriers are confined within potential barriers that are formed by energy band gap offset between two materials. In order to reduce the tunneling dark current from the ground states in the quantum wells, the use of thicker barrier layers between the wells is very important for high performance of the QWIPs. However, these QWIP structures suffer from the large dark current due to the defect existence in the thicker barrier layers. In order to overcome this problem, very short period superlattice barrier layers are introduced to replace the thicker barrier layers [14]. The superlattice barriers can confine the defects within the thin layer and significantly reduce the dark current. The replacement of the superlattice barrier layer offers several new features over the conventional quantum wells. They are (1) improvement of the roughness at the heterojunction interfaces by superlattice smoothing, (2) reduction of interface recombination, (3) elimination of deep-levels-related phenomena [29], and (4) realization of a coherent conduction with large quantum photocurrent gain [8].
The superlattice barrier quantum wells also involve the confinement of carriers and the determinations of energy eigenvalues and wavefunctions in the heterostructure. When the carrier de Broglie wavelength becomes comparable to the barrier thickness of the superlattice, the wavefunctions of the individual wells tend to overlap due to tunneling, hence the global minibands are formed. The miniband decoupling occurs when the bias voltage across one period of the superlattice becomes larger than the miniband bandwidth. From the carrier transport point of view, the









superlattice can have an adjustable effective barrier height by properly selecting superlattice structure parameters. Due to the adjustability of the superlattice, carrier conduction through the superlattice can be tuned and modulated by the miniband intrinsic transport properties, such as coherent tunneling conduction and ballistic resonant conduction.

2.3.1. Dispersion Relations

In an A-B type-I (two different materials) superlattice with growth direction along the z-axis, one period of the alternating layers is called the basis of the superlattice, denoting L (= L, + Lb, L, for wells and Lb for barriers). Since the superlattice period L is much longer than the lattice constant, the Brillouin zone is divided into a series of minizones, leading to a narrow subband (or miniband). As a result, the actual wavefunction of a superlattice is the product of the Bloch wavefunction, which is a periodic function of the atomic potential, and the envelope wavefunction, which is a function of the superlattice potential, O(k, r) = E �,(z)U,k(z)exp(ikxx + ikyy), (2.14)

where summation is over the band index n and k,,, are the transverse wavevectors in x- and y-direction.

In the effective mass approximation and using the one-band Kronig-Penney model, the envelope wavefunction On(z) can be written as [30]

S Clicos[ka(z - La/2)] + C2sin[ka(z - La/2)] in the well
C3cos[kb(z + Lb/2)] + C4sin[kb(z + Lb/2)] in the barrier, where

ka = h (2.16)

kb = [2mf(E - Eb)]1/2
k = b , (2.17)

C1~4 are constants that depend on boundary conditions and subband index parity, Ea,b are band minima or maxima for the well and barrier layers.









Bastard [28] has shown that, in the parabolic band approximation, the dispersion relation for the unbound states is

cos [kz(La + Lb)] = cos (k,La) cos (kbLb) - 2(1/( + )sin (ka,L) sin (kbLb) (2.18)

with ( = mlka/m*kb and k, defines the superlattice wavevector.

The dispersion relation for the bound states is still valid if one substitutes kb by inb and ( by -ii' with ' m= mka/msnb,

cos [kz(La + Lb)] = cos (kaLa) cosh (rbLb) - 1(1/(' - (')sin (kaLa) sinh (KbLb) .

(2.19)

The minibands for the bound and unbound states can be obtained from Eqs. (2.18) and (2.19). The higher minibands could extend above the potential barriers. However, the electron in-plane wavefunction of superlattice experiences only a regular lattice periodicity, and the dispersion relations in transverse direction (i.e., k, and ky) are much like those for unperturbated cases (i.e., Bloch type wavefunction). It is noted that transverse wavevectors (k,, ky) are conserved across the interfaces since the interface potential in the envelope function approximation depends only on the z coordinate. However, the spatially dependent effective masses are not entirely decoupled and are 3x3 tensors, which introduces nonparabolicity to the subbands. The bandwidth of a miniband is an exponential function of the superlattice barrier thickness Lb,

F ~ exp(-CLb), (2.20)

where C is a constant. The miniband bandwidths and miniband energy levels versus barrier thickness are illustrated in Fig. 2.2. It is noted that the bandwidth becomes wider and wider as the barrier thickness decreases.

Another feature in superlattice is the effective mass modulation. The effective mass mz of a miniband can be deduced from the dispersion relation E,(k,) = E'









(reference) - (1/2)r cos[kz(La + Lb)],
M* 2h'
m - 2 (2.21)
Cxp(CLb)
(La + Lb)2 (2.22)

A smaller effective mass m* with higher electron mobility for both wells and barriers can be obtained along superlattice axis. The wider the miniband bandwidth is, the smaller the tunneling time constant becomes. When the tunneling time is much smaller than the carrier relaxation time and scattering time, a coherent and ballistic carrier conduction through the miniband can be built up, which is desirable for QWIP applications.
The above results hold for a perfect superlattice with a flat band diagram, ignoring the effects of growth layer fluctuations and roughness, electron-electron interaction, electron-phonon interaction, and depolarization. In reality, all these corrections to energy states and wavefunctions should be incorporated in the calculations of the miniband properties. In order precisely to analyze superlattice miniband dispersion relations, the two-band or three-band model should be used in which interband and intervalley interactions are included (see Appendix A).
2.3.2. Transmission Probability IT. TI
The transmission probability through a superlattice can be calculated numerically by using the transfer matrix method [31]. The carrier conduction in each layer of the superlattice potential regions consists of superposition of two components propagating in the forward and backward directions, respectively. The total wavefunctions can be written as
S= Cei e+iki + e+iAi e-iki (2.23)

where

A1 = A2 = 0,

Ai = ki(d2 + d3 + + di)









i= 3,4,.,N (2.24)

2m? i~ 1/2
k = 2(E - E , (2.25)

where + and #{ represent the magnitudes of the particle wave functions propagating along the +z and -z directions, respectively, N is the number of the period of a superlattice, and di, m!, Ei are the thickness, effective mass, and potential energy of i-th layer in the superlattice, respectively. Since 0 and do/dz are continuous at the boundaries, we obtain

t = (e~'f- 1 + re" /+x)/ti (2.26)

b-= (rie ,i+ ei6+ )/t. (2.27)

Here the recurrence relation may be written in matrix form

( = + )r6 , (2.28)

where (at normal incidence) r= ki - k+ (2.29)
ki + ki+1

ti = 2ki (2.30)
ki + ki+l
Si = kid. (2.31)

Thus, we have


1 (=S SS2 ) =- =S1S2 . SN N . (2.32)
( 2+)=S +1
Since there is no backward propagating component in the last medium, i.e., 0+1 = 0, one can find F(i = 2,3,. ,N + 1) in term of E+, where i represents the layer region to be investigated. If we calculate the quantity as a function of E, then we can obtain the resonant peaks with Lorentzian distribution. The transmission probability is given by
2
IT.TI= + (2.33)









2.4. Carrier Transports


The carrier transport in the QWIPs plays a key role in the performance of QWIPs. In general, the carrier conduction processes in the quantum well/ sup erlatti ce structures are quite complicated. Basically, they can be divided into three different conduction processes: the continuum state conduction, the miniband conduction, and the hopping conduction.

2.4.1. Continuum State Conduction

When the excited states of a QWIP lie above the quantum well barrier, the states become continuum states, which have 3-dimensional (3-D) conduction properties. Charge carriers (i.e., either dark or photoexcited carriers) that transport through the continuum states generally have high mobility under applied bias conditions.' If the electric field is high enough, then hot carrier conduction through the 3-D continuum states is expected. This type of conduction has advantages of high efficiency, high photo conductive gain, and long mean free path. In fact, if the excited state is placed just above the barrier, resonant infrared absorption and maximum oscillator strength can be obtained [32]. This type of the conduction is usually the dominant transport process in a bulk barrier QWIP.

2.4.2. Miniband Conduction

The miniband conduction is a coherent resonant tunneling process in which photoexcited carriers are phase-coherent to the incident JR radiation. This coherent conduction can lead to much higher carrier transmission probability through the quantum well and superlattice. Resonant transmission mode builds up in the miniband to the extent that the scattering reflected wave is cancelled out and the conduction transmitted wave is enhanced. The miniband conduction depends strongly on the miniband bandwidth, heterointerface quality, and layer thickness fluctuation. For example, it has been demonstrated that the morphological quality of the heterointerface can be greatly improved by using interruption growth technique for a few tens of seconds [33].









The interruption growth allows one to reduce the density of monolayer terraces in the plane of the heterointerface. As a result, the interface improvement can enhance the coherence of the interfacing electron wave overlapping and resonant coupling. In the miniband conduction, the effective mass of the photoexcited electrons can be modulated by superlattice structure parameters, given by m* = (2h2)/(rL2). An effective mass m* for the miniband smaller than that of both the wells and barrier may be obtained. As a result, photoexcited electron transport in the miniband will have a higher electron mobility, which leads to a large oscillator absorption strength, high quantum efficiency, and high response speed. Furthermore, increasing the miniband bandwidth will reduce the tunneling time constant (i.e., To = h/F = 6.6 x10-16/T(in eV)). The value of To in a QWIP is estimated to be about 20 fs (for F = 30 - 70 meV), while a scattering time constant Ts typically is about 0.1 ps. Thus, for To < Ts, the coherent resonant tunneling can be builtup in the miniband conduction process. The photocurrent strongly depends on the tunneling time constant To, while the intersubband relaxation time constant rn is about 0.4 ps. From the theoretical calculation, Tr0 is found to be about 20 to 100 fs, hence 70 < TR. Thus, the photoexcited electrons can tunnel resonantly out of the quantum well/superlattice barrier via global miniband states.

In the miniband conduction, charge carrier transport through miniband states inside the quantum well has an average wavevector k, = eFTR/h, where F is the applied electric field. The drift velocity Vd along the superlattice axis can be expressed as

Vd = sin eFRL. (2.34)
2h &7 )
At low electric field, the carrier mobility along the superlattice axis is given by eFL2TR
z 2h 2 (2.35)
2h

It is noted that the mobility is proportional to the miniband bandwidth F and the relaxation time Tr if the superlattice basis L is kept constant. Since the miniband









bandwidth is an exponential function of the superlattice barrier thickness, the carrier mobility is also sensitive to the thickness of the superlattice barrier layer. A similar conclusion can also be drawn from the Boltzmann equation using the relaxation time approximation.
2.4.3. Hopping Conduction
When the miniband conduction fails to form coherent conduction at higher electric field, the incoherent conduction becomes the dominant mechanism, which is referred to as the sequential resonant tunneling with a random wave phase. In the incoherent conduction, the states in the quantum wells (i.e., Kane state) become localized within the individual well, and the carriers will transport via phonon-assisted tunneling (hopping) with a frequency of eFL/h. A better approach for analysis of the incoherent hopping conduction is to utilize the carrier scattering mechanism. Carrier scattering tends to destroy the coherency of the wavefunctions, hence the fully resonant threshold value will never be built-up. The mobility of the hopping conduction is usually much lower than that of the miniband conduction. As the barrier layer thickness or the thickness fluctuation increases, the maximum velocity vmax (= F L/2h) and the carrier mobility decrease. This is due to the fact that the relaxation time is nearly independent of superlattice period L. The mobility for the hopping conduction can be expressed as [34]

eL2A 8m*
liz kBT exp[-(---(AE - El))1/2Lb]. (2.36)

It is worth noting that the product of vma'TrR is always greater than the mean free path LP in the miniband conduction. However, it will reduce to even smaller than the superlattice period L in the hopping conduction limit. When the QWIPs are operating at cryogenic temperature, phonon-assisted tunneling is suppressed, and other scattering sources such as ionized impurities, intersubband levels, and interface roughness can also play an important role in the tunneling conduction.









2.5. Corrections on Subband Energy States

2.5.1. Electron-Electron Interaction

In the calculations of electronic states in quantum well/superlattice structures, electron-electron interactions should be taken into consideration when the quantum well is doped to 1018 cm-3 or higher. The interaction includes two components, direct Coulomb force and quantum exchange interaction, which shift energy states in opposite directions. The Coulomb interaction shifts the subband up while the exchange interaction shifts down. In type-I quantum wells, the doping in the quantum well can give rise to charge neutrality within the well, and the exchange energy is more significant than that of Coulomb interaction.

In the one-electron approximation, the solution of the Hartree-Fock equation gives the self-consistent eigenfunctions e and eigenvalues E,. The Hartree-Fock equation can be written as
+V2 [ e21
2~_ .(r) + V(r)O.(r) + Im(r')I2 =(r)
2m,, M kjfkl* 47reIr - r'I


- Z dr'4 r ,1�i(r)n(r)�(r)sn,sm = E.�.(r). (2.37)
m
The third and fourth terms on the left-hand side of the above equation are the direct Coulomb and exchange interaction terms, respectively.
The exchange interaction energy term associated with electrons in the bound ground state is approximately given by [35]

Eexch(k = 0) - 4--- 1 - 0.32 , (2.38)

_2kF [2_kFl
E[h(kF)2-- 0.32-] (2.39)

where k, = r/La, kF = (2ira)1/2, and a = LaND is the two-dimensional electron density in the quantum well. For the unpopulated excited states, the exchangeinduced energy shift is very small, hence the dominant contribution to the energy









shift is due to the electron-electron interaction in the highly populated ground bound state. Figure 2.3 shows a typical exchange-induced energy shift for ND = 1018 cm-3 and La = 100 A.
The energy shift in the ground bound state due to the direct coulomb interaction is given by [36]
Edifice 3 8 Le2 (2.40)


This term has a small contribution to the energy shift compared to the exchangeinduced energy shift (seen in Fig. 2.3).
2.5.2. Depolarization Effects
When IR radiation is impinging on a QWIP, resonant screening of the infrared field by electrons in the quantum well generates a depolarization field effect, which can cause the subband energy shift (also called the plasmon shift). The depolarization effect arises when the external field is screened by the mean Hartree field, which is caused by the other electrons polarized by the external field. The energy shift between subband E, and E1 due to depolarization field effect is given by [37] /2e 2e(Eo - El)Sol (.1
Edap = VE1ia 1 (2.41)


where Sol is the Coulomb matrix element given by

Sol = Jf dz [j0 (z')�l(z')dz'] . (2.42)

It is noted that the depolarization effect increases as dopant density increases (see Fig. 2.3).
2.5.3. Other Effects
Besides the corrections discussed above on energy states, the temperature shift [38], band nonparabolicity [39], and band bending effect [40] due to dopant migration can also alter the energy states in the wells, which make the deviation from the effective mass approximation. However, compared with the correction from the exchange







26


energy and depolarization effect, these effects give only a small correction on subband energy states.















































Figure 2.1.


.D.


Three components of the potential energy V(r) of electrons: V = VL + VE + Vs, (a) perfect lattice periodic potential VL, (b) superlattice periodic potential VE, and
(c) random scattering potential Vs.


VL (r) VE (r) Vs(r)


w























n=3


n=2


. a a


n=1

a ai I a


20 40 60 80 100


Barrier Width (A)




Figure 2.2. Illustration of miniband energy levels and their bandwidths as a function of the superlattice barrier width.


250 200


150 100


















20

10




-10

-20

-30 -L,=ooA
.-. For exchange energy
For plasmon shift
-40 - -- For direct Coulomb Inte

-50 1 1
1014 1016 1016 1017


�I�O~

I
9.
I raction
9.
9.


1018 1019


Dopant Density ND (cni3 )





Figure 2.3. Calculated energy shifts due to the direct Coulomb interaction, the electron-electron interaction, and the depolarization effect for ND = 10"8 cm-3 and La = 100 A.














CHAPTER 3
PRINCIPLES OF QWIP OPERATION AND FIGURES OF MERIT

3.1. Introduction

Recently, rapid progress has been made in the development of high performance quantum well infrared photodetectors (QWIPs) [11-23]. The 128x128 imaging sensor arrays using GaAs/AlGaAs QWIPs for 8 to 14 ym LWIR detection have been demonstrated by using hybrid technology [15, 16]. The detectivity of the LWIR QWIPs has been improved dramatically in recent years and is now high enough to allow fabrication of large two-dimensional (2-D) staring focal plane arrays (FPAs) with performance comparable to the state-of-the-art MCT IR FPAs.
QWIPs fabricated from III-V material systems such as GaAs/AlGaAs and InGaAs/InAlAs offer a number of potential advantages over MCT material. These include (1) III-V material growth by using MBE or MOCVD is more matured than MCT, (2) monolithic integration of III-V QWIPs with GaAs readout circuits on the same chip is possible, (3) GaAs substrates are larger, cheaper, and higher quality than MCT, (4) III-V materials are more thermal stable than MCT, (5) higher yield, lower cost, and higher reliability is expected in III-V QWIPs than in MCT devices, and

(6) III-V QWIPs have inherent advantages in both transient and total dose radiation hardness compared to MCT detectors.

3.2. Intersubband Transition


The intersubband transition in a QWIP takes place between the subband levels of either the conduction band or the valence band. It has some unique features, which include (1) large absorption coefficient [10], (2) narrow absorption bandwidth [41],









(3) large optical nonlinearity [42], (4) fast intersubband relaxation [43], (5) reduced Auger effect [44], (6) wavelength tunability [45], and (7) large photocurrent gain. The intersubband transition process can be analyzed by using the dipole transition model [46]. The transition rate W from the initial state Oi to the final state of can be described by
Wi-]=27r EI Wjq = h O <> 2(,> (E i- - hw), (3.1)

where w is the incident photon frequency and V is the interaction potential between the incident IR radiation and the electrons, which is given by [47] A = P (3.2)
moC

where A0 is the vector potential, c is the speed of light in vacuum, mo is the freeelectron mass, P is the momentum operator of electron, and is the unit polarization vector of the incident photons.

Since the electron wavefunction 0$,(k, r) in the quantum well is the product of Bloch function On,k (r) (= U,,k(z)exp(ikxx + ikyy)) and the envelope function 0,'(z), the transition matrix element can be approximated by

Mi= < (O.,k0-)fIVpI(O,k05)i >

< (O.,k)fJVpI(O.,k)i >cell< 'On1�0ni > +
< (On,k)fIl(O.,k)i >cel< OnflVM1�i >. (3.3)

In the interband transition scheme, the dipole transition occurs between the Bloch states while the envelope states (or momentum vectors) holds constant, hence the second term on the right-hand side of Eq. (3.3) tends to vanish. However, in the intersubband transition scheme such as QWIPs, the dipole transition is between the envelope states while the Bloch states remain nearly constant, thus the first term on the right-hand side of Eq. (3.3) becomes zero. From the calculation of the transition matrix element Mif = < Of IVPIi >, the transition selection rules and the incident polarization requirement for the intersubband transition can be determined.









Finally, the absorption coefficient a can be calculated by using the expression [47]
27rhcWi_.q (3.4)
= nA2w 4
where n, is the refractive index of the medium. This absorption coefficient curve can be fitted by the Lorentzian function. The integrated absorption strength IA for the polarized incidence radiation at the Brewster angle is given by e2 h lo
IA = TNS4 mc n h /- (3.5)
2 2

where N is the number of quantum wells, S is the quantum well structure factor, and f&s is the dipole oscillator strength given by 47rm*fc s'_L/2 of z 2idz (3.6)
hA A\ L/2)

When the incident radiation is perpendicular to the quantum well surface, transition matrix element Mif is zero if the shape of constant energy surface of the material is spherical. A nonzero transition rate can be obtained by using either a 450 polished facet illumination or a grating coupler [48] for the spherical constant energy surface materials. For a transmission grating coupler, the grating equation is given by

nfsnm - sinoi = MAp/A, (3.7)

where AP is the resonant incident wavelength, A is the grating period, 9i,, denote the incident and the m-th order diffracted angle with respect to the superlattice axis, respectively. In a grating coupled QWIP, the integrated absorption strength IA in Eq. (3.5) should be multiplied by a factor of sin2 Om/cosOm.









3.3. PC and PV Detection Modes

A photodetector may be operated in either the photoconductive (PC) mode or the photovoltaic (PV) mode. In the BTC QWIPs, most of the them are operated in the photoconductive (PC) mode and a few are operated in the photovoltaic (PV) mode. However, in the BTM QWIPs, they may be operated in the PC and PV dual-mode detection because of the bandwidth modulation effect in the miniband conduction QWIPs.

A photoconductor exhibits a change in resistance ARd when IR radiation is impinging on it. This change of the resistance is due to the generation of the mobile carriers in the photoconductor. The photogenerated carriers An can be written as A n - 77 A (D�TL (3.8)
V1

where 77 is the quantum efficiency, AO is the incident photon flux, TL is the excess carrier lifetime, V' is the volume of the detector. The photogenerated carriers will transport in the detector under applied bias, thus resulting photovoltage signal. The change in output photovoltage AV due to the resistance change is given by VaRLA Rd
AV yo -(RL + Rd)2' (3.9)

where RL is the load resistance and its value is chosen to be about equal to Rd in order to give optimized output signal.

When a QWIP operates in the photovoltaic detection mode, the photogenerated carriers can be transported in the detector without using externally applied bias. An internal built-in potential, Vj, can be created in the bound-to-miniband intersubband transition, which is due to the growth asymmetry and effective mass filtering effect through the global miniband. In the PV mode detection, the QWIP has an extremely low dark current, and the detector noise is dominated by Johnson noise which is much lower than that of the PC mode detection. The PV mode detector performance can be evaluated by RdAd product, where Ad is the active area of the detector.









3.4. Figures of Merit


In designing a quantum well infrared photodetector, it is important to understand the key parameters that determine the performance of a QWIP. They include: the dark current Id, noise equivalent power (NEP), responsivity (R), and detectivity D*. The QWIP performance can be evaluated by these parameters, which are often called the figures of merit.

3.4.1. Dark Current Id

In a quantum well infrared photodetector, the dark current is due to both the thermionic emission and tunneling conduction. In a conventional QWIP, thermionic emission conduction is dominant, whereas in a BTM QWIP thermionic-assisted tunneling conduction through the miniband is dominant. In order to achieve a background limited performance (BLIP) in a QWIP, the dark current must be kept below the background photocurrent (also called window current).

In the low-field regime, the thermionic emission current is related to the density of mobile carriers nt and the average drift velocity vd. It can be expressed as [49]

Ith = AdeVdnt, (3.10)

where Ad is the detector active area, and VF (3.11)
Vd = [1 + (F/v.)2]'1/2'
n, = (m*kBT/7rh2L)exp[-(Ec,t - EF)/(kBT)]. (3.12)

Here v, is the saturation drift velocity, Ecut is the cutoff energy related to the cutoff wavelength A,, and m*/7rh2 is the 2-dimensional density of states. The Fermi level EF can be obtained from

ND m*ksT [E E )] (3.13)
ND - 2L, in 1 + exp kT (3.13)
ml*
rnLa E(EF - E,). (3.14)
h 2L.n









It is noted that ND expression is valid for summation over subband levels E,' below the Fermi level EF and the approximate expression for ND is only true for cryogenic temperature.
As a result, in the cryogenic temperature range, the dark current from thermionic emission conduction is exponentially proportional to the doping concentration in the quantum well,

Ith c eEFI(kBT) oc eCND/(kBT) (3.15)

where C is a constant. It is noted that the dark current is a strong function of the quantum well doping concentration. On the other hand, the intersubband absorption is proportional to the well doping concentration. Therefore, the optimized QWIP performance is the tradeoff between the high intersubband transition and the low dark current operation.
In the miniband conduction, the coherent tunneling current component is dominant compared to the thermionic emission current component and other components such as sequential tunneling, phonon-assisted tunneling, and defect-assisted tunneling. The coherent tunneling current along the superlattice axis can be expressed by [50, 51]

It. = Ad j IT" Tjg(E ,Vb)dEz (3.16)

where IT - TI is the transmission probability (see Chapter 2.3.2) and g(E,, Vb) is the energy distribution function along superlattice axis at bias voltage Vb, which can be expressed as
4grem kBT, ( 1 + exp[(EF - E )/(kBT)] (3.17)
g(E,Vb)= - 3 kni + exp[(EF - E- eVb)/(kBT)],)"

Modified Fermi level EF resulting from the correction due to exchange energy, cryogenic temperature, depolarization effect should be used in the calculation of both Ith and It,,.









3.4.2. Spectral Responsivity R
Spectral responsivity RA for the PC mode QWIP is defined by the photocurrent output (in ampere) under IR radiation power (in watt) at a specific wavelength. The responsivity depends on the detector quantum efficiency q and the photoconductive gain g, and can be written as
e
RA = e (77" g) = 7C (3.18)
hi' hi'
A
= -7c (3.19)

where
= n(1 - Rf)(1 - Cm). (3.20)

Here Rf is the reflection coefficient (typical 0.3 for GaAs), r. is the polarization correction factor (r, = 0.5 for n-type QWIP and , = 1 for p-type QWIP), m is the number of absorption pass, a is the absorption coefficient for the superlattice, and 1 is the total superlattice thickness.

The spectral responsivity (V/W) for the PV mode QWIP can be obtained from the relationship Rv = RA � Rd, where Rd is differential resistance of a QWIP.
3.4.3. Collection Efficiency 7c

The QWIP collection efficiency 7c describes the converting efficiency from incident radiation photons to net carriers that are collected at the output of the QWIP, and is defined as the product of the quantum efficiency q7 to photoconductive gain g, namely, 7c = 7'g.

Photoconductive gain g is expressed as the ratio of the carrier transport lifetime Ti to the transit time 7T through a QWIP. From the empirical point of view, the photoconductive gain can be described in terms of the capture or trapping probability Pc [52, 53],
1 -Pc (3.21)
g= Npc
The trapping probability pc is defined as the ratio of the escaping time in the well region to the lifetime of the excited carriers from the confined ground state. If the









excited states are resonantly lined up with the top of the barrier, the escaping time will be greatly reduced, thus minimizing trapping probability and maximizing the photoconductive gain.

The final expression for 77, can be given by

7C= r(1 - Rn)(1 - em) 1 -Pc (3.22)
Npc
mat (3.23)
n(1 RI)Npc"

It is noted that the approximate expression is only true for mal < 1 and Pc < 1.

3.4.4. Detectivity D,
The detectivity of a QWIP is a very important figure of merit, which measures the QWIP sensitivity and the normalized QWIP noise equivalent power (NEP) with respect to the detector area and noise bandwidth. It can be calculated by Di = (3.24)
in'

where Af is the noise spectral bandwidth, and i,, is the overall root-mean-square noise current (in unit of A) for a QWIP. In general, the noise current for the QWIP includes two components, one is QWIP's dark current noise ind and the other is 300 K background photon noise current inb.
The dark current noise nd is given by
i2 4eldgAf for G-R noise
nd = Rd --TAf for Johnson noise. (3.25)

The G-R noise is associated with random thermal excitation and decay of the carriers, thus resulting in the fluctuation in the number of the carriers in the QWIP. The G-R noise is the dominant noise current source in the PC mode detection QWIP. However, the Johnson noise is associated with the fluctuation in the velocity of the carriers, which is the dominant noise current source in the PV mode detection QWIP.

The background photon noise is caused by the fluctuations in the number of background photons absorbed by a QWIP, which can be calculated based on the









arrival statistics of the incoherent photons. The background photon noise current .b is given by [54, 55]
� = 4e292 rl _ u B, (3.26)

where Pb is the incident background optical power for unit time, B is the QWIP bandwidth, 71 is the absorption quantum efficiency, n is the polarization correction factor, v is the incident photon frequency, and g is the photoconductive gain.
The overall noise current for the QWIP is expressed by
.2 .2 (3.27)


= 4eg-- (d g)] (3.28)

= 4eg(Id + Ib)Af, (3.29)

where Ib = eg?7J[Pb/(hv)] is the background photocurrent detected by the QWIP. When Id < Ib, the overall noise current i,, ,- inb, and the QWIP is operated under the background photon noise limitation. When Id > lb, the overall noise current in

Znd and the QWIP is operated under the operation of G-R noise or Johnson noise limitation. The detectivity D* for each noise source limitation can be calculated by

nA for background photon noise limitation
DA = ndA for dark current noise limitation.
ind

3.4.5. Background Limited Performance (BLIP)

A mid-wavelength or long-wavelength QWIP has two kinds of backgrounds: (1) high temperature ambient background (T = 300 K) and (2) low temperature cold background (T = 77 or 195 K). Under the normal thermal imaging condition, the total current feeding to the following readout circuits in a QWIP includes both the dark current Id and 300 K background photocurrent lb (i.e., Id + Ib). Due to the limitation on the charge handling capacity in the following readout circuits, the total current level of a QWIP under proper operation must be below this limited charge capacity for a given integration time of the imaging arrays. In addition, in order to achieve









the stable and clear imaging patterns, it is highly desirable to operate QWIPs under the background photon noise limitation, that is the background limited performance (BLIP).
The BLIP operation requires that Ib > Id. In order to reduce Id down to less than Ib, QWIP has to be operated at a low temperature T ~ 77 K for LWIR (8 ~ 14 pm) detection and T - 195 K for MWIR (3 - 5 jm) detection. BLIP temperature TBLIP can be found from

Id(T = TBLIp) = Ib (3.31)

= eg?7 ) (3.32)

= Adeg7rQb (3.33)

where Qb = Pb/(Ad hv) is the incident photon flux density from the background for a given spectral bandwidth Av at peak wavelength Ap. Qb is given by 27r v2Av sin2 ( (334)
Qb = d'h*2BB - 2 (3.34)
C2 ehv/kBgTB - 1 2,'

where 0 is the field of view (FOV) and TB is the background temperature of the QWIPs (TB = 300 K for ambient temperature). On the other hand, the background photocurrent Ib can be modified by using different FOV. As a result, TBLIP for a QWIP can also be changed by using different FOV optical configuration.
In a BLIP QWIP, the dominant noise source is the background photon noise while other noise sources such as G-R noise and Johnson noise are negligible in comparison. Under normal imaging conditions, the photosignal current Iph can be approximated by

Iph = (e/hv)qr-gPh, (3.35)

where Pph is the incident optical signal power for the unit time. By setting the signal-to-noise power ratio equal to unity (i.e., Iph = inb), the background-limited noise equivalent power (NEP)BLIP and the detectivity DBLIP for the QWIPs can be









expressed by

(NEP)BLIP = 2./huBPb/(CjK), (3.36)

D;LIP = / EAdB(NEP)BLIP (3.37)

It is noted that the detectivity D*LIP for the BLIP QWIP is independent of both photoconductive gain g and dark current Id, while the detectivity for the non-BLIP QWIP is dependent of both the g and the Id.
When the readout circuit noise is ignored, %BLIP for a QWIP can be evaluated by using
%BLIP nb (3.38)
(ib + i d)1/2
where inb and ind are the 300 K background photocurrent noise and dark current noise, respectively.














CHAPTER 4
A DUAL-MODE PC AND PV GaAs/AlGaAs QUANTUM WELL
INFRARED PHOTODETECTOR (DM-QWIP) WITH TWO-COLOR DETECTION

4.1. Introduction

Recently, there has been considerable interest in the study of long-wavelength intersubband quantum well infrared photodetectors (QWIPs). A great deal of work has been reported on the lattice-matched GaAs/AlGaAs and InGaAs/InA1As multiple quantum well and superlattice systems using bound-to-bound [20], bound-tominiband (BTM) [14], and bound-to-continuum [12] intersubband transitions. Although a majority of the study on intersubband absorption has been based on the photoconductive (PC) mode operation [56], studies of the photovoltaic (PV) mode operation have also been reported in the literatures [17, 19, 23, 57]. However, due to the relatively low detectivity in these PV mode QWIPs, they have to be operated below 77 K to reduce the Johnson noise. Therefore, improvement of the performance in PV mode QWIPs is highly desirable for large area focal plane array (FPA) image sensor applications.

4.2. Design Consideration

A new GaAs/AlGaAs dual-mode (PC and PV) quantum well infrared photodetectors (DM-QWIP) based on bound-to-continuum state transition mechanism was designed and fabricated [58]. Both PC and PV detection modes for this QWIP can be operated at 77 K with excellent characteristics. By properly selecting the detector parameters, we tuned the PV and PC mode operations to the different response peak wavelengths. The DM-QWIP layer structure was grown on a semi-insulating (SI)









GaAs substrate by using the molecular beam epitaxy (MBE) technique. A 1-timthick GaAs buffer layer with dopant density of 2 x 108 cm-3 was first grown on the SI GaAs substrate as an ohmic contact layer, followed by the growth of 40 periods of enlarged GaAs quantum well with well width of 110 A and a dopant density of 5x 0Is cm-3. The enlarged barrier layer on each side of the GaAs quantum well consists of an undoped A10.25Ga0.75As (875 A) layers. Finally, a n+-GaAs cap layer of 0.45 jim and a dopant density of 2 X 1018 cm-3 was grown on top of the QWIP layer structure to facilitate ohmic contact. The physical parameters of the device structure are chosen so that there are two bound states inside the enlarged well (i.e. EEWO and EEW1), and the continuum states ECN are just slightly above the top of the barrier. A high dopant density of 5x 1018 cm-3 was used in the enlarged GaAs quantum well so that the ground state EEWO and the first excited state EEW1 are heavily populated by electrons to enhance absorption of infrared radiation in the quantum well. In order to minimize the undesirable tunneling current through the barrier layers, a thick (875 A) undoped A10.25Ga0.75As barrier layer was used in this QWIP structure to suppress the tunneling current from the ground state EEWO and the first excited state EEW1.
Figure 4.1 (a) shows the energy band diagram of the DM-QWIP, which illustrates the Fermi-level and two possible intersubband transition schemes. The first transition scheme is from the localized ground state EEWO in the GaAs quantum well to the first continuum band states ECN above the AlGaAs barrier. The second transition scheme takes place from the first excited state EEW1 to the continuum states ECN. Due to the dopant migration into the enlarged AlGaAs barriers from the heavily doped GaAs quantum well during the layer growth, the actual conduction band diagram in the DM-QWIP is shown in Fig 4.1 (b). The asymmetric band bending between two side of the quantum wells induces the internal electric field Ebi, which is opposite to the direction of the quantum well layer growth. To analyze these transition schemes, we performed theoretical calculations of the energy levels of the bound states and









continuum states and transmission probability IT - Tj for this QWIP using a multilayer transfer matrix method [14] and the results are shown in Fig. 4.2. It is noted that the tunneling probability from the ground states and first excited state through the barrier layers are dramatically reduced so that the tunneling current is virtually eliminated. In order to precisely determine the intersubband transition levels, a complex calculation of the energy difference between the subband levels in the DMQWJP should be performed. These include considerations of band nonparabolicity [39], electron-electron interaction (35], electron plasma (37], and energy band bending effect [40]. For simplicity, we have only considered the effects due to energy bending, depolarization, and electron-electron interaction in heavily doped bound states in the quantum well. By taking these effects into account, both bound states EEWO and EEw1 are lowered by about '-5 meV. Thus two intersubband transition peaks should be observed in the DM-QWIP, which corresponds to infrared wavelengths of 7.7 /-m and 12 tim. Due to the thick barrier layers used in this QWIP, only thermal- and photoexcited electrons can be transported through the continuum states above the barrier and collected by the external ohmic contacts. As a result, charges separation occurs under the internal electric field Ebi, which leads to the creation of a potential difference between the two ohmic contacts of the detector. Furthermore, an asymmetrical energy band bending due to heavy doping effect can also promote the creation of internal photovoltage under IR illumination.

4.3. Experiments

The DM-QWJP mesa structure was created by chemical etching through the quantum well active layers and stopped at the 1-yrm-thick heavily doped GaAs buffer layer for ohmic contact. The active area of the detector is 200 x 200 jim2. To enhance the normal incidence coupling efficiency in the quantum well, we apply a planar metal grating coupler on the top of detector for normal illumination. The planar metal grating coupler consists of regularly spaced metal grating strips of 0.2 pim thickness









and was deposited by using electron beam (E-beam) evaporation of AuGe/Ni/Au materials. To achieve high coupling efficiency, the metal grating strips with a grating periodicity of A=5 jm and ratio factor d/A = 0.5 (d: the metal strip width) were used in this DM-QWIP.

The infrared intersubband absorption spectra of the sample were measured at the Brewster angle (OB = - 730) by using a Bruker Fourier transform interferometer (FTIR) at room temperature. The directly measured quantity is the absorbance A = -loglo(transmission), which can be converted to the absorption coefficient a for 450 incident value. The main lobe of absorption coefficient for incident of 45' is shown in Fig. 4.3. It is noted that main absorption peak is centered at Ap = 12.3 pm.
Figure 4.4 shows the current-voltage (I-V) curves and the differential resistance Rd values for the DM-QWIP measured at negative bias and T = 77K (mesa top as positive bias). It is noted that the dark current for bias voltage between - 1 and - 2 V is extremely low, which is attributed to the dramatically reduced tunneling current resulting from the increase of barrier layer thickness. Asymmetric dark current characteristics was observed in the DM-QWIP with a higher current in positive bias than that in negative bias, which results from the asymmetric effective barrier height at different polarity of applied bias as shown in Fig. 4.5. The photocurrent was measured as a function of temperature, bias voltage, polarization direction, and wavelength, using an ORIEL 77250 single grating monochromator and ceramic element infrared source. Figure 4.6 shows a plot of the normalized responsivity versus wavelength for the QWIP measured at T = 77 K. Two responsivity peaks were observed: one at Ap = 7.7 pm and Vb = 0 V, and the other at Ap = 12 pm and Vb > - 1 V. At zero bias condition, the detector operates in the PV detection mode with a peak photovoltage responsivity Rv = 11,000 V/W at A7p = 7.7 jm, which is attributed to the ground state EEWO to the first continuum state ECN transition above the barrier. The photoexcited carriers are driven by the internal Vbi (or Ebi) to generate a PV response









current from the top of mesa to the bottom. At T = 77 K, the zero bias differential resistance was found to be Rd = 5.5 Ml at T = 77 K. Since the detector operating in the PV mode is limited by Johnson noise (i.e. i,, = V4kBTAf/Rd), the detectivity D, for the PV mode was found to be 1.5x109 cm-I/-H/W. In order to verify the zero bias noise, we also measured the noise current by using a lock-in amplifier, which yielded a value of i., = 3.0x10-14 A, in good agreement with the calculated value from Johnson noise expression. When a negative bias voltage Vb is applied to the detector that is opposite to the Vbi, the PV response vanishes, and the PC mode conduction becomes the dominant detection mechanism with a PC response current from the bottom of the mesa to the top. The bias dependence of the photocurrent responsivity RA was measured using a 12 ytm IR radiation at T = 77K, and the result is shown Fig. 4.7. The maximum responsivity RA was found to be 0.48 A/W at Vb = - 2 V and T = 77 K. As expected, the detector responsivity RA increases with the applied bias voltage from Vb = - 1 V to Vb = - 2 V. For b > - 2 V, the photocurrent becomes saturated. The cutoff wavelength for this detector was found to be A,2 = 13.2 tm with a spectral bandwidth AA/Ap of 18.3 %.
From the measured responsivity and dark current, we can calculate the detectivity D, of the detector using formula, D, = RA(AdAf)'/2/i,,, where Ad is the effective area of the detector and Af is the noise bandwidth. The dark current G-R noise in is given by i,, = V/4eIdgA and may be evaluated from the measured responsivity RA = (A/1.24)(r/g) and the unpolarized quantum efficiency expression 7 = (1/2)(1e-2a ). The photoconductive gain, g, can be also derived from noise measurement. The results yielded a peak detectivity D, = 2x10�' cm-v/-H-z/W at Ap = 12 ym and T = 77 K for the PC mode operation. As shown in Fig. 4.7, the value of D, decreases with increasing negative bias voltage.









4.4. Conclusions


In conclusion, we have demonstrated a new high performance PC and PV dualmode operation GaAs QWIP using transition from the highly populated ground state and first excited state in the enlarged GaAs quantum well to the continuum band states above the AlGaAs barrier. The two bound states confined in the quantum well are a result of using the enlarged quantum well structure in the GaAs/AlGaAs DM-QWIP. With high detectivity and low dark current for both the PC and PV mode IR detection, the GaAs/AlGaAs DM-QWIP can be used for high performance two-color and dual-mode operation staring focal planar arrays and infrared imaging sensor applications.














E CN


EF E EWI E EWO


GaAs AIGaAs


E bl


E EWI E EWO


- QW growth direction


Schematic energy-band diagram for a GaAs/AlGaAs DMQWIP structure, (a) ideal case and (b) asymmetric energyband bending which is a result of dopant migration effect in the quantum well. An internal electric field Ebi is generated within the QWIP structure, which is opposite to the growth direction of the QWIP.


Figure 4.1.














0

E CN
-ov /
.2o . 0.4v[ /

-20- *.4V /
. 1.2 V /





E / /
_-40


IE EW1
0
"E/ //
-60 . .*


EEWO /

-80 - .
./ .:
EF

-100 " I I I I I i ai I I I I I
0 50 100 150 200 250

Energy (meV)



Figure 4.2. Calculated energy states and transmission coefficient IT-TI for the GaAs/AlGaAs DM-QWIP structure by using a multiplelayer transfer matrix method.






49










4200


1 3500E: T =300 K
E

= 28002100
0

CL
.o1400
I-.
(0
.0
4 7000 * ' a ' A a I ' S

6 8 10 12 14 16 18
Wavelength (pm)




Figure 4.3. Measured intersubband absorption coefficient (converted to 45 0 incident values) by Bruker FTIR at the
Brewster angle and T = 300 K.






50







10-3 : 109


10-4 T =77K
108


10-5 V


0 1.6 107 r10 10"8 r C

105
10




10"1i 104
1 2 3 4 5
Negative Bias Voltage Vb (V)


Figure 4.4. Dark current and differential resistance versus applied
bias for the GaAs/AlGaAs DM-QWIP at T = 77 K.











O. W growth direction

Zero bias


E F E EWi E EWO


Reverse bias


E EWO


Forward bias


E F E EWI E E~WO


Figure 4.5.


Effective barrier height seen by excited carriers for (a) zero bias, (b) reverse bias, and (c) forward bias. It is noticed that the effective barrier height is higher in reverse bias than in forward bias.















1.0 0.8 0.6 0.4 0.2 0.0


6 8 10 12 14
Wavelength (pm)


Figure 4.6. Relative responsivity versus wavelength for
the GaAs/AlGaAs DM-QWIP at T = 77 K.
















0.6 2.2


0.5
- 1.7

0.4 -E
* T = 77K

0.3 - p = 12pm -1.2
Ac = 13.2 pm

0.2

0.7

0.1 - /


0.0 / , , I , I 0.2
0.0 0.5 1.0 1.5 2.0 2.5 3.0

Negtive Bias Voltage Vb(V)




Figure 4.7. Responsivity and detectivity versus applied bias at A, =
12 pm and T = 77 K for the GaAs/AlGaAs DM-QWIP.














CHAPTER 5
A VOLTAGE-TUNABLE InGaAs/InA1As QUANTUM WELL
INFRARED PHOTODETECTOR (VT-QWIP)

5.1. Introduction


Long-wavelength quantum well infrared photodetectors (QWIPs) based on intersubband transitions for detection in the 8-14 pm atmospheric spectral window have been extensively investigated in recent years. Studies of the intersubband absorption in the InGaAs/InA1As system for 3 to 5 pm and 8 to 14 pm detection have also been reported [18, 59]. Since the InGaAs/InA1As heterostructure has a large conduction band offset (AEc - 500 meV) compared to GaAs/AlGaAs system, it is a promising candidate for both the mid-wavelength infrared (MWIR) and the long-wavelength infrared (LWIR) applications. Recently, we have reported the observation of a largely enhanced intersubband absorption in the InA1As/InGaAs system using intersubband transition for 8-14 pm [59] wavelength detection. The result showed multi-color infrared detection can be realized in the InGaAs/InA1As QWIP due to a much large potential barrier created by using a short period superlattice barrier structure and resonant miniband conduction mechanism.

5.2. Design Consideration


A dual-mode (PV and PC) operation InGaAs/InA1As QWIP [45] based on the voltage-tuned (VT) bound-to-miniband (BTM) transition mechanism was designed and fabricated. The VT-QWIP layer structure was grown on a semi-insulating (SI) InP substrate by using the molecular beam epitaxy (MBE) technique. A 1-jim In0.53Ga0.47As buffer layer with dopant density of 2x10" cm-3 was first grown on









the SI InP substrate, followed by the growth of 20 periods of enlarged Ino.53Gao.47As quantum wells with a well width of 110 A and a dopant density of 5x 1017 cm-3. The barrier layers on each side of the quantum well consist of 6 periods of undoped In0.52Al0.48As (35 A)/Ino.53Gao.47As (50 A) superlattice layers. A 0.3-jim-thick n+In0.53Gao.47As cap layer with a dopant density of 2 x 1018 cm-3 was grown on top of the VT-QWIP layer structure to facilitate the ohmic contact. Figure 5.1 shows the energy band diagram for this VT-QWIP. The transition scheme is from the localized ground state level EEW1 of the enlarged well (EW) to the global resonant-coupled miniband ESL1 in the superlattice (SL) barrier. The physical parameters of the quantum well and superlattices are chosen so that the first excited level EEW2 of the EW is merged and lined up with the ground miniband EsL1 of the SL on both sides of the quantum well to obtain a maximum intersubband absorption strength.
To analyze these bound-to-miniband transition schemes, theoretical calculations of the energy states EEWn, ESL. (n = 1,2,.) and the transmission probability IT . TI for the VT-QWIP were carried out by using the multi-layer transfer matrix method. In this design, a broad and highly degenerated miniband was formed by using the superlattice barrier structure. The center energy position of the first miniband is located at 163 meV above the conduction band edge of InGaAs EW with a bandwidth of I - 60 meV. In order to precisely determine the intersubband transition levels, we have considered both the electron-electron interaction (exchange energy) Eexch and depolarization Edp effects. The results show a lowering of - 5 meV for the heavily populated bound states EEw1 in the quantum well. The peak absorption wavelength can be found from the relation,

1.24
S= EsL1 - EEW1 + Eexch - Edep(Pm)" (5.1)

Now, substituting values of EsL1 = 163 meV, EEW1 = 51 meV, and Eexch - Edep " 5 meV into the above equation, we obtain Ap = 10.6 pm. The infrared intersubband absorption versus wavelength for the VT-QWIP was measured at the Brewster angle









(OB - 730) by using a Perkin-Elmer Fourier transform interferometer (FTIR) at room temperature [59]. The results showed a main absorption peak centered at A7 = 10.7 /rm with a spectral linewidth of Av = 500 cm5.3. Experiments

The mesa structure for the VT-QWIP was formed by chemical etching through the QWIP active layers and stopped at the n+ InGaAs buffer layer for ohmic contact. The active area of the detector is 200 x200 pm2. To enhance coupling efficiency for normal illumination and angular-independent radiation polarization, a planar twodimensional (2-D) metal grating coupler was formed on the VT-QWIP by using electron beam (E-beam) evaporation of 0.2 yrm gold films. The metal grating coupler consists of equally spaced square shape metal grating with a grating periodicity of A = 10 pm and a geometrical ratio factor d/A = 0.5, where d is the width of the square metal grating.
Figure 5.2 shows the dark current-voltage (I-V) and the differential resistance

(Rd) curves for the QWIP measured at T = 67 K. Asymmetric dark current characteristics was observed in the QWIP (mesa top as positive bias). The photocurrent was measured as a function of temperature, bias voltage, polarization direction, and wavelength using an ORIEL 77250 single grating monochromator and ceramic element infrared source. Figure 5.3 shows the normalized responsivity versus wavelength measured at Vb = 0, - 0.5 V and T = 67 K. In the PV mode operation (Vb = 0 V), the detector has a peak wavelength response at Ap = 10 prm with a cutoff wavelength A, = 10.4 jim. When a negative voltage is applied to the QWIP, the PC mode conduction becomes the dominant conduction mechanism. The peak wavelength Ap for the PC mode detection was found to be at AP = 10.3 jm, while a full width at half maximum of Av = 232 cm-1 (- 29 meV) was obtained from Fig. 5.3. The bandwidth AA/Ap = 24 % from PC mode response curve was found to be much narrower than the room temperature FTIR absorption curve [59]. The intersubband transitions of both the









PC mode and PV mode are attributed to the energy resonant transition from the ground state EEW1 to the global miniband ESL1 states which are aligned with the first excited state EEW2 in the quantum well. The intersubband resonant transition (maximum absorption strength or maximum wavefunction overlap) depends strongly on the location of the first excited state EEW2 of the quantum well relative to the miniband edges, ESL1 [16]. In the VT-QWIP structure, the EEW2 lies near the top of the miniband edges EsL1, which results in a strong, blueshift (0.7 ,m compared with room temperature FTIR peak wavelength 10.7 pm), and narrow-band spectral response in the PV mode detection with a linewidth of AA = 0.7 /m at a half maximum. The bound-to-miniband transition QWIP operated in the PV mode offers a unique feature of ultra-narrow bandwidth (AA/Ap = 7 %) infrared detection, which is not attainable in a conventional bound-to-continuum QWIP. As the negative bias increases, relative position between the "embedding" state EEW2 and the "framing" state ESL1 can be adjusted by the "controlling bias" due to the different dependence of EEW2 and ESL1 on the bias voltage. A peak wavelength blueshift of about 0.4 ,m (compared with the FTIR peak wavelength) was observed at Vb = - 0.5 V and T = 67K. As expected, a broad-band spectral linewidth of AA/Ap = 24 % at Vb = - 0.5 V was obtained in the PC mode as shown in Fig. 5.3. It is notice that 0.3 ,tm peak wavelength shift between the PC mode and PV mode operation was obtained by the applied bias. In the bias-tuned QWIP structure, not only can the spectral bandwidth be tailored to the desired width (from 7 % to 24 %), but the spectral response peak can also be tuned as well. This tunability can be obtained by modulating the relative position of the first excited bound state in the quantum wel within miniband states. For example, if the first bound excited state lies at the bottom edge of the miniband, then the spectral response will produce a redshift with a longer short-wavelength tail and narrow bandwidth. On the other hand, if the first bound excited state lies at the top of the miniband, then a blueshift results with a longer long-wavelength tail and









narrow bandwidth. However, if the first excited state is in the middle of the miniband, then a broader photoresponse curve is expected. This tunability is illustrated in Fig. 5.4.

The photocurrent responsivities RA of the PC mode and PV mode operation were measured at T = 67 K, AP = 10.3 pm and 10 pm, respectively, and results are shown in Fig. 5.5. The peak responsivity for PV mode was found to be 12,000 V/W at 10 ftm. The photocurrent responsivity RA for the PC mode, measured at Vb =

0.5, - 1.5 V, was found to be 38 mA/W, 145 mA/W, respectively.

5.4. Results and Discussion

The detectivity D* can be calculated from the measured responsivity and dark current. Photoconductive gain can be also derived from the noise measurement. The results yielded a peak detectivity D* = 5.8x109 cm-x/H-Y/W at Ap = 10.3 Pm, Vb = - 0.5 V, and T = 67 K for the PC mode operation. As shown in Fig. 5.5, the value of D* decreases with increasing negative bias Vb due to the increase of dark current with increasing the bias voltage. The zero bias differential resistance Rd was found to be about 450 KfQ at T = 67 K. Since the detector operating in the PV mode is limited by Johnson noise, the detectivity D, for the PV mode was found to be 5.7 x 10' cm-V-Hz/W. In order to verify the zero bias noise, we also measured the noise current by using a lock-in amplifier, which yielded a value of i, = 9.0 x 10-14 A, in good agreement with the calculated value from the Johnson noise expression.

Due to the dopant migration into superlattice barriers from the doped quantum wells, an internal built-in electric field Ebi is generated with the direction opposite to the QWIP layer growth direction. Schematic energy band diagram of considering the dopant migration effect is illustrated in the Fig. 5.6. The miniband bandwidth on two side of each quantum well was modified by the existence of the Ebi (so called miniband bandwidth modulation (MBM)). As a result, bandwidth of the global miniband becomes spatially nonuniform with broadening on the well right-hand side and









narrowing on the left-hand side as shown in the Fig. 5.6. The 15 meV wider miniband bandwidth on the side of toward-growth-direction of each InGaAs well than that on the side of backward-growth-direction can be identified and confirmed by temperature-dependent dark I-V and photocurrent measurements. For V < - 0.15 V, the photoresponse at Ap = 10.3 jim decreases with increasing bias voltage, indicating that the internal photovoltage is offset by the applied bias voltage in this bias range. For Vb > - 0.15 V, the response starts to increase again, which implies that the PC mode conduction will take over when applied bias exceeds the built-in potential Vbi " + 0.15 V resulting from miniband bandwidth modulation. The built-in electric field Ebi is estimated to be about 2.0x 10 V/cm, which is slightly below the electric field Ep = 3xO V/cm for the peak value of electron drift velocity Vd. Since tunneling time constant 7- is inversely proportional to the miniband bandwidth F ('r" = h/F), the tunneling probability of the photoexcited carriers is 40 % higher toward growth direction than backward growth direction. This different carrier tunneling probability resulting from the MBM gives rise to the PV mode detection.

5.5. Conclusions


In conclusion, we have demonstrated a new high performance PV and PC dualmode operation InGaAs/InAlAs QWIP using voltage-tuned bound-to-miniband transition mechanism. Both the narrow-band PV mode and broad-band PC mode detection at A , 10 ,m peak wavelength have been achieved. Using the dual-mode operation and bound-to-miniband transition InGaAs/InAlAs QWIP structure grown on the InP substrate, it is possible to design high performance two-color staring focal plane arrays and infrared imaging sensor for use in the 3-5 pm and 8-14 jim detection.





















A Ec = 500 meV


. *


E EWI


E SL1 InGaAs


Schematic energy band diagram showing the intersubband transitions from the ground state EEW1 to the miniband states ESL1. The relative position of the first excited state EEW2 to miniband edges strongly influences the resonant intersubband transition [16].


Figure 5.1.


InAIAs/InGaAs















10-2 107


10-3 T = 67K
106

10-4


: 10si
10-s 5
* U)

0 10-6 4
- 10


10-7

103
10"8


10- a 102
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

Negative Bias Voltage Vb M




Figure 5.2. Dark current and differential resistance versus applied bias for
the InGaAs/InAlAs QWIP measured at T = 67 K.















1.0

PC Mode:

Ap = 10.3 pm
0.8 - A = 11.7 pm

PV Mode:
.> Ap = 10 pm

0.6c = 10.4 pm



0.4
SVb = - 0.5 V Q b


0.2

. V =OV


0.0 I 1 . I I
5 7 9 11 13 15
Wavelength (pm)


Figure 5.3. Relative responsivity versus wavelength for the InGaAs/InA1As QWIP measured at T = 67 K.


















Innn lnnn uo I v"i


Rnn n in nnnnnn r oD11111 uIlnvuw


1 10
Wavelength (pm)


Figure 5.4.


Relative spectral response versus wavelength for VTQWIP (a) EEW2 lined up at the top of the ESL1 miniband states (blueshift), (b) EEW2 in the center of the EsL1 miniband states (broad bandwidth), and (c) EEW2 at the bottom of the ESL1 (redshift).


ESL1 SEEW2 E EWI
















150 6.0

T= 67 K

120 - p= 10.3 pm - 5.5


E 0
o


- 4.5

860



3 0 3 .
3.5 *


0 I' 3.0
0.0 0.3 0.6 0.9 1.2 1.5

Negative Bias Voltage Vb )



Figure 5.5. Responsivity and detectivity versus applied bias Vb at
A, = 10.3 pm and T = 67 K.



















- E bi


nnrT --


QW/SL growth direction


Figure 5.6.


Modified energy band diagram at zero bias. An internal electric field Ebi is generated in the VT-QWIP, and a modulation miniband bandwidth is formed with tunneling time constant to the left-hand side larger than that to the right-hand side, ro(left) > To(right).


-. - E bl














CHAPTER 6
A TWO-COLOR PHOTOVOLTAIC GaAs/InGaP QUANTUM
WELL INFRARED PHOTODETECTOR (PV-QWIP)

6.1. Introduction

Quantum well infrared photodetectors (QWIPs) using the intersubband optical transitions for detection in the 3 - 5 ym and 8 - 14 jm have been explored in recent years. Most of the III-V QWIPs have been fabricated from the MBE grown GaAs/AlGaAs and InGaAs/InAlAs material systems using the bound-to-bound [11, 20, 60, 61], bound-to-miniband (BTM) [14, 16, 62] and bound-to-continuum [12, 18, 22] conduction intersubband transitions and operating on photoconductive (PC) detection scheme. Although a majority of the studies on the intersubband absorption has been based on the PC mode operation, studies of the photovoltaic (PV) mode [23, 63, 64] and dual-mode (PV & PC modes) [45, 58] operation have also been reported recently. Since the PV detection mode is operated under zero-bias condition, it has the advantages of lower dark current and lower noise equivalent power compared to PC mode operation.
Since the quality of the interfaces between the quantum well and the barrier layer is extremely important for the fabrication of high performance QWIP, most of the III-V QWIPs reported in the literature are grown by using molecular beam epitaxy (MBE) technique. Recently, several reports have shown [65, 66, 67] that metal-organic chemical vapor deposition (MOCVD) technique is well adapted to the growth of a lattice-matched GaAs/Inl_ GaP material system which has a number of advantages over the AlGaAs/GaAs material system [68, 69]. The main features of this material system include, (1) selective chemical etching between InGaP and GaAs in addition to less surface oxidation during device fabrication process, (2) less









degradation of device performance due to the absence of aluminum, (3) low growth temperature which makes this material compatible with monolithic integration for optoelectronic integrated circuits [70, 71], (4) high crossover of the direct and indirect conduction bands at x = 0.74, therefore, far away from the composition latticematched to GaAs (x = 0.51), which allows operation without significant donor-related DX center problem and interface defect-assisted tunneling, (5) extremely high electron mobility in this heterostructure [72] system, and (6) ultra low recombination velocity [73] at its heterostructure interfaces. The lattice-matched GaAs/Ino.49Gao.51P system has been used in quantum wells and superlattices for electronic and photonic devices such as high electron mobility transistors (HEMTs) [70, 71], heterojunction bipolar transistors (HBTs) [74], lasers [67], light-emitting diodes [75], and photodiodes [65].
A new photovoltaic (PV) mode operation long wavelength quantum well infrared photodetector (QWIP) using a lattice-matched n-type GaAs/InO.49Ga0.51P system has been demonstrated for two-color IR detection. The detection scheme is based on bound-to-continuum states transitions from the ground bound state inside the GaAs quantum well to the first- and second-continuum band states above the InGaP barrier. The peak photovoltaic responsivities were found to be 1,000 V/W and 900 V/W at Ap, = 8.2 ,m and Ap2 = 6.0 jim and T = 77 K, respectively. The spectral response bandwidths corresponding to these two peak wavelengths were found to be 11 % and 13 %, respectively.

6.2. Design Consideration

A two-color PV mode operation QWIP fabricated on the GaAs/Ino.49Ga.51P material system was grown on an undoped GaAs substrate by using MOCVD technique. Trimethylindium (TMI) and triethylgallium (TEG) were used as indium and gallium sources, and arsine (AsH3) and phosphine (PH3) were used as arsenic and phosphorus sources. In order to obtain an high quality heterointerface, an 11-second interrupt growth between different layers was carried out at a substrate temperature









of 550 'C. A 0.7-jIm GaAs buffer layer with sulphur (S) dopant density of 1 x10"s cm-3 was first grown on the GaAs substrate as the ohmic contact layer, followed by the growth of a 15-period of GaAs quantum wells with a well width of 50 A and a sulphur dopant density of 5 X 1017 cm-3. The barrier layers on each side of the GaAs quantum well consist of an undoped In0.49Ga0.51P (360 A) layer. Finally, a GaAs cap layer of 1 ,m thick and a sulphur dopant density of 1 x1018 cm-3 was grown on top of the QWIP layers to facilitate the top ohmic contact. The physical parameters of the QWIP are chosen so that only one electron populated bound state is located inside the quantum well and the first excited band states are just slightly above the top of the barrier layers in such a way to enhance the intersubband absorption strength. To analyze the transition schemes for this QWIP, we performed theoretical calculations of the energy levels of the bound state and the continuum states and transmission probability IT- TI for the QWIP using multilayer transfer matrix method [14, 62]. In this calculation, we have used a conduction band offset AE, = 220 meV and an electron effective mass m* = 0.1 m, for the InGaP [76]. The calculated energy levels for the ground state is Eo = 75 meV in the well, the first continuum state E1 = 221 meV, and the second continuum state E2 = 300 meV from the bottom of the quantum well. This design leads to a resonant absorption, hence maximizing the absorption strength in this QWIP. As a result, two absorption peaks at about 8.5 prm and 5.5 'Urm wavelengths from the intersubband transitions are expected from this QWIP. Although the effects of band nonparabolicity, electron-electron interaction, and electron plasma are responsible for modifying the transition energy levels, the energy band bending resulted from the sulphur dopant migration in the quantum wells to the InGaP barrier layers plays an important role in the PV intersubband detection. Figure 6.1 shows the energy band diagram based on the dopant migration model and intersubband transition probability calculated from the multilayer transfer matrix method. The asymmetric energy barrier at quantum well/barrier layer interfaces causes a built-in









potential distribution [58], and hence gives rise to the photovoltaic effect. In addition, the interface scattering process also leads to a preferential escape direction of the photoexcited carriers [63], which can enhance the photovoltaic detection in the QWIP.

6.3. Experiments

The mesa structure for the QWIP was formed by the chemical etching through the quantum well active layers using HCl:H3PO4 (1:1) for the InGaP barrier layers, and H3PO4:H202:H20 (1:1:8) for the GaAs well layers. Au-Ge/Ni/Au ohmic contact films were deposited on the top and bottom contact layers. The active area of the detector is 200 x200 ttm2. To enhance the coupling efficiency for normal illumination and angular independent radiation polarization, a planar 2-D metal grating coupler was formed on the QWIP top surface by using electron beam (E-beam) evaporation of 0.2 yrm gold film. The 2-D metal grating coupler consists of equally spaced square shape metals with a periodicity of A = 10 ysm and a geometrical ratio factor g = d/A = 0.5, where d is the width of the square shape metal grating.
Figure 6.2 shows the dark current-voltage (I-V) curves measured at room temperature. It is interesting to note that a Schottky diode characteristic with a turn-on voltage - 220 mV was observed at room temperature. The high resistance property observed in this GaAs/InGaP QWIP compared to the conventional GaAs/AlGaAs and InGaAs/InAlAs QWIPs may attribute to the effects of sulphur dopant migration into InGaP barrier layers, which makes InGaP barrier layers showing persistent photoconductivity [70]. Meanwhile, the high resistance is also related to the sulphur dopant loss during the sample growth due to its high diffusivity. The photocurrent was measured as a function of temperature and polarization direction and wavelength using an ORIEL motor-driven 77250 single grating monochromator, a globar IR source, and a lock-in amplifier. Figure 6.3 shows the normalized PV responsivity versus wavelength measured at T = 77 K for this QWIP. Two response peaks were









observed, one at Ap, = 8.2 ,im with a spectral bandwidth of AA/Ap, = 11 % and the other at Ap2 = 6.0 jim with a spectral bandwidth AA/Ap2 = 13 %, which are attributed to the intersubband transition from the ground bound state to the first and second continuum states above the barrier layer, respectively. Compared with the theoretical calculation, the peak A, has an about 6 meV blueshift at T = 77 K, while the peak Ap2 has an about 18 meV redshift at T = 77 K. The blueshift of A, can be caused by the temperature dependence of electron effective mass, the conduction band nonparabolicity [39], the Fermi level, the conduction band offset, and the electron-electron exchange interaction [77]. Among these corrections on the subband states, the electron-electron exchange interaction is a dominant factor which could give rise to a significant blueshift as the temperature is decreased. The redshift of Ap2 may be associated with defects in the InGaP barrier layers [78, 79]. The measured peak responsivity is 1,000 V/W at , = 8.2 pm and 900 V/W at Ap2 = 6.0 um and T = 77 K. The detectivity D* for both wavelengths is estimated to be about 3x10s cm-x/Y-Hz/W. This low detectivity may be attributed to the sulphur-dopant loss in the well (thus lowering the oscillator absorption strength) and the formation of persistent photoconductivity in the InGaP barrier layers. The performance of this QWIP could be greatly improved by using a stable dopant impurity such as silicon [70], instead of the sulphur-dopant impurity used in the present case.
The photovoltaic behavior of this QWIP was studied in the temperature range between 77 and 30 K. The peak photovoltaic response versus inverse temperature (100/T) is shown in Fig. 6.4. It is showed that the photoresponse was increased by a factor of 6 at Ap2 and only a factor of 2 at A, as temperature decreased from 77 K to 30 K. The response at Ap2 is more sensitive to the temperature change than that at Apl. This may be due to the temperature dependence of the conduction band offset AE, (220 meV at 300 K). As the temperature decreases, conduction band offset AE, is increased, and so does the energy band bending. As a result, the first continuum









state will be gradually immersed into the wells and converted to the confined state at temperature below 70 K, which in turn will reduce its absorption strength. Therefore, the increase in the photoresponse at A , will be partially offset by the reducing escape probability, whereas the photoresponse at Ap2 will increase more rapidly.

6.4. Conclusions

We have demonstrated the first two-color long-wavelength GaAs/In.49Gao.51P QWIP grown by using MOCVD technique, based on the bound-to-continuum states intersubband transition and the PV mode operation. The low responsivity and detectivity observed in the MOCVD grown GaAs/InGap QWIP are attributed to the sulfur dopant loss in the quantum wells, thus leading to insufficient free carrier density in the quantum wells and low photoresponse. By using a stable dopant impurity such as silicon source during the MOCVD growth, a high performance GaAs/InGaP QWIP can be fabricated. The results reveal that the lattice-matched GaAs/In0.49Gao.51P materials system grown on undoped GaAs substrate has a great potential for fabricating high performance monolithic IR focal plan arrays for IR image sensor applications.










E2
.A

El
-E F AE C


GaAs
QW growth direction


InGaP


0


-10


-20


-30


-40
E

-50 a I
0 50 100 150


200 250 300 350


Energy (meV)

(b)

Figure 6.1. Schematic energy band diagram (a) and transmission coefficient ITTI and energy levels (b) for the GaAs/InGaP
QWIP grown on GaAs by using MOCVD technique


m


m















300 200100




0



-100
-1.0


-0.6 -0.2 0.2 0.6


Bias Voltage (V)







Figure 6.2. Typical dark current versus bias voltage for the
GaAs/InGaP QWIP measured at room temperature.


1.0
















1.00


0.75 0.50 0.25


0.00 1 1 4 1 1 I
5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 Wavelength (pm)






Figure 6.3. Normalized PV photoresponse versus wavelength at T
= 77 K for the GaAs/InGaP QWIP.



















GaAs/InGaP QWIP


I I I I I I I


1.0


1.5


2.0 2.5 3.0


100 /T (1/K)




Figure 6.4. Peak photovoltage versus inverse temperature for the
GaAs/InGaP QWIP at Ap1 = 8.2 pm and Ap2 = 6.0 pm.














CHAPTER 7
A NORMAL INCIDENCE TYPE-II QUANTUM WELL INFRARED
PHOTODETECTOR USING AN INDIRECT BANDGAP AlAs/A0.5Ga0.5As
GROWN ON (110) GaAs SUBSTRATE FOR MID- AND LONGWAVELENGTH MULTICOLOR DETECTION

7.1. Introduction

A normal incidence n-doped type-II indirect AlAs/Alo.5Gao.5As quantum well infrared photodetector (QWIP) grown on (110) semi-insulating (SI) GaAs substrate with MBE technique has been developed for mid- and long-wavelength multicolor detection. The normal IR absorption for the n-doped quantum wells (QWs) was achieved in the X-band confined AlAs quantum wells. Six absorption peaks including four from X-band to F-band intersubband resonant transitions were observed at AP1p6 = 2.2, 2.7, 3.5, 4.8, 6.5 and 12.5 ftm. The resonant transport from X-band to F-band gives rise to high photoconductive gain and large photoresponsivity, which are highly desirable for multicolor image sensor applications.

Quantum well infrared photodetectors (QWIPs) using type-I structures have been investigated extensively in recent years [80-88]. In type-I quantum well structure, the direct bandgap material systems are usually used, hence the shape of constant energy surfaces is spherical. As a result, only the component of IR radiation with electric field perpendicular to the quantum well layers will give rise to intersubband transition. Therefore, there is no intersubband absorption for normal IR incidence in the n-doped quantum wells. In order to achieve strong absorption for normal IR radiation in the quantum wells, grating couplers [89, 90] are required to induce absorbable component from the normal IR radiation. On the other hand, the intersubband absorption for normal IR incidence from indirect bandgap semiconductors such









as SiGe/Si was observed [91, 92]. In indirect bandgap materials, conduction electrons occupy indirect valleys with ellipsoidal constant energy surfaces. The effective-mass anisotropy (mass tensor) of electrons in the ellipsoidal valleys can provide coupling between the parallel and perpendicular motions of the electrons when the principal axes of one of the ellipsoids are tilted with respect to the growth direction. As a result of the coupling, intersubband transitions at normal incidence in an indirect bandgap QWIP structure are allowed.
Since the A1As/A1O.5Gao.5As system is an indirect bandgap material, the conduction band minima for the AlAs quantum wells are located at the X-point of the Brillouin zone (BZ). The constant energy surface will also undergo change from a typical sphere at the zone center for a direct bandgap material (i.e. GaAs) to off-center ellipsoids of an indirect bandgap material (i.e. AlAs). For AlAs, there are six ellipsoids along [100] axes with the centers of the ellipsoids located at about three-fourth of the distance from the BZ center. By choosing a proper growth direction such as [110], [111], [113], or [115] direction [86, 87], due to the anisotropic band structures and the tilted growth direction with respect to principal axes of ellipsoidal valley, it is possible to realize large area normal incidence IR detection in AlAs/AlGaAs QWIPs.

7.2. Theory

The normal incidence type-Il QWIP using an indirect bandgap AlAs/AlGaAs material system [86, 88] was grown on (110) SI GaAs substrate by using molecular beam epitaxy (MBE) technique. A 1.0-/im-thick n-doped GaAs buffer layer with ND = 2x10s cm-3 was first grown on the [110] oriented SI GaAs substrate, followed by the growth of 20 periods of AlAs/Alo.5Gao.5As quantum wells with a well width of 30 A and dopant density of 2x108 cm-3. The barrier layers on either side of the quantum well consist of an undoped A10I5Ga0.5As (500 A) barrier layer. Finally, a 0.3 ym thick n+-GaAs cap layer with a dopant density of 2x10's cm-3 was grown on top of the quantum well layers for ohmic contacts. The dopant density of 2 x 1018









cm-3 in the quantum well is chosen so that only the ground state is populated, and tradeoff between the low dark current and strong absorption strength is considered. We use the indirect bandgap AlAs for the quantum well layer and Alo.5Gao.5As for the barrier layer. Since AlGal_ As becomes an indirect bandgap material for x > 0.45, the conduction-band minimum shifts from the F-band to the X-band. Analyzing band ordering in the AlAs/AO.5GaO.5As MQW is a complicated subject in photonic device engineering [93]. We have used large enough quantum well and barrier layer thicknesses ( > 10 monolayers) so that the QWIP under study has a type-II band structure. The conduction band offset of Al05.Ga0.5As relative to AlAs is about 170 meV. Figure 7.1 shows a schematic conduction-band (F- and X-band) diagram for the type-II indirect AlAs/AO.5GaO.5As quantum well structure, in which electrons are confined inside the AlAs QW layer. The intersubband transition energy levels between the ground bound state (Eo) in the AlAs quantum well and the first excited state (El) in the well or the continuum states (E2 . E6) above the Alo.5Gao.5As barrier layers are also shown in Fig. 7.1 (a). It is noted that band splitting between the F-band and the X-band edge is about 50 meV in the AlGaAs layer, and the conduction band offset in the F-band is found to be 630 meV.

To derive the basic equations for the normal induced intersubband transitions and the corresponding indirect type-II QWIPs, we start with the Hamiltonian description of quantum mechanics for an electron [6]
~h
H, = 2m* + V(r) -j- 4 2c----� - (V(r) x p), (7.1)
-2m* 4"c vr

where m*, p, and o- are the effective mass, momentum, and spin operators of an electron, respectively. V(r) is a periodic potential function. The system under consideration consists of an assembly of electrons and the infrared radiation field. The Hamiltonian of this system, H, may be written as the sum of the unperturbed Hamiltonian Ho and the perturbing Hamiltonian Had which represents the interaction









between the electrons and the incident infrared photon and is given by [94]

H'ad = e A - P + -c x ) V(r)] , (7.2)
H'ad m*c 4m vc2

where A is the vector potential of the IR radiation field and P is the canonical momentum.
The matrix element of intersubband transition in the quantum well is given by [95, 96]
P 27r\ 1/2
Msf = kf Had kidr = -e Vch) e, Vkk (7.3)

where Oki(orf) is the total wavefunction for a state in i-th (or f-th) intersubband, the parameters i and f denote the initial and the final states, e, is the unit polarization vector of the incident photon, w is the light frequency, e is the electronic charge, V' is the volume of the crystal, n, is the refractive index at the wavelength of incident IR radiation, and �k is the conduction band energy of the X-valley material in the well.
It can be shown that the intersubband transition rate W may be expressed as [95, 97]

W = IMf 12S(Ef - E - hw)
Bok,2 82Ek 82Ck
= [- (e. - xo) + O (ek yo)
wL 8kak., a kzaky
a2Ek 2
+k zk (e, zo) S(Ef - E - hwo) (7.4)
e2 2

where Bo0 is a constant equal to ;2; x0, yo, and zo are the directional unit vectors. The result indicates that the nonzero intersubband transition probability at normal incidence can be obtained only when either of the crossover terms in the second partial derivatives is nonzero.
For an indirect gap type-II AlAs quantum well layer grown along [110] direction of GaAs substrate, due to the tilted anisotropic energy band with minimum point away from BZ center (see Fig. 7.1(b)), the second partial derivatives 82s (i = x, Oknavki
y) can be different from zero. Therefore, it is possible to excite long wavelength









intersubband transitions in the quantum well under normal incidence IR radiation. However, for a direct type-I system (i.e. GaAs) due to the isotropic spherical energy surface and the axis symmetric parabolic band E = E, + h 2(k2 + k2)/2m*, it always has a2 =0, (where i 54 z). The corresponding transition rate for direct type-I quantum well becomes
= Bk a2 C zo)] 2 8(Ef - - hw) (7.5)

The above equation reveals that, due to e,_ I z0, the optical transitions would become zero for type-I structures under normal incidence radiation.

7.3. Coupling between F- and X-bands

To analyze the intersubband transition mechanism and energy level positions in a type-II AlAs/AlGaAs QWIP, theoretical calculations of the energy states E,, (n = 0,1,2.) for the X-band and F-band and the transmission coefficient IT' TI for the QWIP were performed by using a multi-layer transfer matrix method [14]. To determine the intersubband transition levels, we use the one-band effective mass envelope function approximation (see Appendix A) and take into account the effects of band nonparabolicity and electron-electron interaction. In comparison with the more sophisticated energy band models such as two-band and three-band models, the oneband effective mass envelope function approach will give the first order approximation, thus yielding a reasonable prediction for the QWIP performance. The simulated results are summarized in Table 7.1. Each energy level listed in the Table 7.1 is referred to the center of its bandwidth. It is noted that E0 (ground state) and E1 (first excited state) are bound states which are confined in the AlAs X-band well, while E2 to E6 are all continuum states in X-band. The continuum states in the X-band can find their resonant pair levels in the F-band except E2 which is located below the F-band minima (about 30 meV).
In a type-II indirect AlAs/AlGaAs QWIP, free carriers are confined in the AlAs quantum well formed in the X-conduction band minimum, which has a larger electron









effective mass than that in the P-band valley. When normal incidence radiation impinges on this QWIP, electrons in the ground-state of the X-well are excited to either the excited state E1 or one of the continuum states E2 to E6. If the continuum state in the X-band valley is resonantly aligned with a state in the F-band valley, the photon-generated electrons in the X-band will undergo resonant transport to the resonant state in the F-band provided that the F-band barrier layer (in the present case, AlAs layer) is so thin that it is transparent to the conduction electrons [99, 100]. This resonant transport from X-band to F-band is expected to be a coherent resonance which can greatly enhance the transmission if the electron lifetime r in these continuum states is much shorter than the X-band to P-band scattering time constant rS. The .r can be estimated from the uncertainty principle, r h
c t TeEFwHM
- 10 fs (where AEFWHM is the spectral full width at half maximum), while Ts - 1 ps [19], hence 7L < 7S. The peak transmission at resonance is expected to be increased by the ratio of rs/r "- 100. In addition, due to the effective mass difference between the X-band and the P-band, electron velocity and mobility in the P-valley will be much higher than the value in the X-band valley. Since the photocurrent is proportional to the electron velocity and mobility (i.e., Iph = AdevdG7rR, where Ad is the effective area of the detector, Vd is the drift velocity, G is the photogeneration rate, 1/TR is the recombination rate of electrons in the F-band), a large increase in the photocurrent is expected when photon-generated electron resonant transport from the X-band to F-band takes place under certain bias conditions as illustrated in Fig. 7.2. It is known that photoconductive gain g = TL/rT, where 7T is transit time (=-L, 1 superlattice thickness, /I electron mobility, and F electric field). In the coherent resonance and certain bias condition, the gain g will be significantly enlarged as well.

7.4. Experiments

A BOMEN interferometer was used to measure the infrared absorbance of the AlAs/AlGaAs QWIP sample. In order to eliminate substrate absorption, we per-









formed absorbance measurements with and without the quantum well layers. The absorbance data were taken using normal incidence at 77 K and room temperature. The absorption coefficients deduced from the absorbance data are shown in Fig. 7.3. Two broad absorption peaks at wavelengths A1, = 6.8 yrm and 14 ytm were detected, while four additional narrow absorption peaks at A1. = 2.3 /tm , 2.7 pim, 3.5 pum, and 4.8 pim at NIR were also observed. The measured absorption peak wavelengths are in excellent agreement with the theoretical prediction. All the absorption coefficients measured at 77 K were found to be about a factor of 1.2 higher than the room temperature values. From our theoretical analysis, the 14 ftm peak with an absorption coefficient of about 2000 cm-1 is attributed to the transition between the ground state E0 and the first excited state El in quantum well, while the 6.8 PLm peak with absorption coefficient of about 1600 cm-1 is due to transition between the ground state E0 and the continuum state E2. The absorption peaks at 2.3 pum, 2.7 tim, 3.5 ftm, and 4.8 ptm are attributed to the transitions between the ground state E0 and other high order continuum states listed in Table 7.1. It is interesting to note that the high order intersubband transitions have relatively larger absorption coefficient of about 4000 cm-1, which is quit different from the intersubband transition in type-I QWIPs. However, the absorption at 6.8 1im, which is also due to the transition between bound state and continuum state, has a small absorption coefficient compared to the other high order continuum transitions. This indicates that the 6.8 ptm absorption peak has a different absorption and conduction mechanism, which we shall discuss it later.

To facilitate the normal incidence JR illumination, an array of 210 x 210 pim' mesas were chemically etched down to n+-GaAs buffer contact layer on the GaAs substrate. Finally, AuGe/Ni/Au ohmic contacts were formed on the QWIP structures, leaving a central sensing area of 190 x 190 jtm' for normal incidence illumination on top contact of the QWIP. Device characterization was performed in a liquid-helium cryogenic dewar. A HP4145 semiconductor parameter analyzer was used to measure









the dark current versus bias voltage. Figure 7.4 shows the measured dark current as a function of the bias voltage for temperatures between 68 and 98 K. Substantial reduction of device dark current was achieved in the present type-II structure. The photocurrent was measured using a CVI Laser Digikrom 240 monochromator and an ORIEL ceramic element infrared source. A pyroelectric detector was used to calibrate the radiation intensity from the source. The measured data for the QWIP are tabulated in Table 7.2, which showed six absorption peaks. The peaks for Apl,2 only exhibited the photoconductive (PC) detection mode, while the peaks for Ap3~6 operated in both the PC mode and photovoltaic (PV) mode.
Figure 7.5 shows the QWIP's photoresponse and absorption coefficient for wavelengths from 9 to 18 tm. The peak photoresponse was observed at Apl =12.5 ,m with a cutoff wavelength at 14.5 ,m and a peak responsivity of RA= 24 mA/W at T = 77 K and Vb= - 2 V. A broader spectral bandwidth of AA/Apl = 30% was obtained for this QWIP, which is larger than the type-I QWIP [58]. The property of a broader spectral bandwidth within X-band intersubband transition was also found in [113] GaAs substrate growth direction [87, 98]. Detectivity for this peak wavelength Ap1 = 12.5 jim was found to be about 1.1 x109 cm-v/-H-/W under the above specified condition. A relative small absorption peak at Ap2 = 6.5 1um was detected, which is attributed to the transition between the ground state E0 and the first continuum state E2. The peak responsivity for Ap2 was found to be about RA = 5 mA/W at T = 77 K and Vb = - 2 V, which was not shown in the figure. About 8 - 11 meV blueshifts were found at these two peak wavelengths.

Figure 7.6 shows the normalized photovoltaic (PV) spectral response bands at the peak wavelengths of A4 = 3.5 pm and Ap6 = 2.2 pm. The two spectral response bands cover wavelengths from 2.2 ym to 6.5 pm for peak wavelength at Ap4 = 3.5 Pm and from 2.0 ptm to 3.25 ptm for peak wavelength at Ape = 2.2 pm. The spectral band for Ap6 has an additional peak at Ap5 - 2.7 tm, while the spectral band for Ap4 also









has a large tail which results from another peak contribution at about Ap3- 4.8 ym. The positions for all four peak wavelengths Ap3-6 are in excellent agreement with the values deduced from the FTIR measurements and theoretical calculations. The main peak responses occurred at Ap4 = 3.5 pm and Ap6 = 2.2 pm with responsivities of RA = 29 mA/W and 32 mA/W, respectively, at Vb = 0 V and T = 77 K. The responsivities of two main peaks have a different voltage dependence. The peak for Ap4 increases rapidly for V > - 0.5 V, and it reaches a saturation responsivity value of 18.3 A/W at Vb > - 3 V as shown in Fig. 7.7. On the other hand, the responsivity for Ap6 remains nearly constant for Vb < - 2 V, and then exponentially increases to R = 110 A/W at Vb "- - 6 V, as shown in Fig. 7.8. Extremely large photoconductivity gains of 630 and 3,200 for Ap4 and Ap6 (as compared to the value at Vb = 0 V) were obtained at Vb = 3 V and - 6 V, respectively. The larger responses at Ap4 and Ap6 wavelengths are due to a better alignment of these resonant levels, while the relatively lower responses for the Ap3 and Ap5 wavelengths are ascribed to a slightly misalignment in the resonant levels, which results from the F-X coupling strength difference [101]. However, no photoconductivity gain is expected to be observed at Ap, and A,,2 peak wavelengths due to the absence of the resonant transition from the X-band to the F-band in the electronic conduction.
The PV mode operation at peak wavelengths of Ap3~6 in the type-II AlAs/AlGaAs QWIP is resulted from the macroscopic polarization field (i.e. Hartree potential) caused by the energy band bending effect and spatial separation of electrons and holes [45, 58, 102, 103]. However, the PV operation was not observed in the wavelengths of Apl-2. This is probably due to the novel resonant transport feature which enhances the photogenerated electron conduction.









7.5. Conclusions

In conclusion, we have demonstrated a normal incidence type-II QWIP using an indirect X-band AlAs/AlO.5GaO.sAs system grown on (110) GaAs substrate with multicolor responses for 2 ,-' 18 pm wavelength detection. The desirable normal incidence radiation is allowed due to the tilted and anisotropic energy band structure of AlAs/ AlGaAs grown on (110) GaAs substrate. The detector was found to have six peak wavelength responses at Apl~6 =12.5, 6.5, 4.8, 3.5, 2.7 and 2.2 tim. The spectral responses for wavelengths at Ap3~6 = 4.8, 3.5, 2.7, and 2.2 jm are ascribed to the novel resonant interaction between the X-band and F-band that yields a large photoconductive gain in electron conduction. The spectral response at wavelength of 12.5 yrm has a broader bandwidth (AA/Ap, = 30 %), covering wavelength ranging from 9 to 18 jym. The capabilities of normal incidence, large spectral sensing range, ultra high photoconductive gain, multicolor detection, and ultra low noise characteristics make the type-Il AlAs/AlGaAs QWIPs highly desirable for many infrared applications. Further studies of the interaction effects between the X- and F-bands, transition coupling, bandgap engineering, and hot electron transport mechanisms in the type II indirect III-V multiple quantum well structures may lead to the development of novel quantum well infrared detectors, lasers, and modulators.
















Table 7.1. The simulated intersubband transition energy levels in
the X-band and F-band for the type-II A1As/AlGaAs
QWIP.






Eo El E2 E3 E4 E5 E6 X-band 20 110 189 270 365 475 600 F-band 265 370 460 595



Notes:The energy levels, E3, E4, E5, and E6 in

the F-band and X-band formed the resonant levels for the photoexcited electrons in this QWIP. The parameters used in calculation of X-band and F-band, respectively, are m* = 0.78 mo, 0.15 mo for AlAs and 0.82 mo, 0.11 mo for Al0.sGao.sAs. (All the energy levels shown are measured from the AlAs quantum well X-conduction band edge in unit of meV.)















Table 7.2. The measured peak wavelengths, responsivities, and detectivities for the type-II A1As/AlGaAs QWIP at T =
77 K.


AP1 Ap2 Ap3 Ap4 Ap5 Ap6 Peak (ptm) 12.5 6.5 4.8 3.5 2.7 2.2

RA (A/W) (PV) 0.029 0.032
RA (A/W) (PC) 0.024 0.005 18.3 110
2V 2V 3V 6V

D, (cmv/-H--/W) 1.1 x10' 3.0x1011 1.1 x1012


















-a



S ~ J


6'


------------------.
S
S


[110]


Al. Ga . As
0.5 0.5nm
50 nm


Figure 7.1. (a) The conduction band diagram for the type-II
A1As/Alo.5Ga0o.sAs QWIP. The solid line is for the Xband and the dashed line denotes the F-band. (b) The six ellipsoids of X-band minima along the (100) axes with center of the ellipsoids located at about threefourth of the distance from BZ center for AlAs. The preferred [110] growth direction is indicated by the arrow.


E6 E4 E2


r
AEc






r-band


.5


S
S
S

S
S


X-band




x
AE
C


AIAs


3 nm



















[001]


[010]


1110]


[100]


Figure 7.1. Continued.

















Energy


AlAs


r-x coupling


Al Ga As


hv
L valley r valley X valley









Figure 7.2. Schematic diagram of the conduction band minima for
L-, F-, and X-valleys. F-X coupling transport is illustrated by the dot-dashed arrow.





































4 8 12
Wavelength (p/m)


16 20


Absorption coefficients versus wavelength measured by BOMEN interferometer at normal incidence for the AlAs/AlGaAs QWIP at T = 77 K and room temperature.


5000


4000 3000 2000 1000


E
0




0
0


C.
L.
0


Figure 7.3.















10-2

10-3

10-4 T = 98K

10-5 77K

w -6
S 106 68K

10-7
E 10"

10-9
109 AIAs/AIGaAs QWIP

10- 10

10-11
0 1 2 3 4 5
Negative Bias Voltage V (V)



Figure 7.4. Dark currents versus negative bias voltage for the
A1As/AlGaAs QWIP measured at T = 68, 77, 98 K,
respectively.



































9 10 11


12 13 14 15 16 17 18


Wavelength (pm)





Figure 7.5. Spectral responsivity and absorption coefficient versus
wavelength for Apr = 12.5 im transition at normal incidence, Vb = - 2 V and T = 77 K for the A1As/AlGaAs
QWIP.


2000


25 20


E
< 15 " 10
0




Full Text

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xml record header identifier oai:www.uflib.ufl.edu.ufdc:UF0008238800001datestamp 2009-02-24setSpec [UFDC_OAI_SET]metadata oai_dc:dc xmlns:oai_dc http:www.openarchives.orgOAI2.0oai_dc xmlns:dc http:purl.orgdcelements1.1 xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.openarchives.orgOAI2.0oai_dc.xsd dc:title Development of new III-V semiconductor quantum well infrared photodetectors for mid-and long-wavelength infrared detectiondc:creator Wang, Yanhuadc:publisher Yanhua Wangdc:date 1994dc:type Bookdc:identifier http://www.uflib.ufl.edu/ufdc/?b=UF00082388&v=0000132490061 (oclc)002007922 (alephbibnum)dc:source University of Floridadc:language English