Title Page
 Table of Contents
 Quantum well and superlattice...
 Principles of qwip operation and...
 Principles of qwip operation and...
 A dual-mode pc and pv GaAs/AlGaAs...
 A voltage-tunable InGaAs/InAlAs...
 A two-color photovoltaic GaAs/InGaP...
 A normal incidence type-II quantum...
 P-type strained-layer quantum well...
 Summary and conclusions
 Biographical sketch

Title: Development of new III-V semiconductor quantum well infrared photodetectors for mid-and long-wavelength infrared detection
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00082388/00001
 Material Information
Title: Development of new III-V semiconductor quantum well infrared photodetectors for mid-and long-wavelength infrared detection
Physical Description: vii, 146 leaves : ill. ; 29 cm.
Language: English
Creator: Wang, Yanhua, 1955-
Publication Date: 1994
Subject: Quantum wells   ( lcsh )
Optoelectronic devices   ( lcsh )
Infrared detectors   ( lcsh )
Electrical Engineering thesis Ph. D
Dissertations, Academic -- Electrical Engineering -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
Thesis: Thesis (Ph. D.)--University of Florida, 1994.
Bibliography: Includes bibliographical references (leaves 139-145).
Statement of Responsibility: by Yanhua Wang.
General Note: Typescript.
General Note: Vita.
 Record Information
Bibliographic ID: UF00082388
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: aleph - 002007922
oclc - 32490061
notis - AKJ5195

Table of Contents
    Title Page
        Page i
        Page ii
    Table of Contents
        Page iii
        Page iv
        Page v
        Page vi
        Page vii
        Page 1
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        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
    Quantum well and superlattice structures
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
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        Page 23
        Page 24
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        Page 26
        Page 27
        Page 28
        Page 29
    Principles of qwip operation and figures of merit
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
    Principles of qwip operation and figures of merit
        Page 38
        Page 39
        Page 40
    A dual-mode pc and pv GaAs/AlGaAs quantum well infrared photodetector (dm-qwip) with two-color detection
        Page 41
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
        Page 53
    A voltage-tunable InGaAs/InAlAs quantum well infrared photodetector (vt-qwip)
        Page 54
        Page 55
        Page 56
        Page 57
        Page 58
        Page 59
        Page 60
        Page 61
        Page 62
        Page 63
        Page 64
        Page 65
    A two-color photovoltaic GaAs/InGaP quantum well infrared photodetector (pv-qwip)
        Page 66
        Page 67
        Page 68
        Page 69
        Page 70
        Page 71
        Page 72
        Page 73
        Page 74
        Page 75
    A normal incidence type-II quantum well infrared photodetector using an indirect bandgap AlAs/Al0.5Ga0.5As grown on (110) GaAs substrate for the mid-and long-wavelength mulitcolor detection
        Page 76
        Page 77
        Page 78
        Page 79
        Page 80
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        Page 91
        Page 92
        Page 93
        Page 94
        Page 95
        Page 96
    P-type strained-layer quantum well infrared photodetectors with blip at t less than or equal to 100 K
        Page 97
        Page 98
        Page 99
        Page 100
        Page 101
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        Page 119
        Page 120
        Page 121
        Page 122
        Page 123
    Summary and conclusions
        Page 124
        Page 125
        Page 126
        Page 127
        Page 128
        Page 129
        Page 130
        Page 131
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        Page 139
        Page 140
        Page 141
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        Page 144
        Page 145
    Biographical sketch
        Page 146
        Page 147
        Page 148
Full Text








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 III-V QWIP structures and to Dr. K. C. Chou for the growth of the

GaAs/InGaP QWIP using MOCVD.

I am greatly indebted to my parents, wife, and daughter for their love, support

and patience during the course of this study.

Finally, the financial support of ARPA is gratefully acknowledged.



ACKNOW LEDGEMENTS ..................................................ii

ABSTRACT ................................................................ vi


1 INTRODUCTION ....................................................1


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. Electron-Electron Interaction ............................ 24
2.5.2. Depolarization Effects ................................... 25
2.5.3. Other Effects ............................................. 25


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

DETECTION ...................................................... 41

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

INFRARED PHOTODETECTOR (VT-QWIP) ....................54

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


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

BANDGAP AlAs/Alo.sGao.sAs GROWN ON (110) GaAs
MULTICOLOR DETECTION ......... .................... .......76

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

PHOTODETECTORS WITH BLIP AT T < 100 K ................. 97

8.1. Introduction ................... ................................ 97

8.2. Theory ......................................... .............. 98
8.3. A Tensile Strained-layer InGaAs/InA1As QWIP .............. 102
8.3.1. Inversion between Heavy- and Light-hole States ...........103
8.3.2. Experiments ........................................ 103
8.3.3. Conclusions .......................................... 105
8.4. A Compressive Strained-layer InGaAs/GaAs QWIP ............ 106
8.4.1. Interaction between Type-I and Type-II QW States .......106
8.4.2. Experiments ................ .... .... ..................... 108
8.4.3. Conclusions ........................................... 110

9 SUMMARY AND CONCLUSIONS ...............................124




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



Yanhua Wang

August 1994

Chairman: Sheng-San Li
Major Department: Electrical Engineering
In this dissertation, three types of III-V semiconductor quantum well infrared

photodetectors (QWIPs) have been developed for 3-5 y/m mid-wavelength infrared
(MWIR) and 8-14 /m long-wavelength infrared (LWIR) detection. They are (1)
GaAs/AlGaAs, GaAs/InGaP bound-to-continuum (BTC) QWIPs and InGaAs/InA1As
bound-to-miniband (BTM) QWIP, (2) normal-incidence type-II indirect bandgap
A1As/AlGaAs QWIP, and (3) normal-incidence p-type strained-layer InGaAs/InA1As
and InGaAs/GaAs QWIPs. These QWIP structures were grown by the molecular
beam epitaxy (MBE) technique, with the exception of the GaAs/InGaP QWIP, which
was grown by the metal-organic chemical vapor deposition (MOCVD) technique. De-
tectivity ranging from 109 to 1012 cm-i/-Hz/W was obtained for these QWIPs at T
= 77 K.
The BTC and BTM QWIPs exhibited both photoconductive (PC) and photo-
voltaic (PV) dual-mode (DM) detection characteristics. The peak wavelengths for the
GaAs/A1GaAs QWIP were found to be at 7.7 pm and 12 pm. The peak wavelengths

for the GaAs/InGaP QWIP were found to be at 6.0 ym and 8.2 fm. The voltage-
tunable InGaAs/InA1As QWIP showed a peak wavelength of 10 fPm with dual-mode

A normal-incidence type-II 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 normal-incidence p-type tensile strained-layer 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 cm-v/-H/W at peak wavelength of 8.1 /m,

Vb = 2 V, and T = 77 K. Finally, a normal-incidence p-type compressive strained-layer
InGaAs/GaAs QWIP grown on GaAs substrate was also demonstrated for the first

time in this work, which showed a two-color detection feature with peak wavelengths
at 5.5 pm and 8.9 pm.


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) 1-3 pim short-wavelength infrared (SWIR), (2) 3-5 ,Pm mid-wavelength

infrared (MWIR), and (3) 8-14 pm long-wavelength infrared (LWIR) (see Fig. 1.2).

The 1-3 ym band has been found to be very attractive in fiber optical communications.

The 8-14 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 3-5 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 temperature-sensitive 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 photon-induced

transitions that excite carriers from bound states into mobile states. The detectors

respond only to incident photons with energy equal to or greater than the difference
between transition states. Photodetectors can be operated at two detection modes:
photoconductive (PC) and photovoltaic (PC) modes. In some practical applications,

the PV mode operation may be more preferred than the PC mode detection due to
its low noise level, low power dissipation, and large array size. The primary 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 3-5 im MWIR and the 8-14 pm LWIR bands can be realized

by using the quantum well and superlattice heterostructures.
Studies of heterojunction superlattices and their transport properties were first

reported by Esaki and Tsu [2, 3]. Due to coupling effects between adjacent quantum
wells, the resonant tunneling behavior between the different states of adjacent wells
along the superlattice growth axis was observed in 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 two-dimensional electron gap (2-DEG) 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 deep-levels-related photoconductive phenomena, (3) realization of

coherent tunneling through miniband conduction, and (4) large oscillator strength.

In general, based on the energy bandgap alignments, the heterointerface 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 lattice-mismatched 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 bound-to-bound (BTB) intersubband
transition for 8-14 ym LWIR detection. Since then, the rapid progress in QWIP per-
formance has been made based on bound-to-continuum [12, 13], bound-to-miniband
[14] intersubband transition schemes. Figure 1.4 shows the energy bandgaps and

lattice constants of some III-V and II-IV compound materials used for the QWIP
fabrication. The detectivity of the GaAs/AlGaAs LWIR QWIP for operating at 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 3-5 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 tracking-and-searching and forward-looking infrared (FLIR) systems.

The development of III-V semiconductor QWIPs for MWIR and LWIR detection is
the main motivation of this dissertation.

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


















T (K)






















128 x128

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










1.6 x1010

5.8x 109









or Array





128 x128
























0.1 A



loo .

...'0.1 p




i..1 cm

1 cm..

10 cm

1 m

100 m

1 km

10 km

100 km

Wavelength, p










- 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.








...g ....'..: E .. g
.* .....1 .... Ev

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

S -e EE
E g I . .. . .
......... ..... .......... E v

(c) Type-II Misaligned (d) Type-III

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,.



2.0 G





6.0 6.2 6.4 6.6

Lattice Constant (A)

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

5.6 5.8


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 bound-to-bound [11, 20], bound-to-
quasicontinuum [21], bound-to-miniband [14], bound-to-continuum [12, 22], and mini-

band-to-miniband [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 electron-electron, electron-nuclei, and nuclei-nuclei interactions,

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

T = -Z V2 (2.2)
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 many-body problem. However, most of the systems such as the super-
lattice can be described by using the one-electron approximation, which assumes that

the motion of a single electron experiences some average force due to vibrating lattice
and all other particles. These one-electron wavefunctions satisfy the self-consistent
Hartree-Fock equations [26]. The solution of the Hartree-Fock equation is still a very
difficult mathematical problem. For this reason, the band approximation is often em-
ployed, i.e., one solves the Schridinger equation with an assumed crystal potential

V(r) [27]. The time-independent one electron Schridinger equation and the potential
are given by

-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 k-space for n-th band is E,(k). For example,
near the bottom of the conduction band, the eigenvalues of electrons in a superlattice
can be described by

E,(k) = E.(k.) + 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
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,

semi-empirical approaches and interpolation schemes (i.e., k.p theory) are also very
powerful tools in determining effective masses and densities of states (DOS) near high
symmetry points in k space such as k = 0 of Brillouin zone center. Based on the k.p
method, calculations of the band structure of a superlattice have been carried out by
using the Kronig-Penney model and the modifications of the boundary condition [28].
The nonparabolicity effects in the band structures have been taken into account by
using the Kane model [6].
By considering only the periodic potential VL(r) in V(r) (ignoring VE and Vs),

the solution of the 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 n-th 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 z-direction (x- and y-directions 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
deep-levels-related phenomena [29], and (4) realization of a coherent conduction with

large quantum photocurrent gain [8].

The superlattice barrier quantum wells also involve the confinement of carriers

and the determinations of energy eigenvalues and wavefunctions in the 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 A-B type-I (two different materials) superlattice with growth direction

along the z-axis, one period of the alternating layers is called the basis of the 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)
where summation is over the band index n and k,,y are the transverse wavevectors in
x- and y-direction.
In the effective mass approximation and using the one-band Kronig-Penney

model, the envelope wavefunction On(z) can be written as [30]

{ 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,


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) .

The minibands for the bound and unbound states can be obtained from Eqs.

(2.18) and (2.19). The higher minibands could extend above the potential barriers.
However, the electron in-plane wavefunction of superlattice experiences only a 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)],

m L (2.21)
~ (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, electron-electron interac-

tion, electron-phonon interaction, and depolarization. In reality, all these corrections
to energy states and wavefunctions should be incorporated in the calculations of the
miniband properties. In order precisely to analyze superlattice miniband dispersion
relations, the two-band or three-band model should be used in which interband and

intervalley interactions are included (see Appendix A).
2.3.2. Transmission Probability IT TI
The transmission probability through a superlattice can be calculated 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 = +e-ii e+iki + e+ii e-iki (2.23)


A1 = A2 = 0,

Ai = ki(d2 + d3 + + di)

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

k, = [2 -(E-E) (2.25)

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

Ct = (e~b-15" + 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
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 3-dimensional (3-D) conduction properties.

Charge carriers (i.e., either dark or photoexcited carriers) that transport through the

continuum states generally have high mobility under applied bias conditions. If the

electric field is high enough, then hot carrier conduction through the 3-D continuum

states is expected. This type of conduction has advantages of high efficiency, high

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 phase-coherent 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 xl0-16/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

Vd = r (ieF RL (2.34)

At low electric field, the carrier mobility along the superlattice axis is given by

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

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 phonon-assisted

tunneling (hopping) with a frequency of eFL/h. A better approach for analysis of the

incoherent hopping conduction is to utilize the carrier scattering mechanism. Carrier

scattering tends to destroy the coherency of the wavefunctions, hence the fully reso-

nant threshold value will never be built-up. The mobility of the hopping conduction

is usually much lower than that of the miniband conduction. As the barrier layer
thickness or the thickness fluctuation increases, the maximum velocity 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, phonon-assisted tunneling is suppressed, and

other scattering sources such as ionized impurities, intersubband levels, and interface

roughness can also play an important role in the tunneling conduction.

2.5. Corrections on Subband Energy States

2.5.1. Electron-Electron Interaction
In the calculations of electronic states in quantum well/superlattice structures,
electron-electron interactions should be taken into consideration when the quantum
well is doped to 1018 cm-3 or higher. The interaction includes two components,
direct Coulomb force and quantum exchange interaction, which shift energy states
in opposite directions. The Coulomb interaction shifts the subband up while the
exchange interaction shifts down. In type-I quantum wells, the doping in the quantum
well can give rise to charge neutrality within the well, and the exchange energy is more
significant than that of Coulomb interaction.
In the one-electron approximation, the solution of the Hartree-Fock equation
gives the self-consistent eigenfunctions n and eigenvalues E,. The Hartree-Fock
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 left-hand side of the above equation are the direct
Coulomb and exchange interaction terms, respectively.
The exchange interaction energy term associated with electrons in the bound
ground state is approximately given by [35]

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


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

energy states.

V, (r)

VE (r)

Vs (r)


Figure 2.1.


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.




a a



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.






10 -

:,.. ,.::=---_-----'----
0 -- ................



30 La= 100
---* For exchange energy
-..- For plasmon shift
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 electron-electron interaction, and the depolar-
ization effect for ND = 1018 cm-3 and La = 100 A.






3.1. Introduction

Recently, rapid progress has been made in the development of high performance

quantum well infrared photodetectors (QWIPs) [11-23]. The 128x128 imaging 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 two-dimensional (2-D) staring focal plane arrays (FPAs)
with performance comparable to the state-of-the-art MCT IR FPAs.
QWIPs fabricated from III-V material systems such as GaAs/AlGaAs and In-

GaAs/InA1As offer a number of potential advantages over MCT material. These
include (1) III-V material growth by using MBE or MOCVD is more matured than
MCT, (2) monolithic integration of III-V QWIPs with GaAs readout circuits on the
same chip is possible, (3) GaAs substrates are larger, cheaper, and higher quality than
MCT, (4) III-V materials are more thermal stable than MCT, (5) higher yield, lower
cost, and higher reliability is expected in III-V QWIPs than in MCT devices, and

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

3.2. Intersubband Transition

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

(3) large optical nonlinearity [42], (4) fast intersubband relaxation [43], (5) reduced
Auger effect [44], (6) wavelength tunability [45], and (7) large photocurrent gain. The
intersubband transition process can be analyzed by using the dipole transition model
[46]. The transition rate W from the initial state Oi to the final state of can be
described by

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]
V, = -o P, (3.2)
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 right-hand side of Eq. (3.3) tends to vanish. However, in the
intersubband transition scheme such as QWIPs, the dipole transition is between the
envelope states while the Bloch states remain nearly constant, thus the first term on
the right-hand side of Eq. (3.3) becomes zero. From the calculation of the transition
matrix element Mif = < f\IVp|Iii >, 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

27rhcWjf (3
at-" = n (3.4)
where n, is the refractive index of the medium. This absorption coefficient curve can

be fitted by the Lorentzian function. The integrated absorption strength IA for the

polarized incidence radiation at the Brewster angle is given by

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 m-th order diffracted angle with respect to the superlattice axis,

respectively. In a grating coupled QWIP, the integrated absorption strength IA in

Eq. (3.5) should be multiplied by a factor of sin2 Om/cosOm.

3.3. PC and PV Detection Modes

A photodetector may be operated in either the photoconductive (PC) mode or

the photovoltaic (PV) mode. In the BTC QWIPs, most of the them are operated

in the photoconductive (PC) mode and a few are operated in the photovoltaic (PV)
mode. However, in the BTM QWIPs, they may be operated in the PC and PV
dual-mode detection because of the bandwidth modulation effect in the miniband

conduction QWIPs.

A photoconductor exhibits a change in resistance ARd when IR radiation is

impinging on it. This change of the resistance is due to the generation of the mobile
carriers in the photoconductor. The photogenerated carriers An can be written as

A n 77 A (DTL (3.8)
An= (3.8)

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 built-in potential, V1i, can be created in the bound-to-miniband intersubband
transition, which is due to the growth asymmetry and effective mass filtering effect
through the global miniband. In the PV mode detection, the QWIP has an extremely

low dark current, and the detector noise is dominated by Johnson noise which is much
lower than that of the PC mode detection. The PV mode detector performance can

be evaluated by RdAd product, where Ad is the active area of the detector.

3.4. Figures of Merit

In designing a quantum well infrared photodetector, it is important to understand
the key parameters that determine the performance of a QWIP. They include: the
dark current Id, noise equivalent power (NEP), responsivity (R), and detectivity D*.
The QWIP performance can be evaluated by these parameters, which are often called
the figures of merit.
3.4.1. Dark Current Id
In a quantum well infrared photodetector, the dark current is due to both the
thermionic emission and tunneling conduction. In a conventional QWIP, thermionic
emission conduction is dominant, whereas in a BTM QWIP thermionic-assisted 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 low-field regime, the thermionic emission current is related to the density

of mobile carriers nt and the average drift velocity vd. It can be expressed as [49]

Ith = Adevdnt, (3.10)

where Ad is the detector active area, and

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 2-dimensional 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, phonon-assisted tunneling, and defect-assisted 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)

r = n(1 Rf)(1 e-m'). (3.20)

Here Rf is the reflection coefficient (typical 0.3 for GaAs), r is the polarization cor-

rection factor (a = 0.5 for n-type QWIP and a = 1 for p-type QWIP), m is the

number of absorption pass, a is the absorption coefficient for the superlattice, and 1

is the total superlattice thickness.

The spectral responsivity (V/W) for the PV mode QWIP can be obtained from

the relationship Rv = RA Rd, where Rd is differential resistance of a QWIP.

3.4.3. Collection Efficiency 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 e-m) (3.22)
mal (3.23)
K (1 Rf) (3.23)
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

DX = (3.24)

where Af is the noise spectral bandwidth, and i, is the overall root-mean-square
noise current (in unit of A) for a QWIP. In general, the noise current for the QWIP

includes two components, one is QWIP's dark current noise ind and the other is 300

K background photon noise current inb.
The dark current noise id is given by

i2 4eldgAf for G-R noise
Znd = (3.25)
d 4 TAf for Johnson noise.

The G-R noise is associated with random thermal excitation and decay of the carriers,

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

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

arrival statistics of the incoherent photons. The background photon noise current 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 G-R 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.
3.4.5. Background Limited Performance (BLIP)
A mid-wavelength or long-wavelength QWIP has two kinds of backgrounds: (1)
high temperature ambient background (T = 300 K) and (2) low temperature cold
background (T = 77 or 195 K). Under the normal thermal imaging condition, the total
current feeding to the following readout circuits in a QWIP includes both the dark
current Id and 300 K background photocurrent 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
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 G-R noise and Johnson noise are negligible in comparison.
Under normal imaging conditions, the photosignal current Iph can be approximated
Iph = (e/hv)rlKgPph, (3.35)

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

expressed by

(NEP)BLIP = 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 non-BLIP
QWIP is dependent of both the g and the Id.
When the readout circuit noise is ignored, %BLIP for a QWIP can be evaluated
by using
%BLIP Znb (3.38)
(inb + id)1/2
where inb and ind are the 300 K background photocurrent noise and dark current
noise, respectively.


4.1. Introduction

Recently, there has been considerable interest in the study of long-wavelength
intersubband quantum well infrared photodetectors (QWIPs). A great deal of work

has been reported on the lattice-matched GaAs/AlGaAs and InGaAs/InA1As mul-
tiple quantum well and superlattice systems using bound-to-bound [20], bound-to-

miniband (BTM) [14], and bound-to-continuum [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 dual-mode (PC and PV) quantum well infrared photode-
tectors (DM-QWIP) based on bound-to-continuum state transition mechanism was
designed and fabricated [58]. Both PC and PV detection modes for this QWIP can

be operated at 77 K with excellent characteristics. By properly selecting the detector
parameters, we tuned the PV and PC mode operations to the different response peak
wavelengths. The DM-QWIP layer structure was grown on a semi-insulating (SI)

GaAs substrate by using the molecular beam epitaxy (MBE) technique. A 1-ptm-
thick GaAs buffer layer with dopant density of 2x101s cm-3 was first grown on the
SI GaAs substrate as an ohmic contact layer, followed by the growth of 40 periods
of enlarged GaAs quantum well with well width of 110 A and a dopant density of

5x101s cm-3. 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 cm-3 was grown on top of the QWIP layer

structure to facilitate ohmic contact. The physical parameters of the device structure

are chosen so that there are two bound states inside the enlarged well (i.e. EEWO and

EEW1), and the continuum states ECN are just slightly above the top of the barrier.
A high dopant density of 5x 018 cm-3 was used in the enlarged GaAs quantum well
so that the ground state EEWO and the first excited state EEW1 are heavily populated
by electrons to enhance absorption of infrared radiation in the quantum well. In order

to minimize the undesirable tunneling current through the barrier layers, a thick (875

A) undoped A10.25Ga0.75As barrier layer was used in this QWIP structure to suppress
the tunneling current from the ground state EEWO and the first excited state EEW1.
Figure 4.1 (a) shows the energy band diagram of the DM-QWIP, which illustrates

the Fermi-level and two possible intersubband transition schemes. The first transition
scheme is from the localized ground state EEWO in the GaAs quantum well to the first
continuum band states ECN above the AlGaAs barrier. The second transition scheme

takes place from the first excited state EEW1 to the continuum states ECN. Due to
the dopant migration into the enlarged A1GaAs barriers from the heavily doped GaAs
quantum well during the layer growth, the actual conduction band diagram in the

DM-QWIP is shown in Fig 4.1 (b). The asymmetric band bending between two side
of the quantum wells induces the internal electric field Ebi, which is opposite to the
direction of the quantum well layer growth. To analyze these transition schemes,

we performed theoretical calculations of the energy levels of the bound states and

continuum states and transmission probability IT Tj for this QWIP using a 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], electron-electron interaction [35], electron plasma [37], and energy band bending
effect [40]. For simplicity, we have only considered the effects due to energy bending,

depolarization, and electron-electron interaction in heavily doped bound states in the

quantum well. By taking these effects into account, both bound states EEWO and

EEW1 are lowered by about -5 meV. Thus two intersubband transition peaks should
be observed in the DM-QWIP, which corresponds to infrared wavelengths of 7.7 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 DM-QWIP mesa structure was created by chemical etching through the

quantum well active layers and stopped at the 1-yrm-thick heavily doped GaAs buffer

layer for ohmic contact. The active area of the detector is 200 x 200 /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 (E-beam) evaporation of AuGe/Ni/Au

materials. To achieve high coupling efficiency, the metal grating strips with a grating
periodicity of A=5 jm and ratio factor d/A = 0.5 (d: the metal strip width) were
used in this DM-QWIP.
The infrared intersubband absorption spectra of the sample were measured at
the Brewster angle (OB = ~ 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 current-voltage (I-V) curves and the differential resistance
Rd values for the DM-QWIP measured at negative bias and T = 77K (mesa top as
positive bias). It is noted that the dark current for bias voltage between 1 and 2 V

is extremely low, which is attributed to the dramatically reduced tunneling current
resulting from the increase of barrier layer thickness. Asymmetric dark current char-
acteristics was observed in the DM-QWIP with a higher current in positive bias than

that in negative bias, which results from the asymmetric effective barrier height at 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 cm-V/-Hz/W. In order to verify the
zero bias noise, we also measured the noise current by using a lock-in amplifier, which

yielded a value of in = 3.0x10-14 A, in good agreement with the calculated value
from Johnson noise expression. When a negative bias voltage Vb is applied to the
detector that is opposite to the Vbi, the PV response vanishes, and the PC mode
conduction becomes the dominant detection mechanism with a PC response current
from the bottom of the mesa to the top. The bias dependence of the photocurrent
responsivity RA was measured using a 12 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 G-R 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-
e-2a1). The photoconductive gain, g, can be also derived from noise measurement.

The results yielded a peak detectivity D, = 2x1010 cm-v/H-z/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

DM-QWIP. With high detectivity and low dark current for both the PC and PV

mode IR detection, the GaAs/AlGaAs DM-QWIP can be used for high performance

two-color and dual-mode operation staring focal planar arrays and infrared imaging

sensor applications.


E bi

QW growth direction


Schematic energy-band 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.







Figure 4.1.

...ittrr (C ,r |e -- ----L .. .


f E CN
ov / :

-20 .... .4V I
...1.2V /

EW/ /

-40 -
P- /.

Y/ E F

0 50 100 150 200 250

Energy (meV)

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



1 3500
ST = 300 K

0 2800


-. 1400

4 700

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.


10-3 -109

10-4 T = 77K



10-8 6
S10I-7 7
0 106

105 0


1 2 3 4 5
Negative Bias Voltage Vb (V)

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

- QW growth direction

Zero bias




Reverse bias



Figure 4.5.


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.








6 8 10 12 14
Wavelength (pm)

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

0.6 2.2


0.4 E
C T=77K

0.3 p = 12 pm A 1.2
Ac = 13.2 pm

0.2 ."

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 DM-QWIP.


5.1. Introduction

Long-wavelength quantum well infrared photodetectors (QWIPs) based on inter-
subband transitions for detection in the 8-14 pm atmospheric spectral window have
been extensively investigated in recent years. Studies of the intersubband absorption
in the InGaAs/InA1As system for 3 to 5 /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 mid-wavelength infrared (MWIR) and the long-wavelength 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 8-14 im [59] wavelength detection. The result showed multi-color 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 dual-mode (PV and PC) operation InGaAs/InA1As QWIP [45] based on the
voltage-tuned (VT) bound-to-miniband (BTM) transition mechanism was designed
and fabricated. The VT-QWIP layer structure was grown on a semi-insulating (SI)

InP substrate by using the molecular beam epitaxy (MBE) technique. A 1-jim

Ino.53Gao.47As buffer layer with dopant density of 2x1018 cm-3 was first grown on

the SI InP substrate, followed by the growth of 20 periods of enlarged Ino.53Gao.47As
quantum wells with a well width of 110 A and a dopant density of 5x1017 cm-3.
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 0.3-jim-thick n+-
Ino.53Gao.47As cap layer with a dopant density of 2x 1018 cm-3 was grown on top of
the VT-QWIP layer structure to facilitate the ohmic contact. Figure 5.1 shows the
energy band diagram for this VT-QWIP. The transition scheme is from the localized
ground state level EEW1 of the enlarged well (EW) to the global resonant-coupled
miniband ESL1 in the superlattice (SL) barrier. The physical parameters of the 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 bound-to-miniband transition schemes, theoretical calculations
of the energy states EEWn, ESLn (n = 1,2,...) and the transmission probability IT TI
for the VT-QWIP were carried out by using the multi-layer transfer matrix method.
In this design, a broad and highly degenerated miniband was formed by using the
superlattice barrier structure. The center energy position of the first miniband is

located at 163 meV above the conduction band edge of InGaAs EW with a bandwidth
of r 60 meV. In order to precisely determine the intersubband transition levels, we
have considered both the electron-electron 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,

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 VT-QWIP was measured at the Brewster angle

(OB ~ 730) by using a Perkin-Elmer Fourier transform interferometer (FTIR) at room
temperature [59]. The results showed a main absorption peak centered at A, = 10.7
/jm with a spectral linewidth of Av = 500 cm-.

5.3. Experiments

The mesa structure for the VT-QWIP was formed by chemical etching through

the QWIP active layers and stopped at the n+ InGaAs buffer layer for ohmic contact.

The active area of the detector is 200x200 pm2. To enhance coupling efficiency for
normal illumination and angular-independent radiation polarization, a planar two-

dimensional (2-D) metal grating coupler was formed on the VT-QWIP by using elec-
tron beam (E-beam) 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 current-voltage (I-V) 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 cm-1 (~ 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 VT-QWIP 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 narrow-band spectral
response in the PV mode detection with a linewidth of AA = 0.7 /m at a half max-
imum. The bound-to-miniband transition QWIP operated in the PV mode offers a
unique feature of ultra-narrow bandwidth (AA/Ap = 7 %) infrared detection, which
is not attainable in a conventional bound-to-continuum QWIP. As the negative bias
increases, relative position between the "embedding" state EEW2 and the "framing"
state ESL1 can be adjusted by the "controlling bias" due to the different dependence
of EEW2 and ESL1 on the bias voltage. A peak wavelength blueshift of about 0.4 ,m

(compared with the FTIR peak wavelength) was observed at Vb = 0.5 V and T =
67K. As expected, a broad-band spectral linewidth of AA/Ap = 24 % at Vb = 0.5
V was obtained in the PC mode as shown in Fig. 5.3. It is notice that 0.3 pm peak
wavelength shift between the PC mode and PV mode operation was obtained by the
applied bias. In the bias-tuned QWIP structure, not only can the spectral bandwidth

be tailored to the desired width (from 7 % to 24 %), but the spectral response peak
can also be tuned as well. This tunability can be obtained by modulating the relative
position of the first excited bound state in the quantum wel within miniband states.
For example, if the first bound excited state lies at the bottom edge of the miniband,
then the spectral response will produce a redshift with a longer short-wavelength tail
and narrow bandwidth. On the other hand, if the first bound excited state lies at the
top of the miniband, then a blueshift results with a longer long-wavelength tail and

narrow bandwidth. However, if the first excited state is in the middle of the 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 cm-x/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 cm-VHz/W. In order to verify the zero bias noise, we also measured the
noise current by using a lock-in amplifier, which yielded a value of i, = 9.0 x10-14 A,
in good agreement with the calculated value from the Johnson noise expression.
Due to the dopant migration into superlattice barriers from the doped quantum

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

band becomes spatially nonuniform with broadening on the well right-hand side and

narrowing on the left-hand side as shown in the Fig. 5.6. The 15 meV wider mini-
band bandwidth on the side of toward-growth-direction of each InGaAs well than
that on the side of backward-growth-direction can be identified and confirmed by

temperature-dependent dark I-V and photocurrent measurements. For 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 built-in potential Vbi ~

+ 0.15 V resulting from miniband bandwidth modulation. The built-in 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 voltage-tuned bound-to-miniband tran-
sition mechanism. Both the narrow-band PV mode and broad-band PC mode de-
tection at AX ~ 10 um peak wavelength have been achieved. Using the dual-mode

operation and bound-to-miniband transition InGaAs/InA1As QWIP structure grown

on the InP substrate, it is possible to design high performance two-color staring focal
plane arrays and infrared imaging sensor for use in the 3-5 pm and 8-14 ptm detection.

A Ec = 500 meV

E Ll



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].


Figure 5.1.


10-2 107

10-3 T = 67 K

10"4 0

10- s


103 3
10-8 r

10-9 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

SVb= 0.5 V
Q b


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<

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

5.0 E

h4.5 "

60 *
am 4.0


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

To(left) ft


-- E b

1 7o(right)

QW/SL growth direction

Figure 5.6.

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


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 III-V QWIPs have been fabricated from the MBE grown
GaAs/AlGaAs and InGaAs/InA1As material systems using the bound-to-bound [11,
20, 60, 61], bound-to-miniband (BTM) [14, 16, 62] and bound-to-continuum [12, 18,
22] conduction intersubband transitions and operating on photoconductive (PC) 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 dual-mode (PV & PC modes) [45, 58] operation have also been re-
ported recently. Since the PV detection mode is operated under zero-bias condition, it
has the advantages of lower dark current and lower noise equivalent power compared
to PC mode operation.
Since the quality of the interfaces between the quantum well and the barrier
layer is extremely important for the fabrication of high performance QWIP, most
of the III-V QWIPs reported in the literature are grown by using molecular beam
epitaxy (MBE) technique. Recently, several reports have shown [65, 66, 67] that
metal-organic chemical vapor deposition (MOCVD) technique is well adapted to the
growth of a lattice-matched GaAs/Inl_.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 donor-related
DX center problem and interface defect-assisted tunneling, (5) extremely high electron
mobility in this heterostructure [72] system, and (6) ultra low recombination velocity
[73] at its heterostructure interfaces. The lattice-matched GaAs/Ino.49Gao.51P system
has been used in quantum wells and superlattices for electronic and photonic devices

such as high electron mobility transistors (HEMTs) [70, 71], heterojunction bipolar
transistors (HBTs) [74], lasers [67], light-emitting diodes [75], and photodiodes [65].
A new photovoltaic (PV) mode operation long wavelength quantum well infrared
photodetector (QWIP) using a lattice-matched n-type GaAs/Ino.49Gao.s1P system
has been demonstrated for two-color IR detection. The detection scheme is based
on bound-to-continuum states transitions from the ground bound state inside the
GaAs quantum well to the first- and second-continuum band states above the InGaP
barrier. The peak photovoltaic responsivities were found to be 1,000 V/W and 900
V/W at Ap, = 8.2 ,m and Ap2 = 6.0 jim and T = 77 K, respectively. The spectral
response bandwidths corresponding to these two peak wavelengths were found to be
11 % and 13 %, respectively.

6.2. Design Consideration

A two-color PV mode operation QWIP fabricated on the GaAs/Ino.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 11-second
interrupt growth between different layers was carried out at a substrate temperature

of 550 "C. A 0.7-jim GaAs buffer layer with sulphur (S) dopant density of 1x101
cm-3 was first grown on the GaAs substrate as the ohmic contact layer, followed by
the growth of a 15-period of GaAs quantum wells with a well width of 50 A and a
sulphur dopant density of 5 1017 cm-3. 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 cm-3 was grown on top of
the QWIP layers to facilitate the top ohmic contact. The physical parameters of the

QWIP are chosen so that only one electron populated bound state is located inside
the quantum well and the first excited band states are just slightly above the top of
the barrier layers in such a way to enhance the intersubband absorption strength. To
analyze the transition schemes for this QWIP, we performed theoretical calculations
of the energy levels of the bound state and the continuum states and transmission
probability IT 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, electron-electron interaction, and electron plasma
are responsible for modifying the transition energy levels, the energy band bending
resulted from the sulphur dopant migration in the quantum wells to the InGaP barrier

layers plays an important role in the PV intersubband detection. Figure 6.1 shows
the energy band diagram based on the dopant migration model and intersubband
transition probability calculated from the multilayer transfer matrix method. The
asymmetric energy barrier at quantum well/barrier layer interfaces causes a built-in

potential distribution [58], and hence gives rise to the photovoltaic effect. In 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


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. Au-Ge/Ni/Au ohmic contact

films were deposited on the top and bottom contact layers. The active area of the

detector is 200 x200 /m2. To enhance the coupling efficiency for normal illumination
and angular independent radiation polarization, a planar 2-D metal grating coupler

was formed on the QWIP top surface by using electron beam (E-beam) evaporation

of 0.2 ym gold film. The 2-D 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 current-voltage (I-V) curves measured at room tem-
perature. It is interesting to note that a Schottky diode characteristic with a turn-on

voltage ~ 220 mV was observed at room temperature. The high resistance property

observed in this GaAs/InGaP QWIP compared to the conventional GaAs/AlGaAs

and InGaAs/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 motor-driven 77250 single grating monochromator, a globar

IR source, and a lock-in amplifier. Figure 6.3 shows the normalized PV responsivity

versus wavelength measured at T = 77 K for this QWIP. Two response peaks were

observed, one at 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

electron-electron exchange interaction [77]. Among these corrections on the subband

states, the electron-electron exchange interaction is a dominant factor which could

give rise to a significant blueshift as the temperature is decreased. The redshift of Ap2

may be associated with defects in the InGaP barrier layers [78, 79]. The measured

peak responsivity is 1,000 V/W at 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
cm-x-Hz/W. This low detectivity may be attributed to the sulphur-dopant loss in the

well (thus lowering the oscillator absorption strength) and the formation of persistent

photoconductivity in the InGaP barrier layers. The performance of this QWIP could

be greatly improved by using a stable dopant impurity such as silicon [70], instead of
the sulphur-dopant impurity used in the present case.

The photovoltaic behavior of this QWIP was studied in the temperature range

between 77 and 30 K. The peak photovoltaic response versus inverse temperature

(100/T) is shown in Fig. 6.4. It is showed that the photoresponse was increased by a

factor of 6 at Ap2 and only a factor of 2 at 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 two-color long-wavelength GaAs/Ino.49Gao.51P

QWIP grown by using MOCVD technique, based on the bound-to-continuum states

intersubband transition and the PV mode operation. The low responsivity and 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 lattice-matched 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.

QW growth direction






-40 5

-50 50 100 150
0 50 100 150

200 250 300 350

Energy (meV)
Figure 6.1. Schematic energy band diagram (a) and transmission co-
efficient IT-TI and energy levels (b) for the GaAs/InGaP
QWIP grown on GaAs by using MOCVD technique



+v- K+ T__ t








-100 L

-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.






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.



I I a I I I a


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.


7.1. Introduction

A normal incidence n-doped type-II indirect A1As/Alo.sGao.sAs quantum well

infrared photodetector (QWIP) grown on (110) semi-insulating (SI) GaAs substrate

with MBE technique has been developed for mid- and long-wavelength multicolor

detection. The normal IR absorption for the n-doped quantum wells (QWs) was
achieved in the X-band confined AlAs quantum wells. Six absorption peaks including

four from X-band to F-band intersubband resonant transitions were observed at Apl-6

= 2.2, 2.7, 3.5, 4.8, 6.5 and 12.5 /m. The resonant transport from X-band to F-band

gives rise to high photoconductive gain and large photoresponsivity, which are highly
desirable for multicolor image sensor applications.

Quantum well infrared photodetectors (QWIPs) using type-I structures have
been investigated extensively in recent years [80-88]. In type-I quantum well 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 n-doped quantum wells. In order to achieve strong absorption for normal IR

radiation in the quantum wells, grating couplers [89, 90] are required to induce 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 effective-mass
anisotropy (mass tensor) of electrons in the ellipsoidal valleys can provide coupling

between the parallel and perpendicular motions of the electrons when the principal
axes of one of the ellipsoids are tilted with respect to the growth direction. As a result
of the coupling, intersubband transitions at normal incidence in an indirect bandgap
QWIP structure are allowed.

Since the AIAs/Alo.sGao.sAs system is an indirect bandgap material, the con-
duction band minima for the AlAs quantum wells are located at the X-point of the
Brillouin zone (BZ). The constant energy surface will also undergo change from a typ-
ical sphere at the zone center for a direct bandgap material (i.e. GaAs) to off-center
ellipsoids of an indirect bandgap material (i.e. AlAs). For AlAs, there are six ellip-

soids along [100] axes with the centers of the ellipsoids located at about three-fourth
of the distance from the BZ center. By choosing a proper growth direction such as

[110], [111], [113], or [115] direction [86, 87], due to the anisotropic band structures
and the tilted growth direction with respect to principal axes of ellipsoidal valley, it is
possible to realize large area normal incidence IR detection in A1As/AlGaAs QWIPs.

7.2. Theory

The normal incidence type-II 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-/m-thick n-doped GaAs buffer layer with ND
= 2x01s cm-3 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 cm-3. 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 cm-3 was grown
on top of the quantum well layers for ohmic contacts. The dopant density of 2 x101

cm-3 in the quantum well is chosen so that only the ground state is populated, and

tradeoff between the low dark current and strong absorption strength is considered.
We use the indirect bandgap AlAs for the quantum well layer and Alo.sGao.sAs for the

barrier layer. Since A1,Gal_,As becomes an indirect bandgap material for x > 0.45,

the conduction-band minimum shifts from the F-band to the X-band. Analyzing
band ordering in the 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 type-II band
structure. The conduction band offset of Alo0.Gao.sAs relative to AlAs is about 170
meV. Figure 7.1 shows a schematic conduction-band (F- and X-band) diagram for

the type-II indirect 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 F-band and the X-band edge is about 50 meV in the AlGaAs layer, and the

conduction band offset in the F-band is found to be 630 meV.

To derive the basic equations for the normal induced intersubband transitions and
the corresponding indirect type-II QWIPs, we start with the Hamiltonian description

of quantum mechanics for an electron [6]

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

[95, 97]

W 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 type-II AlAs quantum well layer grown along [110] direction
of GaAs substrate, due to the tilted anisotropic energy band with minimum point
away from BZ center (see Fig. 7.1(b)), the second partial derivatives 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 type-I 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 type-I
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 type-I structures under normal incidence radiation.

7.3. Coupling between r- and X-bands

To analyze the intersubband transition mechanism and energy level positions
in a type-II A1As/AlGaAs QWIP, theoretical calculations of the energy states E,,

(n = 0,1,2...) for the X-band and F-band and the transmission coefficient IT TI
for the QWIP were performed by using a multi-layer transfer matrix method [14].
To determine the intersubband transition levels, we use the one-band effective mass
envelope function approximation (see Appendix A) and take into account the effects of

band nonparabolicity and electron-electron interaction. In comparison with the more
sophisticated energy band models such as two-band and three-band models, the 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 X-band well,
while E2 to E6 are all continuum states in X-band. The continuum states in the
X-band can find their resonant pair levels in the F-band except E2 which is located
below the F-band minima (about 30 meV).
In a type-II indirect A1As/AlGaAs QWIP, free carriers are confined in the AlAs
quantum well formed in the X-conduction band minimum, which has a larger electron

effective mass than that in the r-band valley. When normal incidence radiation
impinges on this QWIP, electrons in the ground-state of the X-well are excited to
either the excited state E1 or one of the continuum states E2 to E6. If the continuum
state in the X-band valley is resonantly aligned with a state in the r-band valley,
the photon-generated electrons in the X-band will undergo resonant transport to the
resonant state in the F-band provided that the F-band barrier layer (in the present
case, AlAs layer) is so thin that it is transparent to the conduction electrons [99,

100]. This resonant transport from X-band to F-band is expected to be a coherent
resonance which can greatly enhance the transmission if the electron lifetime Tr in
these continuum states is much shorter than the X-band to r-band 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 X-band and the r-band, electron velocity and mobility in the T-valley will be much
higher than the value in the X-band valley. Since the photocurrent is proportional
to the electron velocity and mobility (i.e., Iph = 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 F-band), a large increase in the photocurrent
is expected when photon-generated electron resonant transport from the X-band to

F-band takes place under certain bias conditions as illustrated in Fig. 7.2. It is known
that photoconductive gain g = TL/rT, where 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 cm-1 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 cm-1 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 cm-1, which is quit different from the intersubband transition in type-I 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 liquid-helium

cryogenic dewar. A HP4145 semiconductor parameter analyzer was used to measure

the dark current versus bias voltage. Figure 7.4 shows the measured dark current
as a function of the bias voltage for temperatures between 68 and 98 K. Substan-
tial reduction of device dark current was achieved in the present type-II structure.

The photocurrent was measured using a CVI Laser Digikrom 240 monochromator
and an ORIEL ceramic element infrared source. A pyroelectric detector was used to
calibrate the radiation intensity from the source. The measured data for the QWIP

are tabulated in Table 7.2, which showed six absorption peaks. The peaks for Apl,2

only exhibited the photoconductive (PC) detection mode, while the peaks for Ap3~6

operated in both the PC mode and photovoltaic (PV) mode.
Figure 7.5 shows the QWIP's photoresponse and absorption coefficient for 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 type-I QWIP [58]. The property of a broader
spectral bandwidth within X-band intersubband transition was also found in [113]
GaAs substrate growth direction [87, 98]. Detectivity for this peak wavelength Ap1
= 12.5 jim was found to be about 1.1 x109 cm--Hz/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 Ap3-6 are in excellent agreement with the

values deduced from the FTIR measurements and theoretical calculations. The main

peak responses occurred at Ap4 = 3.5 pm and Ap6 = 2.2 pm with responsivities of RA =

29 mA/W and 32 mA/W, respectively, at Vb = 0 V and T = 77 K. The responsivities

of two main peaks have a different voltage dependence. The peak for Ap4 increases

rapidly for 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 F-X 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 X-band to the F-band in the

electronic conduction.

The PV mode operation at peak wavelengths of Ap3~6 in the type-II 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 Apl-2. This is probably due to the novel resonant transport feature which

enhances the photogenerated electron conduction.

7.5. Conclusions

In conclusion, we have demonstrated a normal incidence type-II QWIP using an
indirect X-band 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 X-band and F-band 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 type-II A1As/AlGaAs QWIPs highly desirable for many infrared applications.

Further studies of the interaction effects between the X- and F-bands, transition cou-

pling, bandgap engineering, and hot electron transport mechanisms in the type II
indirect III-V multiple quantum well structures may lead to the development of novel
quantum well infrared detectors, lasers, and modulators.

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

Eo El E2 E3 E4 E5 E6

X-band 20 110 189 270 365 475 600

r-band 265 370 460 595

Notes:The energy levels, E3, E4, E5, and E6 in
the F-band and X-band formed the resonant

levels for the photoexcited electrons in this

QWIP. The parameters used in calculation of
X-band and F-band, respectively, are m* =

0.78 mo, 0.15 mo for AlAs and 0.82 mo, 0.11

mo for Alo.5Gao.sAs. (All the energy levels
shown are measured from the AlAs quantum

well X-conduction band edge in unit of meV.)

Table 7.2. The measured peak wavelengths, responsivities, and de-
tectivities for the type-II 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




- -

I---- -------------- S
S S__ __ _


Alo.s Ga .As
0.5 0.5

50 nm

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












3 nm





Figure 7.1. Continued.



Al Ga As
.5 .s


r-X coupling

L valley r valley X valley

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









Figure 7.3.



10-4 T = 98K

g 10-5 77K

1 10-7




10-11 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,



< 15

It 10

9 10 11


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

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