DEVELOPMENT OF NEW IIIV SEMICONDUCTOR
QUANTUM WELL INFRARED PHOTODETECTORS FOR
MID AND LONGWAVELENGTH 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
ACKNOWLEDGEMENTS
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. Neugroschel, 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 IIIV 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
ACKNOW LEDGEMENTS ..................................................ii
ABSTRACT ................................................................ vi
CHAPTERS
1 INTRODUCTION ....................................................1
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 TI ..........................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. ElectronElectron 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 Efficiency r.c ......... ............ ...........36
3.4.4. Detectivity D, ........................................... 37
3.4.5. Background Limited Performance (BLIP) ................ 38
4 A DUALMODE PC AND PV GaAs/AlGaAs QUANTUM WELL
INFRARED PHOTODETECTOR (DMQWIP) WITH TWOCOLOR
DETECTION ...................................................... 41
4.1. Introduction .................................................... 41
4.2. Design Consideration ........................................ 41
4.3. Experiments ....................................................43
4.4. Conclusions ............................................... 46
5 A VOLTAGETUNABLE InGaAs/InA1As QUANTUM WELL
INFRARED PHOTODETECTOR (VTQWIP) ....................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 TWOCOLOR PHOTOVOLTAIC GaAs/InGaP QUANTUM
WELL INFRARED PHOTODETECTOR (PVQWIP) ...............66
6.1. Introduction ................................................... 66
6.2. Design Consideration .................... ........................67
6.3. Experiments ....................................................69
6.4. Conclusions .....................................................71
7 A NORMAL INCIDENCE TYPEII QUANTUM WELL
INFRARED PHOTODETECTOR USING AN INDIRECT
BANDGAP AlAs/Alo.sGao.sAs GROWN ON (110) GaAs
SUBSTRATE FOR THE MID AND LONGWAVELENGTH
MULTICOLOR DETECTION ......... .................... .......76
7.1. Introduction .................................. ... ............. 76
7.2. Theory ......................................................... 77
7.3. Coupling between F and Xbands ............................. 80
7.4. Experiments ................................................... 81
7.5. Conclusions .....................................................85
8 PTYPE STRAINEDLAYER QUANTUM WELL INFRARED
PHOTODETECTORS WITH BLIP AT T < 100 K ................. 97
8.1. Introduction ................... ................................ 97
8.2. Theory ......................................... .............. 98
8.3. A Tensile Strainedlayer InGaAs/InA1As QWIP .............. 102
8.3.1. Inversion between Heavy and Lighthole States ...........103
8.3.2. Experiments ........................................ 103
8.3.3. Conclusions .......................................... 105
8.4. A Compressive Strainedlayer InGaAs/GaAs QWIP ............ 106
8.4.1. Interaction between TypeI and TypeII 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 STRAINEDLAYER 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 IIIV SEMICONDUCTOR
QUANTUM WELL INFRARED PHOTODETECTORS FOR
MID AND LONGWAVELENGTH INFRARED DETECTION
By
Yanhua Wang
August 1994
Chairman: ShengSan Li
Major Department: Electrical Engineering
In this dissertation, three types of IIIV semiconductor quantum well infrared
photodetectors (QWIPs) have been developed for 35 y/m midwavelength infrared
(MWIR) and 814 /m longwavelength infrared (LWIR) detection. They are (1)
GaAs/AlGaAs, GaAs/InGaP boundtocontinuum (BTC) QWIPs and InGaAs/InA1As
boundtominiband (BTM) QWIP, (2) normalincidence typeII indirect bandgap
A1As/AlGaAs QWIP, and (3) normalincidence ptype strainedlayer 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 metalorganic chemical vapor deposition (MOCVD) technique. De
tectivity ranging from 109 to 1012 cmi/Hz/W was obtained for these QWIPs at T
= 77 K.
The BTC and BTM QWIPs exhibited both photoconductive (PC) and photo
voltaic (PV) dualmode (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 ym and 8.2 fm. The voltage
tunable InGaAs/InA1As QWIP showed a peak wavelength of 10 fPm with dualmode
operation.
A normalincidence typeII indirect bandgap A1As/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 tm. Extremely
large photoconductivity gains of 630 and 3,200 at peak wavelengths of 3.5 and 2.2 pm
were obtained at Vb = 3 and 6 V, respectively, while a broad spectral photoresponse
with peak wavelength at 12.5 fm was observed.
A normalincidence ptype tensile strainedlayer InGaAs/InA1As 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 cmv/H/W at peak wavelength of 8.1 /m,
Vb = 2 V, and T = 77 K. Finally, a normalincidence ptype compressive strainedlayer
InGaAs/GaAs QWIP grown on GaAs substrate was also demonstrated for the first
time in this work, which showed a twocolor detection feature with peak wavelengths
at 5.5 pm and 8.9 pm.
CHAPTER 1
INTRODUCTION
Infrared photodetectors are transducers that can convert invisible IR 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 pm as shown in Fig. 1.1. In the entire infrared radiation spectrum,
wavelengths ranging from 1 pm to 20 pm were found to be very important in the image
applications. In atmospheric window applications, there are three main detection
bands: (1) 13 pim shortwavelength infrared (SWIR), (2) 35 ,Pm midwavelength
infrared (MWIR), and (3) 814 pm longwavelength infrared (LWIR) (see Fig. 1.2).
The 13 ym band has been found to be very attractive in fiber optical communications.
The 814 pm 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 35 pm 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 de
tectors and photon (quantum) detectors. Thermal detectors such as bolometers and
pyroelectric detectors are made from temperaturesensitive materials. When IR ra
diation 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 photoninduced
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 pho
todetectors used for thermal imaging in past decades are summarized in Table 1.1.
In LWIR detectors, the most important detectors are fabricated from ternary com
pounds, HgCdTe (MCT). However, due to the volatility, high dislocation density,
small wafer size, different temperature expansion between the MCT and silicon read
out 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 35 im MWIR and the 814 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 A1As/GaAs system by Esaki and
Chang [4]. The quantization of the energy states in the quantum wells was experimen
tally 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 twodimensional electron gap (2DEG) proper
ties such as high electron mobility transistors (HEMTs), whereas in the perpendicular
transport carriers can move along the superlattice growth axis with the wavevector
kz, 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 trans
port 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 con
duction, 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 lay
ers 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 quan
tum 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 con
duction 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 deeplevelsrelated 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 multi
quantum well/superlattice structures may be divided into four types: type I, type II
staggered, type II 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/InA1As, GaAs/InGaP, and GaSb/AISb. 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 latticemismatched material systems if the individual epilayer thickness
is within the critical thickness. In these lattice mismatched quantum well and su
perlattice 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 reorienta
tion" 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 boundtobound (BTB) intersubband
transition for 814 ym LWIR detection. Since then, the rapid progress in QWIP per
formance has been made based on boundtocontinuum [12, 13], boundtominiband
[14] intersubband transition schemes. Figure 1.4 shows the energy bandgaps and
lattice constants of some IIIV and IIIV compound materials used for the QWIP
fabrication. The detectivity of the GaAs/AlGaAs LWIR QWIP for operating at pho
toconductive 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 imag
ing 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 35 tm 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 demon
strated yet. The image sensors at both the MWIR and the LWIR bands offer practical
applications in trackingandsearching and forwardlooking infrared (FLIR) systems.
The development of IIIV semiconductor QWIPs for MWIR and LWIR detection is
the main motivation of this dissertation.
Table 1.1. Primary photon detectors for mid and longwavelength
infrared detection.
Material
InSb
PbSe
PbTe
PtSi
Pb.17Sn.s3Te
Hgo.799Cdo.2o0Te
Mode
PC
PC,PV
PC
PC
PC
Schottky
PV
PC,PV
Operating
T (K)
195
77
195
77
77
77
77
77
Ac
(pm)
6.0
5.7
5.1
6.6
5.4
5.1
11
13
Array
Size
640x840
1024x1024
128 x128
Table 1.2. Performance status of the GaAs/AlGaAs QWIPs at T
= 77K.
p
(ptm)
10.8
8.0
10
8.9
7.7
7.5
Dc
cmV/H/W
4x1010
2x109
1.6 x1010
5.8x 109
References
[11]
[12]
[13]
[14]
[15,16]
[17]
Single
or Array
Single
Single
Single
Single
128 x128
4x4
Year
1987
1990
1990
1991
1991
1992
mode
PC
PC
PC
PC
PC
PV
Wavelength
rrays
Xrays
UV
Visible
IR
Microwave
Radiowaves

0.1 A
1A
ioA
loo .
...'0.1 p
1/p
10p
100p
i..1 cm
1 cm..
10 cm
1 m
10m
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.
30
 r< R
oK t "
S ...... .........



Near IR

Mid IR

Far IR
Extreme IR
Figure 1.1. Chart of electromagnetic spectrum.
1 3 5 7 9
Wavelength (pm)
11 13
Figure 1.2. Atmospheric transmission through 1 km path.
100
80
60
40
20
0
EI
...g ....'..: E .. g
.* .....1 .... Ev
(a) TypeI (b) TypeII Staggered
S e EE
E g I . .. . .
......... ..... .......... E v
(c) TypeII Misaligned (d) TypeIII
Figure 1.3. Possible types of band alignments at semiconductor in
terfaces. Solid lines denote the conduction band Ec 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 IIIV
and IIVI 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 in
frared (LWIR) photodetectors using the superlattice and quantum well structures
have been extensively investigated based on boundtobound [11, 20], boundto
quasicontinuum [21], boundtominiband [14], boundtocontinuum [12, 22], and mini
bandtominiband [23, 24] intersubband transition mechanisms. In order to under
stand 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 + Vee + VeN + VNN, (2.1)
where Te and TN are the kinetic energy of electrons and nuclei, respectively, and Vee,
VeN, and VNN are the electronelectron, electronnuclei, and nucleinuclei 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
T = Z V2 (2.2)
Ze*
S= e2 (2.3)
V 47rIrir rjl'
where Z = 1 is for the electron, otherwise for the nuclei charges.
The system Schradinger equation can be written as
Ht'W(R,r) = E (R,r). (2.4)
The system wavefunction I(R, r) can be expressed as the product of the nuclei wave
function x(R) and the electron wavefunction O(R, r),
W (R,r) = x(R) (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
[Te + V, + VeN]n (R, r) = E,(R).,(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 manybody problem. However, most of the systems such as the super
lattice can be described by using the oneelectron approximation, which assumes that
the motion of a single electron experiences some average force due to vibrating lattice
and all other particles. These oneelectron wavefunctions satisfy the selfconsistent
HartreeFock equations [26]. The solution of the HartreeFock equation is still a very
difficult mathematical problem. For this reason, the band approximation is often em
ployed, i.e., one solves the Schridinger equation with an assumed crystal potential
V(r) [27]. The timeindependent one electron Schridinger equation and the potential
are given by
22 + V(r) ,(k,r) = E.(k)'.(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 pe
riodic 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 Cn(k, r) and
the eigenvalue of the electron in the kspace for nth 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.) + 2m (kI + k2), (2.10)
where E,(kz) is the energy dispersion relation along the superlattice axis (longitudi
nal) 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 in
variant 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 cel
lular 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,
semiempirical 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 KronigPenney 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 Schridinger equation is the Bloch type wavefunction,
on,k(r) = Un,k(r)exp(ik r), (2.11)
where Un,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 nth band can be written as
[E,(iv) + VE+ Vs]on(r) = E n(r), (2.12)
where ,n(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 zdirection (x and ydirections within super
lattice plane), then the Bloch function becomes
n,k(r) = Un,k(z)exp(ikxX + ikyy) (2.13)
and the envelope function 0n(r) becomes a function of coordinate z, that is, 0,n(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
deeplevelsrelated 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 heterostruc
ture. When the carrier de Broglie wavelength becomes comparable to the barrier
thickness of the superlattice, the wavefunctions of the individual wells tend to over
lap due to tunneling, hence the global minibands are formed. The miniband de
coupling 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 su
perlattice 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 AB typeI (two different materials) superlattice with growth direction
along the zaxis, one period of the alternating layers is called the basis of the super
lattice, denoting L (= La + 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 4,(z)Un,k(z)exp(ikxx + ikyy), (2.14)
n
where summation is over the band index n and k,,y are the transverse wavevectors in
x and ydirection.
In the effective mass approximation and using the oneband KronigPenney
model, the envelope wavefunction On(z) can be written as [30]
{ Cicos[ka(z La/2)] + C2sin[ka(z La/2)] in the well
n(f>nz = (2.15)
C3cos[kb(z + Lb/2)] + C4sin[kb(z + Lb/2)] in the barrier,
where
S[2m (E Eb)1/2
k b (1 (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 (kaLa) cos (kbLb) 2(1/( + )sin (kaLa) sin (kbLb) (2.18)
with m = 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 (' = mrka/ml sb,
cos [kz(La + Lb)] = cos (kaLa) cosh (nbLb) (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 inplane wavefunction of superlattice experiences only a reg
ular 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,
Fr 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 m, of a miniband can be deduced from the dispersion relation E,(k,) = E'
(reference) (1/2)r cos[kz(La + Lb)],
2h2
m L (2.21)
exp(CLb)
~ (2.22)
(L, + Lb)2
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, ignor
ing the effects of growth layer fluctuations and roughness, electronelectron interac
tion, electronphonon 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 twoband or threeband 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 numeri
cally by using the transfer matrix method [31]. The carrier conduction in each layer of
the superlattice potential regions consists of superposition of two components propa
gating in the forward and backward directions, respectively. The total wavefunctions
can be written as
i = +eii e+iki + e+ii eiki (2.23)
where
A1 = A2 = 0,
Ai = ki(d2 + d3 + + di)
i = 3,4,...,N (2.24)
k, = [2 (EE) (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, mi, Ei are the thickness, effective mass, and potential energy of
ith layer in the superlattice, respectively. Since 0 and do/dz are continuous at the
boundaries, we obtain
Ct = (e~b15" + r7e"i+1)/ti (2.26)
b = (rie'61 + e" ~ )/ti. (2.27)
Here the recurrence relation may be written in matrix form
S = r6 ) ,+ (2.28)
O VT ti \re i6i e i6i O ^+
where (at normal incidence)
k. ki+i
k; + kIci+l
ti = 2k (2.30)
ki + ki+1
i = kidi. (2.31)
Thus, we have
1 ) = S = SiS2 = = SlS2 ... SN ( (2.32)
7 0+ ) N+1
Since there is no backward propagating component in the last medium, i.e.,
N+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
S(2.33)
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/superlattice
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 3dimensional (3D) 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 3D continuum
states is expected. This type of conduction has advantages of high efficiency, high
photoconductive 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 pho
toexcited carriers are phasecoherent to the incident IR radiation. This coherent con
duction 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 transmit
ted 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 modu
lated 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 = ht/ = 6.6 xl016/P(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 rs 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 Tr is about 0.4 ps. From the theoretical
calculation, Tr is found to be about 20 to 100 fs, hence 70 < TR. Thus, the photoex
cited 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 = r (ieF RL (2.34)
At low electric field, the carrier mobility along the superlattice axis is given by
eFL2r
z= 2h2 (2.35)
2h 2
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 elec
tric field, the incoherent conduction becomes the dominant mechanism, which is re
ferred 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 lo
calized within the individual well, and the carriers will transport via phononassisted
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 reso
nant threshold value will never be builtup. 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 v,ma (= 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*
iz BT exp[( (AE EI))1/2Lb]. (2.36)
It is worth noting that the product of vmas'TR 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, phononassisted 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. ElectronElectron Interaction
In the calculations of electronic states in quantum well/superlattice structures,
electronelectron interactions should be taken into consideration when the quantum
well is doped to 1018 cm3 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 typeI 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 oneelectron approximation, the solution of the HartreeFock equation
gives the selfconsistent eigenfunctions n and eigenvalues E,. The HartreeFock
equation can be written as
a2 2
2m* .(r) + V(r) 0.(r) + dr'4cr r' m(r')2 C(r)
dr' ,(r )n(r')~m(r)sn,s = E.O.(r). (2.37)
The third and fourth terms on the lefthand 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]
e2kF, k
Eexch(k = 0) 1 0.32 (2.38)
47re Iki
e2kF 2 kFl
Eezch(kF) 0.32 (2.39)
47rc 17 ki
where kl = 7r/La, kF = (2i7r)1/2, and a = LaND is the twodimensional electron
density in the quantum well. For the unpopulated excited states, the exchange
induced energy shift is very small, hence the dominant contribution to the energy
shift is due to the electronelectron interaction in the highly populated ground bound
state. Figure 2.3 shows a typical exchangeinduced energy shift for ND = 1018 cm3
and La = 100 A.
The energy shift in the ground bound state due to the direct coulomb interaction
is given by [36]
3oe2
Edifrect = (2.40)
This term has a small contribution to the energy shift compared to the exchange
induced 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 Eo and E1 due to depolarization field effect is given by [37]
2ae2(Eo E1)Sol
Edep = \ ) (2.41)
where So0 is the Coulomb matrix element given by
oo z 2
Sol = J dz 0[ o(z')1(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 effec
tive 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.
V, (r)
VE (r)
Vs (r)
I
Figure 2.1.
.D.
Three components of the potential energy V(r) of elec
trons: V = VL + VE + Vs, (a) perfect lattice periodic
potential VL, (b) superlattice periodic potential VE, and
(c) random scattering potential Vs.
\I
n=3
n=2
~Zz
a a
n=1
I I I I I I
20 40 60 80 100
Barrier Width (A)
Figure 2.2. Illustration of miniband energy levels and their band
widths as a function of the superlattice barrier width.
250
200
150
100
20
10 
:,.. ,.::=_'
0  ................
10
20
30 La= 100
30
* For exchange energy
.. For plasmon shift
40
4  For direct Coulomb Inte
50 I I i
1014 1015 1016 1017
1018 1019
Dopant Density ND (cm3 )
Figure 2.3. Calculated energy shifts due to the direct Coulomb inter
action, the electronelectron interaction, and the depolar
ization effect for ND = 1018 cm3 and La = 100 A.
\
\
reaction
9.
9.
9.
9.
9.
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) [1123]. The 128x128 imaging sen
sor arrays using GaAs/A1GaAs 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 twodimensional (2D) staring focal plane arrays (FPAs)
with performance comparable to the stateoftheart MCT IR FPAs.
QWIPs fabricated from IIIV material systems such as GaAs/AlGaAs and In
GaAs/InA1As offer a number of potential advantages over MCT material. These
include (1) IIIV material growth by using MBE or MOCVD is more matured than
MCT, (2) monolithic integration of IIIV QWIPs with GaAs readout circuits on the
same chip is possible, (3) GaAs substrates are larger, cheaper, and higher quality than
MCT, (4) IIIV materials are more thermal stable than MCT, (5) higher yield, lower
cost, and higher reliability is expected in IIIV QWIPs than in MCT devices, and
(6) IIIV 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
Wi1 = < lY > 12 (E/ E hw), (3.1)
where w is the incident photon frequency and Vp is the interaction potential between
the incident IR radiation and the electrons, which is given by [47]
eAo^
V, = o P, (3.2)
moc
where Ao is the vector potential, c is the speed of light in vacuum, mo is the free
electron mass, P is the momentum operator of electron, and c is the unit polarization
vector of the incident photons.
Since the electron wavefunction C,(k, r) in the quantum well is the product of
Bloch function On,k (r) (= Un,k(z)exp(ikxx + ikyy)) and the envelope function n,(z),
the transition matrix element can be approximated by
Mi = < (V'.,k0n)fIVp,(n,kn)i >
~ < (On,k)f/VplI(n,k)i >cell< nIf1ni > +
< (On,k)/ l(~,k)i >cell< fnflVni > (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 righthand 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 righthand side of Eq. (3.3) becomes zero. From the calculation of the transition
matrix element Mif = < f\IVpIii >, 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]
27rhcWjf (3
at" = n (3.4)
n,A2
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
e2h f
IA = aNS4 5)f (3.5)
2 2r
4com*c n2 VG +
where N is the number of quantum wells, S is the quantum well structure factor, and
fo, is the dipole oscillator strength given by
47rm*c / L./2 z
fos = AA z ^idz (3.6)
hA L/2 )
When the incident radiation is perpendicular to the quantum well surface, transi
tion matrix element Miy 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
n,rsinOm sinOi = mAp/A, (3.7)
where AX is the resonant incident wavelength, A is the grating period, i,,m denote
the incident and the mth 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
dualmode 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 (DTL (3.8)
An= (3.8)
V1
where 77 is the quantum efficiency, A0o 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 AVo due to the resistance change is given by
AVy = RL Rd)2 (3.9)
(RL + Rd 2'
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 builtin potential, V1i, can be created in the boundtominiband 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 thermionicassisted tun
neling conduction through the miniband is dominant. In order to achieve a back
ground limited performance (BLIP) in a QWIP, the dark current must be kept below
the background photocurrent (also called window current).
In the lowfield 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
V =F (3.11)
d = [1 + (yF/v.)2]1/2'
n, = (m*kT/1rh'L)exp[(Ecu EF)/(kBT)]. (3.12)
Here v, is the saturation drift velocity, Ecut is the cutoff energy related to the cutoff
wavelength Ac, and m*/7rhi2 is the 2dimensional density of states. The Fermi level
EF can be obtained from
ND m*kBT [ ep(E En (3.13)
rND 2L, n + exp F (3.13)
E(EF E). (3.14)
h 2La. 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,
th o 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 domi
nant compared to the thermionic emission current component and other components
such as sequential tunneling, phononassisted tunneling, and defectassisted tunnel
ing. The coherent tunneling current along the superlattice axis can be expressed by
[50, 51]
Itn = Ad j IT Tjg(E, Vb)dEz (3.16)
where IT TI is the transmission probability (see Chapter 2.3.2) and g(Ez, Vb) is the
energy distribution function along superlattice axis at bias voltage Vb, which can be
expressed as
4g(rem kBT, ( 1 + exp[(EF E)/(kT)] (3.17)
g b) h 1 + 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 7 and the photoconductive
gain g, and can be written as
e e
RA = ( g)= c (3.18)
hv hv
= 7c, (3.19)
1.24
where
r = n(1 Rf)(1 em'). (3.20)
Here Rf is the reflection coefficient (typical 0.3 for GaAs), r is the polarization cor
rection factor (a = 0.5 for ntype QWIP and a = 1 for ptype 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 rc
The QWIP collection efficiency 77c describes the converting efficiency from inci
dent 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, rc = 7 g.
Photoconductive gain g is expressed as the ratio of the carrier transport lifetime
TL to the transit time rT 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 r7c can be given by
7C = r(1 Rf)(1 em) (3.22)
Npc
mal (3.23)
K (1 Rf) (3.23)
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
RA/A7XJ
DX = (3.24)
where Af is the noise spectral bandwidth, and i, is the overall rootmeansquare
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 id is given by
i2 4eldgAf for GR noise
Znd = (3.25)
d 4 TAf for Johnson noise.
The GR 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 GR
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 i,
is given by [54, 55]
i = 4e2g2 (r) B, (3.26)
where Pb is the incident background optical power for unit time, B is the QWIP
bandwidth, r7 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
.= d 2 (3.27)
= 4eg Id + eg (7Pb (3.28)
= 4eg(Id + b)Af, (3.29)
where Ib = egrl?7[Pb/(hv)] is the background photocurrent detected by the QWIP.
When Id < Ib, the overall noise current i,n inb, and the QWIP is operated under
the background photon noise limitation. When Id > Ib, the overall noise current in
Sind and the QWIP is operated under the operation of GR noise or Johnson noise
limitation. The detectivity D* for each noise source limitation can be calculated by
n A~ for background photon noise limitation
D* " (3.30)
A.A d tfor dark current noise limitation.
rid
3.4.5. Background Limited Performance (BLIP)
A midwavelength or longwavelength 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 Ib (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 /m) detection. BLIP temperature
TBLIP can be found from
Id(T = TBLI) = Ib (3.31)
= eg ( ) (3.32)
= AdegrlKQb (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
2x v2Av sin O\
Qb = 2ev2A _. 2 (2) (3.34)
c2 ehv/kBTB 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 GR noise and Johnson noise are negligible in comparison.
Under normal imaging conditions, the photosignal current Iph can be approximated
by
Iph = (e/hv)rlKgPph, (3.35)
where Pph is the incident optical signal power for the unit time. By setting the
signaltonoise power ratio equal to unity (i.e., Iph = inb), the backgroundlimited
noise equivalent power (NEP)BLIP and the detectivity DBLIP for the QWIPs can be
expressed by
(NEP)BLIP = 2l/hvBPb/(7K), (3.36)
D;LIP = AB(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 nonBLIP
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 Znb (3.38)
(inb + id)1/2
where inb and ind are the 300 K background photocurrent noise and dark current
noise, respectively.
CHAPTER 4
A DUALMODE PC AND PV GaAs/AlGaAs QUANTUM WELL
INFRARED PHOTODETECTOR (DMQWIP)
WITH TWOCOLOR DETECTION
4.1. Introduction
Recently, there has been considerable interest in the study of longwavelength
intersubband quantum well infrared photodetectors (QWIPs). A great deal of work
has been reported on the latticematched GaAs/AlGaAs and InGaAs/InA1As mul
tiple quantum well and superlattice systems using boundtobound [20], boundto
miniband (BTM) [14], and boundtocontinuum [12] intersubband transitions. Al
though 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 dualmode (PC and PV) quantum well infrared photode
tectors (DMQWIP) based on boundtocontinuum 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 DMQWIP layer structure was grown on a semiinsulating (SI)
GaAs substrate by using the molecular beam epitaxy (MBE) technique. A 1ptm
thick GaAs buffer layer with dopant density of 2x101s cm3 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
5x101s cm3. The enlarged barrier layer on each side of the GaAs quantum well
consists of an undoped A10.25Gao.75As (875 A) layers. Finally, a n+GaAs cap layer of
0.45 ,im and a dopant density of 2x1018 cm3 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 018 cm3 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 DMQWIP, which illustrates
the Fermilevel 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 A1GaAs barriers from the heavily doped GaAs
quantum well during the layer growth, the actual conduction band diagram in the
DMQWIP 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 multi
layer 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 virtu
ally eliminated. In order to precisely determine the intersubband transition levels, a
complex calculation of the energy difference between the subband levels in the DM
QWIP should be performed. These include considerations of band nonparabolicity
[39], electronelectron 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 electronelectron 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 DMQWIP, which corresponds to infrared wavelengths of 7.7 pm
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 asymmet
rical energy band bending due to heavy doping effect can also promote the creation
of internal photovoltage under IR illumination.
4.3. Experiments
The DMQWIP mesa structure was created by chemical etching through the
quantum well active layers and stopped at the 1yrmthick heavily doped GaAs buffer
layer for ohmic contact. The active area of the detector is 200 x 200 /m2. 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 pm thickness
and was deposited by using electron beam (Ebeam) 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 DMQWIP.
The infrared intersubband absorption spectra of the sample were measured at
the Brewster angle (OB = ~ 73) 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 450 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 currentvoltage (IV) curves and the differential resistance
Rd values for the DMQWIP 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 char
acteristics was observed in the DMQWIP with a higher current in positive bias than
that in negative bias, which results from the asymmetric effective barrier height at dif
ferent 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 A,
= 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 Ap = 7.7 /m, which is attributed to the ground
state EEWO to the first continuum state ECN transition above the barrier. The pho
toexcited 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 MQ at T = 77 K. Since the detector operating in
the PV mode is limited by Johnson noise (i.e. in = /4kBTAf//Rd), the detectivity
D, for the PV mode was found to be 1.5x109 cmV/Hz/W. In order to verify the
zero bias noise, we also measured the noise current by using a lockin amplifier, which
yielded a value of in = 3.0x1014 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 ptm 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 Vb > 2 V, the photocurrent
becomes saturated. The cutoff wavelength for this detector was found to be Ac = 13.2
pm with a spectral bandwidth AA/Ap of 18.3 %.
From the measured responsivity and dark current, we can calculate the detectiv
ity 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 GR noise in
is given by i, = f/4eIdgJAf and may be evaluated from the measured responsivity
RA = (A/1.24)(r7g) and the unpolarized quantum efficiency expression r7 = (1/2)(1
e2a1). The photoconductive gain, g, can be also derived from noise measurement.
The results yielded a peak detectivity D, = 2x1010 cmv/Hz/W at Ap = 12 pm 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 dual
mode 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
DMQWIP. With high detectivity and low dark current for both the PC and PV
mode IR detection, the GaAs/AlGaAs DMQWIP can be used for high performance
twocolor and dualmode operation staring focal planar arrays and infrared imaging
sensor applications.
AIGaAs
E bi
QW growth direction
(b)
Schematic energyband diagram for a GaAs/AlGaAs DM
QWIP structure, (a) ideal case and (b) asymmetric energy
band 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.
E CN
EF
E EWI
E EWO
GaAs
E
EW1
E EWO
Figure 4.1.
...ittrr (C ,r e  L .. .
0
f E CN
ov / :
O
20 .... .4V I
...1.2V /
EW/ /
40 
P /.
E EWE
....
Y/ E F
100
0 50 100 150 200 250
Energy (meV)
Figure 4.2. Calculated energy states and transmission coefficient ITTI for
the GaAs/AlGaAs DMQWIP structure by using a multiple
layer transfer matrix method.
49
4200
1 3500
ST = 300 K
0 2800
2100
0)
. 1400
0
4 700
0
6 8 10 12 14 16 18
Wavelength (pm)
Figure 4.3. Measured intersubband absorption coefficient (con
verted to 45 o incident values) by Bruker FTIR at the
Brewster angle and T = 300 K.
50
103 109
104 T = 77K
108
105
1067
108 6
S10I7 7
0 106
105 0
109
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 DMQWIP at T = 77 K.
 QW growth direction
Zero bias
EF
E
EW1
E EWO
Reverse bias
E
E EW1
E EWO
Figure 4.5.
E EWO
Forward bias
Effective barrier height seen by excited carriers for (a)
zero bias, (b) reverse bias, and (c) forward bias. It is no
ticed 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 DMQWIP at T = 77 K.
0.6 2.2
0.5
1.7
0.4 E
C T=77K
0.3 p = 12 pm A 1.2
x
Ac = 13.2 pm
0.2 ."
0.7
0.1
0.0 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 AX =
12 um and T = 77 K for the GaAs/AlGaAs DMQWIP.
CHAPTER 5
A VOLTAGETUNABLE InGaAs/InA1As QUANTUM WELL
INFRARED PHOTODETECTOR (VTQWIP)
5.1. Introduction
Longwavelength quantum well infrared photodetectors (QWIPs) based on inter
subband transitions for detection in the 814 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 /m 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 midwavelength infrared (MWIR) and the longwavelength in
frared (LWIR) applications. Recently, we have reported the observation of a largely
enhanced intersubband absorption in the InA1As/InGaAs system using intersubband
transition for 814 im [59] wavelength detection. The result showed multicolor in
frared 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 dualmode (PV and PC) operation InGaAs/InA1As QWIP [45] based on the
voltagetuned (VT) boundtominiband (BTM) transition mechanism was designed
and fabricated. The VTQWIP layer structure was grown on a semiinsulating (SI)
InP substrate by using the molecular beam epitaxy (MBE) technique. A 1jim
Ino.53Gao.47As buffer layer with dopant density of 2x1018 cm3 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 5x1017 cm3.
The barrier layers on each side of the quantum well consist of 6 periods of undoped
Ino.52Al0.48As (35 A)/Ino.53Gao.47As (50 A) superlattice layers. A 0.3jimthick n+
Ino.53Gao.47As cap layer with a dopant density of 2x 1018 cm3 was grown on top of
the VTQWIP layer structure to facilitate the ohmic contact. Figure 5.1 shows the
energy band diagram for this VTQWIP. The transition scheme is from the localized
ground state level EEW1 of the enlarged well (EW) to the global resonantcoupled
miniband ESL1 in the superlattice (SL) barrier. The physical parameters of the quan
tum 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 boundtominiband transition schemes, theoretical calculations
of the energy states EEWn, ESLn (n = 1,2,...) and the transmission probability IT TI
for the VTQWIP were carried out by using the multilayer 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 r 60 meV. In order to precisely determine the intersubband transition levels, we
have considered both the electronelectron interaction (exchange energy) Eexch and
depolarization Edep 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
AP = (Pm). (5.1)
ESL1 EEW1 + Eexch Edep
Now, substituting values of EsL1 = 163 meV, EEW1 = 51 meV, and Eexch Edep "
5 meV into the above equation, we obtain Ap = 10.6 im. The infrared intersubband
absorption versus wavelength for the VTQWIP was measured at the Brewster angle
(OB ~ 730) by using a PerkinElmer Fourier transform interferometer (FTIR) at room
temperature [59]. The results showed a main absorption peak centered at A, = 10.7
/jm with a spectral linewidth of Av = 500 cm.
5.3. Experiments
The mesa structure for the VTQWIP 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 200x200 pm2. To enhance coupling efficiency for
normal illumination and angularindependent radiation polarization, a planar two
dimensional (2D) metal grating coupler was formed on the VTQWIP by using elec
tron beam (Ebeam) evaporation of 0.2 1um 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 currentvoltage (IV) and the differential resistance
(Rd) curves for the QWIP measured at T = 67 K. Asymmetric dark current charac
teristics 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 ele
ment 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 jpm with a cutoff wavelength Ac =
10.4 jm. 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 pm, while a full width at half maximum
of Av = 232 cm1 (~ 29 meV) was obtained from Fig. 5.3. The bandwidth AA/A,
= 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 VTQWIP structure, the EEW2 lies near the top
of the miniband edges EsL1, which results in a strong, blueshift (0.7 ym compared
with room temperature FTIR peak wavelength 10.7 pm), and narrowband spectral
response in the PV mode detection with a linewidth of AA = 0.7 /m at a half max
imum. The boundtominiband transition QWIP operated in the PV mode offers a
unique feature of ultranarrow bandwidth (AA/Ap = 7 %) infrared detection, which
is not attainable in a conventional boundtocontinuum 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 broadband 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 pm peak
wavelength shift between the PC mode and PV mode operation was obtained by the
applied bias. In the biastuned 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 shortwavelength 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 longwavelength tail and
narrow bandwidth. However, if the first excited state is in the middle of the mini
band, 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 fum. 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 cmx/H/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 Kf 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 109 cmVHz/W. In order to verify the zero bias noise, we also measured the
noise current by using a lockin amplifier, which yielded a value of i, = 9.0 x1014 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 builtin 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 mini
band becomes spatially nonuniform with broadening on the well righthand side and
narrowing on the lefthand side as shown in the Fig. 5.6. The 15 meV wider mini
band bandwidth on the side of towardgrowthdirection of each InGaAs well than
that on the side of backwardgrowthdirection can be identified and confirmed by
temperaturedependent dark IV and photocurrent measurements. For Vb < 0.15 V,
the photoresponse at Ap = 10.3 jm 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 builtin potential Vbi ~
+ 0.15 V resulting from miniband bandwidth modulation. The builtin electric field
Ebi is estimated to be about 2.0 x103 V/cm, which is slightly below the electric field
Ep = 3x103 V/cm for the peak value of electron drift velocity vd. Since tunneling
time constant ro is inversely proportional to the miniband bandwidth F (To = 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 dual
mode operation InGaAs/InA1As QWIP using voltagetuned boundtominiband tran
sition mechanism. Both the narrowband PV mode and broadband PC mode de
tection at AX ~ 10 um peak wavelength have been achieved. Using the dualmode
operation and boundtominiband transition InGaAs/InA1As QWIP structure grown
on the InP substrate, it is possible to design high performance twocolor staring focal
plane arrays and infrared imaging sensor for use in the 35 pm and 814 ptm detection.
A Ec = 500 meV
E Ll
InGaAs
HUH
Schematic energy band diagram showing the intersub
band transitions from the ground state EEW1 to the
miniband states ESL1. The relative position of the first
excited state EEW2 to miniband edges strongly influ
ences the resonant intersubband transition [16].
E EW1
Figure 5.1.
InAIAs/InGaAs
102 107
103 T = 67 K
106
10"4 0
10 s
S5\105
107
103 3
108 r
109 I I I 1 I  102
1.5 1.0 0.5 0.0 0.5 1.0 1.5
Negative Bias Voltage Vb (V)
Figure 5.2. Dark current and differential resistance versus applied bias for
the InGaAs/InAlAs QWIP measured at T = 67 K.
PC Mode:
Ap = 10.3 pm T
T = 67 K
0.8 Ac = 11.7 jm
PV Mode:
.E Ap = 10pm
O Ac = 10.4pm
0.4
SVb= 0.5 V
Q b
0.2
V b=OV
0.0 1 1
5 7 9 11 13 15
Wavelength (pm)
Figure 5.3. Relative responsivity versus wavelength for the In
GaAs/InA1As QWIP measured at T = 67 K.
in flflllflflfl fl in flllflilfl Ifl nllrnflfll fl o<
E EW
1 10
Wavelength (prm)
Figure 5.4.
Relative spectral response versus wavelength for VT
QWIP (a) EEW2 lined up at the top of the ESL1 mini
band states (blueshift), (b) EEW2 in the center of the
EsL1 miniband states (broad bandwidth), and (c) EEW2
at the bottom of the ESL1 (redshift).
150 6.0
T = 67 K
120 Ap = 10.3 m / 5.5
120
5.0 E
E90
S90
h4.5 "
60 *
am 4.0
30
3.5
0 3.0
0.0 0.3 0.6 0.9 1.2 1.5
Negative Bias Voltage Vb V)
Figure 5.5. Responsivity and detectivity versus applied bias Vb at
,p = 10.3 um and T = 67 K.
E bi
nnflflnnnnfl
To(left) ft
U U
 E b
Hnnnnn
1 7o(right)
I I I I I I II
QW/SL growth direction
Figure 5.6.
Modified energy band diagram at zero bias. An internal
electric field Ebi is generated in the VTQWIP, and a
modulation miniband bandwidth is formed with tunnel
ing time constant to the lefthand side larger than that
to the righthand side, To(left) > To(right).
CHAPTER 6
A TWOCOLOR PHOTOVOLTAIC GaAs/InGaP QUANTUM
WELL INFRARED PHOTODETECTOR (PVQWIP)
6.1. Introduction
Quantum well infrared photodetectors (QWIPs) using the intersubband optical
transitions for detection in the 3 5 ym and 8 14 /m have been explored in re
cent years. Most of the IIIV QWIPs have been fabricated from the MBE grown
GaAs/AlGaAs and InGaAs/InA1As material systems using the boundtobound [11,
20, 60, 61], boundtominiband (BTM) [14, 16, 62] and boundtocontinuum [12, 18,
22] conduction intersubband transitions and operating on photoconductive (PC) de
tection 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 dualmode (PV & PC modes) [45, 58] operation have also been re
ported recently. Since the PV detection mode is operated under zerobias 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 IIIV QWIPs reported in the literature are grown by using molecular beam
epitaxy (MBE) technique. Recently, several reports have shown [65, 66, 67] that
metalorganic chemical vapor deposition (MOCVD) technique is well adapted to the
growth of a latticematched GaAs/Inl_.Ga.P 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 lattice
matched to GaAs (x = 0.51), which allows operation without significant donorrelated
DX center problem and interface defectassisted tunneling, (5) extremely high electron
mobility in this heterostructure [72] system, and (6) ultra low recombination velocity
[73] at its heterostructure interfaces. The latticematched 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], lightemitting diodes [75], and photodiodes [65].
A new photovoltaic (PV) mode operation long wavelength quantum well infrared
photodetector (QWIP) using a latticematched ntype GaAs/Ino.49Gao.s1P system
has been demonstrated for twocolor IR detection. The detection scheme is based
on boundtocontinuum states transitions from the ground bound state inside the
GaAs quantum well to the first and secondcontinuum 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 twocolor PV mode operation QWIP fabricated on the GaAs/Ino.49Gao.51P
material system was grown on an undoped GaAs substrate by using MOCVD tech
nique. 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 11second
interrupt growth between different layers was carried out at a substrate temperature
of 550 "C. A 0.7jim GaAs buffer layer with sulphur (S) dopant density of 1x101
cm3 was first grown on the GaAs substrate as the ohmic contact layer, followed by
the growth of a 15period of GaAs quantum wells with a well width of 50 A and a
sulphur dopant density of 5 1017 cm3. The barrier layers on each side of the GaAs
quantum well consist of an undoped Ino.49Gao.51P (360 A) layer. Finally, a GaAs cap
layer of 1 pm thick and a sulphur dopant density of 1 xl018 cm3 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 T for the QWIP using multilayer transfer matrix method [14, 62]. In
this calculation, we have used a conduction band offset AEc = 220 meV and an elec
tron 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 pum and 5.5 'm wave
lengths from the intersubband transitions are expected from this QWIP. Although
the effects of band nonparabolicity, electronelectron 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 builtin
potential distribution [58], and hence gives rise to the photovoltaic effect. In addi
tion, 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 H3P04:H202:H20 (1:1:8) for the GaAs well layers. AuGe/Ni/Au ohmic contact
films were deposited on the top and bottom contact layers. The active area of the
detector is 200 x200 /m2. To enhance the coupling efficiency for normal illumination
and angular independent radiation polarization, a planar 2D metal grating coupler
was formed on the QWIP top surface by using electron beam (Ebeam) evaporation
of 0.2 ym gold film. The 2D metal grating coupler consists of equally spaced square
shape metals with a periodicity of A = 10 ym 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 currentvoltage (IV) curves measured at room tem
perature. It is interesting to note that a Schottky diode characteristic with a turnon
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/InA1As QWIPs may attribute to the effects of sulphur dopant migra
tion 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 wave
length using an ORIEL motordriven 77250 single grating monochromator, a globar
IR source, and a lockin 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 Ap1 = 8.2 ym with a spectral bandwidth of AA/Ap1 = 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 Ap1 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 Ap1
can be caused by the temperature dependence of electron effective mass, the conduc
tion band nonparabolicity [39], the Fermi level, the conduction band offset, and the
electronelectron exchange interaction [77]. Among these corrections on the subband
states, the electronelectron 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 Apl = 8.2 pm and 900 V/W at Ap2 = 6.0 pum and
T = 77 K. The detectivity D* for both wavelengths is estimated to be about 3x108
cmxHz/W. This low detectivity may be attributed to the sulphurdopant 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 sulphurdopant 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 Ap1 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
AEc (220 meV at 300 K). As the temperature decreases, conduction band offset AEc
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 Ap, 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 twocolor longwavelength GaAs/Ino.49Gao.51P
QWIP grown by using MOCVD technique, based on the boundtocontinuum states
intersubband transition and the PV mode operation. The low responsivity and detec
tivity 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 sil
icon source during the MOCVD growth, a high performance GaAs/InGaP QWIP can
be fabricated. The results reveal that the latticematched GaAs/Ino.49Gao.5iP mate
rials system grown on undoped GaAs substrate has a great potential for fabricating
high performance monolithic IR focal plan arrays for IR image sensor applications.
I I
H H
GaAs
QW growth direction
InGaP
0
10
20
30
40 5
50 50 100 150
0 50 100 150
200 250 300 350
Energy (meV)
(b)
Figure 6.1. Schematic energy band diagram (a) and transmission co
efficient ITTI and energy levels (b) for the GaAs/InGaP
QWIP grown on GaAs by using MOCVD technique
1it
AE
c
+v K+ T__ t
H
~rt+r~lrr~tIr~Clt~ltr~r
H
300
200
a
100
a
0
100 L
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 I' 1 1 1 I 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.
1.0
GaAs/InGaP QWIP
I I a I I I a
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 TYPEII QUANTUM WELL INFRARED
PHOTODETECTOR USING AN INDIRECT BANDGAP A1As/Alo.Gao.sAs
GROWN ON (110) GaAs SUBSTRATE FOR MID AND LONG
WAVELENGTH MULTICOLOR DETECTION
7.1. Introduction
A normal incidence ndoped typeII indirect A1As/Alo.sGao.sAs quantum well
infrared photodetector (QWIP) grown on (110) semiinsulating (SI) GaAs substrate
with MBE technique has been developed for mid and longwavelength multicolor
detection. The normal IR absorption for the ndoped quantum wells (QWs) was
achieved in the Xband confined AlAs quantum wells. Six absorption peaks including
four from Xband to Fband intersubband resonant transitions were observed at Apl6
= 2.2, 2.7, 3.5, 4.8, 6.5 and 12.5 /m. The resonant transport from Xband to Fband
gives rise to high photoconductive gain and large photoresponsivity, which are highly
desirable for multicolor image sensor applications.
Quantum well infrared photodetectors (QWIPs) using typeI structures have
been investigated extensively in recent years [8088]. In typeI quantum well struc
ture, the direct bandgap material systems are usually used, hence the shape of con
stant 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 ndoped quantum wells. In order to achieve strong absorption for normal IR
radiation in the quantum wells, grating couplers [89, 90] are required to induce ab
sorbable component from the normal IR radiation. On the other hand, the intersub
band 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 effectivemass
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 AIAs/Alo.sGao.sAs system is an indirect bandgap material, the con
duction band minima for the AlAs quantum wells are located at the Xpoint of the
Brillouin zone (BZ). The constant energy surface will also undergo change from a typ
ical sphere at the zone center for a direct bandgap material (i.e. GaAs) to offcenter
ellipsoids of an indirect bandgap material (i.e. AlAs). For AlAs, there are six ellip
soids along [100] axes with the centers of the ellipsoids located at about threefourth
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 A1As/AlGaAs QWIPs.
7.2. Theory
The normal incidence typeII QWIP using an indirect bandgap A1As/AlGaAs
material system [86, 88] was grown on (110) SI GaAs substrate by using molecular
beam epitaxy (MBE) technique. A 1.0/mthick ndoped GaAs buffer layer with ND
= 2x01s cm3 was first grown on the [110] oriented SI GaAs substrate, followed by
the growth of 20 periods of A1As/Alo.5Gao.5As quantum wells with a well width of
30 A and dopant density of 2x1018 cm3. The barrier layers on either side of the
quantum well consist of an undoped Alo.1Gao.sAs (500 A) barrier layer. Finally, a
0.3 /m thick n+GaAs cap layer with a dopant density of 2x1018 cm3 was grown
on top of the quantum well layers for ohmic contacts. The dopant density of 2 x101
cm3 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.sGao.sAs for the
barrier layer. Since A1,Gal_,As becomes an indirect bandgap material for x > 0.45,
the conductionband minimum shifts from the Fband to the Xband. Analyzing
band ordering in the A1As/Alo.sGao.sAs 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 typeII band
structure. The conduction band offset of Alo0.Gao.sAs relative to AlAs is about 170
meV. Figure 7.1 shows a schematic conductionband (F and Xband) diagram for
the typeII indirect A1As/Alo.sGao.sAs 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.sAs
barrier layers are also shown in Fig. 7.1 (a). It is noted that band splitting between
the Fband and the Xband edge is about 50 meV in the AlGaAs layer, and the
conduction band offset in the Fband is found to be 630 meV.
To derive the basic equations for the normal induced intersubband transitions and
the corresponding indirect typeII QWIPs, we start with the Hamiltonian description
of quantum mechanics for an electron [6]
Ho = 2 + V(r)+ (7V(r) x p), (7.1)
2m* 4m*2c2
where m*, p, and r are the effective mass, momentum, and spin operators of an
electron, respectively. V(r) is a periodic potential function. The system under con
sideration 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 Hamil
tonian Ho and the perturbing Hamiltonian H ad which represents the interaction
between the electrons and the incident infrared photon and is given by [94]
H'ad = A P+( x ) V( )] (7.2)
Hrad m*c 4
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
Mf = /kfH'adkidr = e V' cT en, hVkk (7.3)
where Oki(orf) is the total wavefunction for a state in ith (or fth) 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 Xvalley material in the well.
It can be shown that the intersubband transition rate W may be expressed as
[95, 97]
297
W M= Mf;12(Ef E hw)
Bok ,2 2Ek ,2 k
S [(e xo) + (eOk o)
w 8kY k, a, ak, kdk,
a2Ek 2
+akaz (e, zo) S(Ef Ei hw) (7.4)
where Bo is a constant equal to 2,2 ; xo, 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 typeII 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 2 (i = x,
y) can be different from zero. Therefore, it is possible to excite long wavelength
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 typeI system (i.e. GaAs) due to the isotropic spherical energy
surface and the axis symmetric parabolic band E = Ez + 2(k + )/2m*, it always
has 2 = 0, (where i 5 z). The corresponding transition rate for direct typeI
quantum well becomes
2 Bok2 2k (
W = Bk l k e zo) 2 (E Ei hw) (7.5)
Lu [Okz kz J
The above equation reveals that, due to e, I zo, the optical transitions would become
zero for typeI structures under normal incidence radiation.
7.3. Coupling between r and Xbands
To analyze the intersubband transition mechanism and energy level positions
in a typeII A1As/AlGaAs QWIP, theoretical calculations of the energy states E,,
(n = 0,1,2...) for the Xband and Fband and the transmission coefficient IT TI
for the QWIP were performed by using a multilayer transfer matrix method [14].
To determine the intersubband transition levels, we use the oneband effective mass
envelope function approximation (see Appendix A) and take into account the effects of
band nonparabolicity and electronelectron interaction. In comparison with the more
sophisticated energy band models such as twoband and threeband models, the one
band 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 Eo (ground state) and E1
(first excited state) are bound states which are confined in the AlAs Xband well,
while E2 to E6 are all continuum states in Xband. The continuum states in the
Xband can find their resonant pair levels in the Fband except E2 which is located
below the Fband minima (about 30 meV).
In a typeII indirect A1As/AlGaAs QWIP, free carriers are confined in the AlAs
quantum well formed in the Xconduction band minimum, which has a larger electron
effective mass than that in the rband valley. When normal incidence radiation
impinges on this QWIP, electrons in the groundstate of the Xwell are excited to
either the excited state E1 or one of the continuum states E2 to E6. If the continuum
state in the Xband valley is resonantly aligned with a state in the rband valley,
the photongenerated electrons in the Xband will undergo resonant transport to the
resonant state in the Fband provided that the Fband 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 Xband to Fband is expected to be a coherent
resonance which can greatly enhance the transmission if the electron lifetime Tr in
these continuum states is much shorter than the Xband to rband scattering time
constant Ts. The rf can be estimated from the uncertainty principle, rr = Ewy
~ 10 fs (where AEFWHM is the spectral full width at half maximum), while Ts ~ 1 ps
[19], hence 7r
by the ratio of rs/Tr ~ 100. In addition, due to the effective mass difference between
the Xband and the rband, electron velocity and mobility in the Tvalley will be much
higher than the value in the Xband valley. Since the photocurrent is proportional
to the electron velocity and mobility (i.e., Iph = AdevdGrR, 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 Fband), a large increase in the photocurrent
is expected when photongenerated electron resonant transport from the Xband to
Fband takes place under certain bias conditions as illustrated in Fig. 7.2. It is known
that photoconductive gain g = TL/rT, where rT is transit time (=, I superlattice
thickness, fi 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
A1As/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 Ap = 6.8 im and 14 /m were detected,
while four additional narrow absorption peaks at Ap = 2.3 /m 2.7 pm, 3.5 pm, and
4.8 pm 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 tem
perature values. From our theoretical analysis, the 14 /m peak with an absorption
coefficient of about 2000 cm1 is attributed to the transition between the ground state
Eo and the first excited state E1 in quantum well, while the 6.8 Pm peak with ab
sorption coefficient of about 1600 cm1 is due to transition between the ground state
Eo and the continuum state E2. The absorption peaks at 2.3 pm, 2.7 /m, 3.5 /sm,
and 4.8 pm are attributed to the transitions between the ground state Eo 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 cm1, which is quit different from the intersubband transition in typeI QWIPs.
However, the absorption at 6.8 utm, 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 IR illumination, an array of 210 x 210 pm2
mesas were chemically etched down to n+GaAs buffer contact layer on the GaAs sub
strate. Finally, AuGe/Ni/Au ohmic contacts were formed on the QWIP structures,
leaving a central sensing area of 190 x 190 /m2 for normal incidence illumination on
top contact of the QWIP. Device characterization was performed in a liquidhelium
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. Substan
tial reduction of device dark current was achieved in the present typeII 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 wave
lengths from 9 to 18 /m. The peak photoresponse was observed at Ap1 =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/Ap1 = 30% was obtained
for this QWIP, which is larger than the typeI QWIP [58]. The property of a broader
spectral bandwidth within Xband 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 cmHz/W under the above specified
condition. A relative small absorption peak at Ap2 = 6.5 ym was detected, which
is attributed to the transition between the ground state Eo 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 Ap4 = 3.5 pm and Ape = 2.2 pm. The two spectral response
bands cover wavelengths from 2.2 pm to 6.5 pm for peak wavelength at Ap4 = 3.5 pm
and from 2.0 tpm to 3.25 pm for peak wavelength at Ape = 2.2 pm. The spectral band
for Ape has an additional peak at Ap5 ~ 2.7 tpm, while the spectral band for Ap4 also
has a large tail which results from another peak contribution at about Ap3 ~ 4.8 pm.
The positions for all four peak wavelengths Ap36 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 Vb > 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 FX coupling strength difference [101]. However, no
photoconductivity gain is expected to be observed at Ap, and Ap2 peak wavelengths
due to the absence of the resonant transition from the Xband to the Fband in the
electronic conduction.
The PV mode operation at peak wavelengths of Ap3~6 in the typeII A1As/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 wave
lengths of Apl2. 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 typeII QWIP using an
indirect Xband A1As/Alo.sGao.sAs system grown on (110) GaAs substrate with mul
ticolor 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 /m. The spectral re
sponses for wavelengths at Ap3~6 = 4.8, 3.5, 2.7, and 2.2 ym are ascribed to the novel
resonant interaction between the Xband and Fband that yields a large photocon
ductive gain in electron conduction. The spectral response at wavelength of 12.5 ym
has a broader bandwidth (AA/Ap1 = 30 %), covering wavelength ranging from 9 to
18 jm. The capabilities of normal incidence, large spectral sensing range, ultra high
photoconductive gain, multicolor detection, and ultra low noise characteristics make
the typeII A1As/AlGaAs QWIPs highly desirable for many infrared applications.
Further studies of the interaction effects between the X and Fbands, transition cou
pling, bandgap engineering, and hot electron transport mechanisms in the type II
indirect IIIV 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 Xband and Fband for the typeII A1As/AlGaAs
QWIP.
Eo El E2 E3 E4 E5 E6
Xband 20 110 189 270 365 475 600
rband 265 370 460 595
Notes:The energy levels, E3, E4, E5, and E6 in
the Fband and Xband formed the resonant
levels for the photoexcited electrons in this
QWIP. The parameters used in calculation of
Xband and Fband, respectively, are m* =
0.78 mo, 0.15 mo for AlAs and 0.82 mo, 0.11
mo for Alo.5Gao.sAs. (All the energy levels
shown are measured from the AlAs quantum
well Xconduction band edge in unit of meV.)
Table 7.2. The measured peak wavelengths, responsivities, and de
tectivities for the typeII A1As/AlGaAs QWIP at T =
77 K.
Api Ap2 Ap3 Ap4 Ap5 Ap6
Peak (tm) 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 1.1x1012
arr~
zzzcI
6'
 
I  S
S S
S S__ __ _
[110]
Alo.s Ga .As
0.5 0.5
50 nm
Figure 7.1. (a) The conduction band diagram for the typeII
A1As/Alo.5Gao.sAs QWIP. The solid line is for the X
band and the dashed line denotes the Fband. (b) The
six ellipsoids of Xband minima along the (100) axes
with center of the ellipsoids located at about three
fourth of the distance from BZ center for AlAs. The
preferred [110] growth direction is indicated by the ar
row.
E
6
E4
E2
r
AEc
rband
.I
S
S
S
Xband
x
AE
C
AlAs
3 nm
[001]
[110]
[100]
(b)
Figure 7.1. Continued.
[010]
AlAs
Al Ga As
.5 .s
Energy
rX coupling
hv
L valley r valley X valley
Figure 7.2. Schematic diagram of the conduction band minima for
L, r, and Xvalleys. FX coupling transport is illus
trated by the dotdashed arrow.
4 8 12
Wavelength (pm)
16 20
Absorption coefficients versus wavelength measured by
BOMEN interferometer at normal incidence for the
A1As/AlGaAs QWIP at T = 77 K and room temper
ature.
5000
4000
3000
2000
1000
'E
0
0
C)
c0
L.
0
O
'C
Figure 7.3.
102
103
104 T = 98K
g 105 77K
1 107
106
S10"
109
0 AIAs/AIGaAs QWIP
1010
1011 I i II
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.
25
20
E
< 15
CD
It 10
o
0
0.
U)
9 10 11
2000
12 13 14 15 16 17 18
Wavelength (pm)
Figure 7.5. Spectral responsivity and absorption coefficient versus
wavelength for Ap1 = 12.5 fm transition at normal inci
dence, Vb = 2 V and T = 77 K for the A1As/AlGaAs
QWIP.
