THERMOPHOTOVOLTAIC DEVICES AND INFRARED PHOTODETECTORS BASED ON INTERBAND CASCADE STRUCTURES

UNIVERSITY OF OKLAHOMA
GRADUATE COLLEGE
THERMOPHOTOVOLTAIC DEVICES AND INFRARED PHOTODETECTORS
BASED ON INTERBAND CASCADE STRUCTURES
A DISSERTATION
SUBMITTED TO THE GRADUATE FACULTY
in partial fulfillment of the requirements for the
Degree of
DOCTOR OF PHILOSOPHY
By
WENXIANG HUANG
Norman, Oklahoma
2020
THERMOPHOTOVOLTAIC DEVICES AND INFRARED PHOTODETECTORS
BASED ON INTERBAND CASCADE STRUCTURES
A DISSERTATION APPROVED FOR THE

HOMER L. DODGE DEPARTMENT OF PHYSICS AND ASTRONOMY
BY THE COMMITTEE CONSISTING OF
Dr. Rui Yang, Chair
Dr. Michael Santos, Co-chair
Dr. Kieran Mullen
Dr. Bruno Uchoa
Dr. Arne Schwettmann
Dr. Bin Wang

© Copyright by WENXIANG HUANG 2020
All Rights Reserved
To my parents, Caijin Huang and Feng Cheng
iv
1 Acknowledgements
It would not have been possible to write this dissertation without the help and
support of the kind people around me, only some of whom will be given special mention
here.
Above all, I would like to express my sincere gratitude to my advisor Prof. Rui Q.
Yang for his selfless support, for prompt and useful advice on my Ph.D. study and research,
and for sharing his motivation and immense knowledge. He assigned me both theoretical
and experimental topics that were interesting and meaningful, as well as beneficial for
improving my analytical skills and hands-on abilities. It has been wonderful to work with
him and I have had a lot of fun interacting with him all the time. I also want to thank him
for the travel support he provided for me to attend several conferences and share our
research results with community members. Besides my advisor, I would like to thank Prof.
Mike Santos for chairing my committee, and for his support and assistance since the start
of my graduate career. He provided the resources for our group to grow our material,
nominated me for several awards, and helped me improve my presentations.
I am grateful to Dr. Kieran Mullen, Dr. Bruno Uchoa, Dr. Arne Schwettmann and
Dr. Bin Wang for serving on my dissertation committee and squeezing out time to review
my general exam and dissertation.
I would also like to thank the current and former members of the Quantum Device
Laboratory at the University of Oklahoma. During my first year in the lab, I was fortunate
to work closely with Dr. Lin Lei. Many thanks go to him for teaching me the
characterization measurements and data analysis of the devices. Many thanks go to Dr. Lu
Li who performed the fabrication of most of the devices studied in this dissertation. I want
v
to extend sincere thanks to Dr. S.M. Shazzad Rassel. He was helpful in carrying out the
dark current measurements for many laser devices. I also want to thank Dr. Hossein Lotfi
for long discussions on band structure modeling and the device theory. Many thanks go to
Dr. Hao Ye for growing some of the structures presented in this work. I want to thank the
current group member Jeremy Massengale for MBE growth and material characterization
of most of the structures presented in this work. I am grateful to Yuzhe Lin for the
fabrication of some devices in this work.
I am also appreciative of our group’s collaborators. Particularly, I would like to
thank Prof. Matthew Johnson for providing our group with both resources and expertise in
device fabrication and material characterization. I would like to thank Dr. James Gupta of
the National Research Council of Canada who performed the MBE growth of some laser
structures for our research group.
I would also like to acknowledge the sources that have provided me with funding
during my Ph.D. career. I am grateful for funding from the NSF (Award Nos. ECCS-
1202318, DMR-1229678, DMR-1608224, and IIP-1640576) and the AFOSR (Award No.
FA9550-15-1-0067).
Last, but definitely not least, I am greatly indebted to my parents. It is their
unconditional love, care, and tolerance that made the hardship of finishing my Ph.D. career
worthwhile. Without their support, I would not have been able to overcome the difficulties
during these years.
vi
Table of Contents
Acknowledgements ........................................................................................................... v
List of Tables .................................................................................................................. xii
List of Figures ................................................................................................................ xiv
Abstract ........................................................................................................................ xxiii
Chapter 1: Introduction ..................................................................................................... 1
1.1 Infrared radiation ............................................................................................ 1
1.2 Overview of infrared thermophotovoltaic energy conversion ........................ 5
1.2.1 Background ............................................................................................... 5
1.2.2 Active components in a TPV system ........................................................ 8
1.2.3 Thermophotovoltaic cells.......................................................................... 9
1.2.4 Thermodynamic analysis of thermophotovoltaic cell efficiency ............ 12
1.3 Overview of infrared detectors ..................................................................... 15
1.3.1 Background ............................................................................................. 15
1.3.2 Photon detection vs thermal detection .................................................... 17
1.3.3 Examples of photon detectors ................................................................. 19
1.3.4 Performance metrics for infrared detectors............................................. 23
1.4 Dissertation organization .............................................................................. 25
Chapter 2: Sb-based interband cascade devices.............................................................. 27
2.1 6.1 Å Semiconductor family ......................................................................... 27
2.2 Interband cascade lasers-the historic origin .................................................. 28
2.2.1 History and operation principle .............................................................. 28
2.2.2 Current status of ICL performance ......................................................... 31
vii
2.3 Interband cascade thermophotovoltaic devices ............................................ 32
2.3.1 InAs/GaSb type-II superlattices .............................................................. 32
2.3.2 Operation principle of ICTPV cells ........................................................ 34
2.3.3 Enhancement of open-circuit voltage in ICTPV cells ............................ 36
2.3.4 Improvement of carrier collection efficiency in IC structures ................ 37
2.4 Interband cascade infrared photodetectors.................................................... 41
2.4.1 Operation principle of ICIPs ................................................................... 41
2.4.2 Noise reduction in ICIPs ......................................................................... 43
2.4.3 Detectivity improvement in ICIPs .......................................................... 45
2.4.4 Comments on detectivity improvement in ICIP ..................................... 46
2.5 Growth and fabrication of interband cascade devices .................................. 47
Chapter 3: Limiting factors and efficiencies of narrow bandgap thermophotovoltaic cells
............................................................................................................................. 50
3.1 Background and motivation .......................................................................... 50
3.2 Practical limitations on single-absorber TPV devices .................................. 51
3.2.1 Quantum efficiency and dark saturation current density ........................ 51
3.2.2 Open-circuit voltage and fill factor ......................................................... 56
3.2.3 Conversion efficiency ............................................................................. 59
3.3 Efficiency improvement in multistage TPV devices .................................... 64
3.3.1 Enhancement of open-circuit voltage ..................................................... 64
3.3.2 Enhancement of conversion efficiency ................................................... 67
3.4 Performance of TPV devices under variable illumination sources ............... 69
3.4.1 Single-absorber TPV cells ...................................................................... 69
viii
3.4.2 Multistage ICTPV devices ...................................................................... 71
3.5 Summary and concluding remarks................................................................ 73
Chapter 4: Experimental comparison between single-absorber and multistage IC
thermophotovoltaic devices ................................................................................ 75
4.2 Device Structure, growth and fabrication ..................................................... 77
4.3 Device characterizations and discussions ..................................................... 79
4.3.1 Quantum efficiency ................................................................................. 79
4.3.2 Particle conversion efficiency ................................................................. 82
4.3.3 Illuminated J-V curve and open-circuit voltage ...................................... 83
4.3.4 Fill Factor and conversion efficiency ..................................................... 87
4.4 Extraction of some important performance related parameters .................... 90
4.4.1 Voltage-dependent collection efficiency ................................................ 90
4.4.2 Thermal generation rate and carrier lifetime .......................................... 93
4.4.3 Series resistance ...................................................................................... 95
4.4.4 Surface leakage ....................................................................................... 96
4.5 Summary and concluding remarks................................................................ 97
Chapter 5: Interband cascade thermophotovoltaic devices with more stages ................. 99
5.2 Device structure, growth and fabrication .................................................... 101
5.3 Energy conversion efficiency ..................................................................... 102
5.4 Device characterization and analysis .......................................................... 105
5.4.1 Dark current density and carrier lifetime .............................................. 105
ix
5.4.2 Quantum efficiency and current mismatch ........................................... 107
5.4.3 Collection efficiency of photogenerated carriers .................................. 111
5.5 Quantification of the effects of the performance limiting factors............... 113
5.5.1 Effect of collection efficiency ............................................................... 113
5.5.2 Effect of current mismatch.................................................................... 115
5.5.3 Effect of material quality ...................................................................... 117
5.6 Summary and concluding remarks.............................................................. 119
Chapter 6: Carrier lifetime in mid wavelength interband cascade devices ................... 121
6.1 Introduction ................................................................................................. 121
6.2 Carrier lifetime in mid-wavelength ICIPs................................................... 123
6.2.1 Device structure, growth and fabrication .............................................. 123
6.2.2 Dark current density .............................................................................. 125
6.2.3 Contribution of SRH process to dark current ....................................... 127
6.2.4 Linear fitting of dark current density .................................................... 129
6.2.5 Estimated thermal generation rate and carrier lifetime ......................... 130
6.3 Interband cascade devices vs quantum cascade devices ............................. 133
6.3.1 Device structures ................................................................................... 133
6.3.2 Semi-empirical model for dark current density .................................... 134
6.3.3 Saturation current densities for cascade devices ................................... 135
6.3.4 Effect of J0 on the performances of detectors ....................................... 138
6.3.5 Effect of J0 on the performances of photovoltaic cells ......................... 142
Chapter 7: Long wavelength interband cascade infrared photodetectors ..................... 145
x
7.1 Introduction ................................................................................................. 145
7.2 Current matched ICIPs vs noncurrent-matched ICIPs ................................ 147
7.2.2 Electrical properties .............................................................................. 148
7.2.3 Responsivity.......................................................................................... 152
7.2.4 Electrical gain ....................................................................................... 155
7.2.5 Johnson-noise limited detectivity ......................................................... 156
7.3 A comprehensive study of electrical gain in ICIPs ..................................... 158
7.3.2 Responsivity.......................................................................................... 160
7.3.3 Electrical gain ....................................................................................... 163
7.3.4 Underlying mechanism of electrical gain ............................................. 165
7.3.5 Net effect of electrical gain ................................................................... 167
7.3.6 Electrical characteristics ....................................................................... 171
7.3.7 Johnson-noise limited detectivity ......................................................... 173
Chapter 8: Concluding notes and future work .............................................................. 178
8.1 Dissertation summary ................................................................................. 178
8.2 Future works ............................................................................................... 182
References ..................................................................................................................... 185
Appendix A: Publications list ....................................................................................... 205
xi
2 List of Tables
Table 1-1: Summary of some demonstrated TPV system performance. .......................... 7
Table 1-2: Summary of various TPV technologies, classified by absorbing material.... 11
Table 1-3: Summary of various photovoltaic photodetectors, classified by detecting
material. .......................................................................................................................... 23
Table 3-1: Parameters used in calculation for InAs/GaSb superlattice. ......................... 55
Table 3-2: Parameters used in calculation for bulk Ga0.44In0.56As0.5Sb0.5 ....................... 70
Table 4-1: Summary of the PV performance and the related parameters of representative
devices (0.2×0.2 mm2) from the three ICTPV wafers at 300 K. The maximum efficiencies
shown in the table for the 3- and 5-stage devices are obtained at a maximum incident power
density of 36 W/cm2........................................................................................................ 90
Table 5-1: Summary of ICTPV devices that have been reported so far. ...................... 100
Table 5-2: Individual and total absorber thicknesses for the four IC TPV structures. . 102
Table 5-3: Summary of device characteristics and some important performance-related
parameters for the four devices at 300 K. ..................................................................... 113
Table 6-1: Summary of the design and material parameters of the seven wafers. ....... 125
Table 7-1: Summary of material and design parameters for the four devices. ............. 148
Table 7-2: Theoretical calculated and experimental extracted values of R0A ratios at high
temperatures. ................................................................................................................. 152
Table 7-3: Experimentally obtained ratio of responsivity for ICIPs at different
temperatures. ................................................................................................................. 153
Table 7-4: Summary of the design and material parameters of the five wafers ........... 160
Table 7-5: Comparison of electrical parameters of the five ICIPs. .............................. 173
xii
Table 7-6: Comparison of D* at 𝜆=7 m, along with the 100% cutoff wavelengths at 300
K, for the five devices. .................................................................................................. 174
xiii
3 List of Figures
Figure 1-1: (a) An infrared thermography applied for virus screening in airport [2], (b)
Schematic illustration of a TPV system consisting of heat source, radiator, emitter, TPV
cells and cooling system. Figure is from [3]. ...................................................................... 2
Figure 1-2: Spectral radiations for blackbodies at various temperatures. The shaded regions
are of interest for applications such as solar cell, thermophotovoltaic and thermal imaging.
............................................................................................................................................. 3
Figure 1-3: Atmospheric transmittance spectrum of infrared radiation. Figure is from [10].
............................................................................................................................................. 4
Figure 1-4: Schematic illustration of a TPV system. .......................................................... 8
Figure 1-5: The calculated efficiencies based on Equation 1-4 for various blackbody
temperatures. The insert shows the optimal bandgap that maximizes the efficiency. ...... 14
Figure 1-6: The development history of modern infrared detectors and systems............. 15
Figure 1-7: Mid infrared absorption spectra of some molecules and gases. Data were
collected from [69]. ........................................................................................................... 17
Figure 1-8: Block diagram of a thermal detector. Figure from [76]. ................................ 18
Figure 1-9: Images created by uncooled and cooled infrared cameras. Figures are from
[77]. ................................................................................................................................... 19
Figure 1-10: Schematic diagram of (a) a photoconductive photodetector made of a
semiconductor slab, (b) a quantum well infrared photodetector based on bound-to-
continuum transition. ........................................................................................................ 20
Figure 1-11: Schematic diagram of a PV detector made of a single p-n junction ............ 21
xiv
Figure 1-12: Schematics of (a) a nBn barrier detector and (b) a complementary barrier
infrared detector; the biases are applied to improve carrier collection. ............................ 21
Figure 1-13: Schematic diagram of a quantum cascade detector. .................................... 22
Figure 2-1: (a) Bandgap, lattice constant and (b) band alignment of the 6.1 Å
semiconductor materials. .................................................................................................. 27
Figure 2-2: Illustration of the photon emission and cascading effect in an interband cascade
laser. Figure from [115]. ................................................................................................... 29
Figure 2-3: Band diagram of the active core for an interband cascade laser. Figure from
[73]. ................................................................................................................................... 31
Figure 2-4: Room temperature threshold current density for both InAs- and GaSb-based
broad-area ICLs. Figure is from [124]. ............................................................................. 32
Figure 2-5: Band structure, minibands and wavefunctions of electrons and holes for (a)
InAs/GaSb superlattice and (b) M-shape Al(In)Sb/GaSb/InAs/GaSb/Al(In)Sb SL. ........ 33
Figure 2-6: (a) Schematic band diagram of an ICTPV cell, (b) Schematic showing the
operation of an ICTPV cell. .............................................................................................. 36
Figure 2-7: Collection probability of carriers as a function of the distance from the
collection point. The absorber thickness is 3.3 m. The number near the curve indicates
the diffusion length. .......................................................................................................... 38
Figure 2-8: Comparison of collection process in single- and four-stage IC devices for a low
L product (L=0.4). The thickness d of the single-stage device equates the absorption
depth. The individual absorber thickness of four-stage IC device is d/4. ......................... 40
Figure 2-9: (a) schematic diagram of a multistage ICIP and (b) the band profile of one stage
under zero bias. The olive and purples lines in the absorber represent the electron and hole
xv
minibands. The dotted olive wavefunction indicates the electron states in hole barrier while
the dotted purple wavefunction represents the hole states in electron barrier. ................. 42
Figure 2-10: Johnson-noise limited detectivity enhancement for current-matched ICIPs
with two, eleven and thirty stages. Figure is from [141]. ................................................. 46
Figure 2-11: (a) Intevac GEN II MBE system (1993) and (b) Veeco GENxplor MBE
system (2013). ................................................................................................................... 48
Figure 2-12: (a) The schematic of a processed ICTPV or ICIP device and (b) Cross-section
scanning electron microscope image of a wet-etch ICTPV structure, the Figure is from
[157]. ................................................................................................................................. 49
Figure 3-1: Calculated open-circuit voltage (solid) and quantum efficiency (dashed) as a
function of normalized absorber thickness for different values of L. The incident power
density is assumed to be 50 W/cm2................................................................................... 53
Figure 3-2: Calculated dark saturation current density as a function of normalized absorber
thickness for a carrier lifetime of 20 ns, 200 ns and the radiative limit. ........................... 55
Figure 3-3: Simulated J-V curves for different values of L and with incident power density
of 25 and 50 W/cm2. ......................................................................................................... 57
Figure 3-4: Calculated fill factor as a function of normalized absorber thickness for
different values of L. The incident power density is assumed to be 50 W/cm2 except in
the ultimate limit. .............................................................................................................. 59
Figure 3-5: Calculated conversion efficiency vs normalized absorber thickness for different
values of L. The incident power density is assumed to be 50 W/cm2 except for the ultimate
limit. .................................................................................................................................. 62
xvi
Figure 3-6: Calculated (a) conversion efficiency and (b) voltage efficiency and fill factor
for L=0.45, 1.5 and 4.5 and the ultimate efficiency limit as a function of bandgap. The
incident power density is 50 W/cm2 except for the ultimate limit.................................... 63
Figure 3-7: Schematic of a three-stage ICTPV device under forward voltage and
illumination. Optical generation gphm, thermal generation gthm and recombination Rm, along
with the chemical potentials m in each stage are shown, where the index m denotes the
stage ordinal. The flat quasi-Fermi levels (designated with 1, 2, 3 and 4) correspond
to the case where the diffusion length is infinite. ............................................................. 65
Figure 3-8: Calculated open-circuit voltage enhancement Voc(Nc)/Voc(1) as a function of
number of stages. The dashed purple line indicates Voc(Nc)/Voc(1)=Nc. In the calculations,
L was set at 0.45. 1.5 and 4.5. The incident power density is 50 W/cm2. ...................... 66
Figure 3-9: Calculated conversion efficiency for optimized multistage cells as a function
of number of stages. The calculation is done for L=0.45 1.5 and 4.5. The incident power
density is 50 W/cm2. ......................................................................................................... 68
Figure 3-10: Calculated maximum conversion efficiency and conversion efficiency
enhancement as a function of L. The incident power density is 50 W/cm2. .................. 69
Figure 3-11: Calculated conversion efficiency of a GaInAsSb single-absorber device vs
wavelength for various values of diffusion length. The incident power density is 50 W/cm2.
........................................................................................................................................... 71
Figure 3-12: Calculated conversion efficiency for the 5- and 20-stage devices with L=1.5
m (solid curves) and 15 m (dashed curves). The absorbers were adjusted to be
photocurrent matched with an absorption coefficient of 3000 cm-1, corresponding to a
wavelength of 4 m. The calculated maximum efficiencies with optimized multi-stage
xvii
structures at every wavelength are represented by the olive curves. The incident power
density is 50 W/cm2. ......................................................................................................... 73
Figure 4-1: (a) Calculated quantum efficiency and collection efficiency, and (b) open-
circuit voltage factor as a function of normalized absorber thickness for several values of
L. VF initially decreases with increasing d/L due to the nearly linear increase of dark
current when d/L is small. ................................................................................................. 77
Figure 4-2: Schematic layer structures of the three TPV devices with one, three and five
stages. ................................................................................................................................ 79
Figure 4-3: Measured QE spectra of 1-, 3- and 5-stage devices at 300 and 340 K. ......... 80
Figure 4-4: Voltage dependent QE at 4 m for the three devices, where different vertical
scales are used in the top and bottom portions to better show variations. ........................ 81
Figure 4-5: (a) Current-voltage characteristics of the three devices at 300 K under a medium
illumination level where the incident power density was about 19 W/cm2. The solid, dotted
and dashed curves correspond to the measured, Rs corrected and ideal cases, respectively.
(b) Current-voltage characteristics of the three devices at 200 K under the same level of
illumination as in (a). The inset shows the emission spectrum of the ICL. ...................... 85
Figure 4-6: (a) Open-circuit voltage, (b) fill factor, (c) maximum output power density and
(d) conversion efficiency as a function of incident power density for the three devices at
300K.................................................................................................................................. 88
Figure 4-7: (a) Voltage dependence of collection efficiency derived from Equation 4-2
using four different pairs of J-V data at 300 K for the three devices. The numbers in the
legend indicate the incident power densities under different illumination levels. (b)
Average collection efficiency over the four pairs in (a). .................................................. 92
xviii
Figure 4-8: The thermal generation rate and minority carrier lifetime for the 1-, 3- and 5-
stage devices at high temperatures. ................................................................................... 95
Figure 4-9: dV/dI data to obtain series resistance at 300 K, which was found from the
intercept of dV/dI. ............................................................................................................. 96
Figure 4-10: Size dependent R0A for the three devices at 300 K. The sidewall resistivity
was smallest for the one-stage device. .............................................................................. 97
Figure 5-1: Schematic layer structure of the four TPV devices with six, seven, sixteen and
twenty-three stages.......................................................................................................... 102
Figure 5-2: (a) Illuminated current density-voltage characteristics for the representative
200×200 m2 devices from the four wafers at 300 K and at an incident power density of
17 W/cm2. The inset shows the emission spectrum of the IC laser used as the illumination
source, (b) Conversion efficiency as a function of incident power density for the four
devices at 300 K. ............................................................................................................. 104
Figure 5-3: (a) Dark current density for the representative 200×200 m2 devices from the
four wafers at 300 K, (b) Linear fitting (dashed lines) of dark current density at reverse
voltage for the four devices at 300 K. ............................................................................. 106
Figure 5-4: (a) Quantum efficiency spectra of the four devices at 300 K and (b) Bias
dependence of quantum efficiency for the four devices at 300 K and at the wavelength of
4.2 m. ............................................................................................................................ 109
Figure 5-5: (a) Calculated effective quantum efficiency based on Equation 2-5 in each stage
of the four devices, (b) Calculated incident power density vs IC laser current based on
Equation 4-1 for the four devices.................................................................................... 110
xix
Figure 5-6: (a) The measured and the 100% collected J-V curves for the four devices at 300
K and at the incident power density of 17 W/cm2, (b) Extracted collection efficiency at 300
K based on Equation 4-2 using J-V data under incident power densities of 7 and 17 W/cm2
for the four devices. ........................................................................................................ 113
Figure 5-7: Comparison of the measured  and the ideal  in the 100% collected case at
300 K for the 6- and 7-stage devices. ............................................................................. 114
Figure 5-8: Calculated (a) short-circuit current density and (b) conversion efficiency based
on Equation 5-1 as a function of absorption coefficient at incident power density of 17
W/cm2 for the four devices. ............................................................................................ 117
Figure 5-9: Calculated conversion efficiency based on Equation 3-10, along with
measurement for the four devices. For each of the four devices, the carrier lifetime used in
the calculation was 27 and 87 ns..................................................................................... 119
Figure 6-1: Radiative and non-radiative recombination processes in semiconductors... 122
Figure 6-2: Dark current density versus applied voltage for the seven devices at (a) 250 K
and (b) 300 K. ................................................................................................................. 127
Figure 6-3: (a) R0A of the seven devices in the temperature range of 200-340 K. (b)
Temperature dependence of bandgap for M3S-312. The fitting Varshni parameters for the
device are shown. ............................................................................................................ 128
Figure 6-4: Linear fitting (dashed) and experimental measurements (solid) of the dark
current density at reverse bias voltage for the five multistage devices at 300 K. The inset
shows the corresponding results of the two single-stage devices at 300 K. ................... 130
Figure 6-5: The thermal generation rate and minority carrier lifetime for the five multistage
and two single-stage devices at high temperatures. ........................................................ 133
xx
Figure 6-6: The measured and fitted Jd-V curves for an 8-stage ICD and a 50-stage QCD at
300 K. The ICD and QCD were mentioned in [115] (wafer R083) and [96], respectively.
......................................................................................................................................... 136
Figure 6-7: The extracted values of J0 for ICDs and QCDs at 300 K. Some ICDs have been
described previously in [83-84, 96, 222-224], while others are from our unpublished
studies. The QCDs are from [115, 120, 179, 225-226]................................................... 138
Figure 6-8: Measured peak (a) responsivities and (b) detectivities for ICDs, ICD_SLs and
QCDs at 300 K. In addition to some of the ICDs presented in Figure 6-6, two ICDs (devices
A and B) [136] and all ICD_SLs from [137, 151, 199, 229-231] are included. One QWIP
is from [236]. .................................................................................................................. 139
Figure 6-9: Estimated Voc at 300 K for the ICDs, ICD_SLs and QCDs shown in Figure 6-
8....................................................................................................................................... 143
Figure 7-1: Schematic illustration of the multi-stage ICIP with (a) regular and (b) reverse
configurations. The two configurations can be realized by reversing the growth order of
layers in one structure without changing the light illumination direction. ..................... 146
Figure 7-2: Extracted R0A of the four representative devices at various temperatures. . 150
Figure 7-3: The theoretical R0A curves at T=300K. The device dark current was dominated
by the diffusion process at this temperature. .................................................................. 151
Figure 7-4: Zero-bias responsivity spectra for the four devices at different temperatures.
......................................................................................................................................... 153
Figure 7-5: Temperature-dependent responsivity of the four devices at 7 m. .............. 154
Figure 7-6: Absorption coefficient and electrical gain at room temperature. The dips near
4.2 m in the gain curves were due to CO2 absorption in the response spectra. ............ 156
xxi
Figure 7-7: Johnson-noise limited D* spectra of the four devices at various temperatures.
......................................................................................................................................... 158
Figure 7-8: (a) Zero-bias responsivity spectra for the five devices at different temperatures.
(b) Theoretically calculated external quantum efficiency of the five devices vs. absorption
coefficient. ...................................................................................................................... 162
Figure 7-9: Absorption coefficient and electrical gain at room temperature. The dips near
4.2 μm in the gain curves were due to CO2 absorption in the response spectra. ............ 164
Figure 7-10: Theoretically calculated photocurrent based on Equation 7-5 and (b) electric
potential calculated based on Equation 7-7 for each stage of the five devices at room
temperature. .................................................................................................................... 167
Figure 7-11: Theoretically calculated and experimentally measured signal current for the
five devices. .................................................................................................................... 169
Figure 7-12: Theoretical and experimental responsivity spectra for two devices at 250 K
with the IR source and a standard blackbody radiation source at 800 and 1200 K. ....... 171
Figure 7-13: Arrhenius plot of dark current density (measured at -50 mV) and R0A of the
five devices in the temperature range of 200-340 K. ...................................................... 172
Figure 7-14: Johnson-noise limited D* spectra of the five devices at various temperature.
......................................................................................................................................... 174
Figure 7-15: Detectivity derived from Equation 7-10 versus the number of stages with
various ratios of the individual absorber thickness to the diffusion length (d/L), which are
labeled near the curves in the two cases. ........................................................................ 176
xxii
4 Abstract
Mid-infrared (IR) optoelectronic devices form the basis for many practical
applications such as thermophotovoltaic (TPV) energy conversion, gas sensing, thermal
imaging, medical diagnostics, free-space communications, infrared countermeasures and
IR illumination. The mid-IR device family based on interband cascade (IC) structures
includes IC lasers (ICLs), ICTPV cells and IC infrared photodetectors (ICIPs). These are
special types of multistage devices whose operation is made possible by the unique
properties of the 6.1 Å material system: InAs, GaSb and AlSb, and their related alloys. One
of the key properties is the type-II broken-gap alignment between InAs and GaSb.
In multistage ICTPV cells and ICIPs, electrons must undergo multiple interband
excitations in order to travel between the electrical contacts. This means that the transport
of a single electron requires multiple photons, which reverses the situation in ICLs where
a single electron can generate multiple photons. Counterintuitively, this transport feature
in ICTPV cells and ICIPs is conducive to improving device performance by enhancing the
open-circuit voltage in ICTPV cells and suppressing the noise in ICIPs. Furthermore, the
collection efficiency of photo-generated carriers in multistage IC devices can be
significantly improved by thinning the absorbers in individual stages. Collectively, these
advantages make IC structures an attractive choice for narrow bandgap optoelectronic
devices, especially for operation at high temperatures. One focus of this dissertation is to
outline and demonstrate the advantages provided by IC structures, both in theory and
experiment. Another focus of this dissertation is to obtain a better understanding of the
physics of IC devices and gain insights into their operation.
Theoretical studies of single-absorber and multistage ICTPV cells are presented.
xxiii
The limitations in efficiency are understood by considering several important practical
factors. These factors are identified to be closely associated with a short carrier lifetime,
high dark saturation current density, small absorption coefficient, and limited diffusion
length. The multistage IC architecture is shown to be able to overcome the diffusion length
limitation that is responsible for the low quantum efficiency (QE) in single-absorber TPV
cells. This ability of the IC architecture offers the opportunity to enhance conversion
efficiency by about 10% for wide ranges of L (product of absorption coefficient and
diffusion length) and bandgaps, resulting in a particle conversion efficiency approaching
100%.
The illustrated theoretical advantage of multistage IC structures is confirmed
experimentally in a comparative study of three fabricated TPV devices, one with a single
absorber and two that are multistage IC structures. The bandgap of the InAs/GaSb type-II
superlattices (T2SLs) in the three devices is close to 0.2 eV at 300 K. The extracted
collection efficiency is considerably higher in multistage IC devices than in the single-
absorber device. To further investigate the prospects of IC TPV cells, detailed
characterization and performance analyses of two sets of four IC devices with similar
bandgaps are performed. The four different configurations enable a comparative study that
shows how device performance is affected by material quality variations, as well as by
current mismatch between stages and collection efficiency.
The carrier lifetime advantage of IC devices over another family of cascade devices,
namely quantum cascade (QC) devices, is manifested in the saturation current density (J0).
The values of J0 extracted using a semi-empirical model, are more than one order of
magnitude lower in IC devices than in QC devices. The significance of J0 on the
xxiv
performances of IR detectors and TPV cells is apparent in a comparison of the measured
detectivity (D*) and the estimated open-circuit voltage (Voc). To extract the carrier lifetime
in IC devices, a simple and effective electrical method is developed. This method is more
generally applicable and considers the parasitic shunt and series resistances found in
practical devices. It provides a simple way to extract the carrier lifetime in InAs/GaSb
T2SLs in a wide range of operating temperatures.
The effect of current mismatch on the performance of ICIPs is investigated using
two sets of devices with current-matched and noncurrent-matched configurations. It is
shown that current matching is necessary to achieve maximum utilization of absorbed
photons for an optimal responsivity. The detectivities of both sets of devices are
comparable largely due to the occurrence of a substantial electrical gain in noncurrent-
matched ICIPs. The electrical gain is shown to be a ubiquitous property for noncurrent-
matched ICIPs through the study of another three devices. To unlock the mechanism
underlying electrical gain, a theory is developed for a quantitative description and the
calculations are in good agreement with the experimental results.
xxv
1 Chapter 1: Introduction
1.1 Infrared radiation
Infrared radiation (IR) is a type of electromagnetic wave with wavelength longer
than for visible light. The wavelength range for IR is between about 700 nm and 1mm,
equivalent to a frequency range of approximate 430 THz to 300 GHz. IR radiation is
commonly divided into several sub-divisions [1]: near-infrared (NIR, 0.7-1.4 m), short
wavelength (SWIR, 1.4-3.0 m), mid wavelength infrared (MWIR, 3-8 m), long
wavelength (LWIR, 8.0-15 m) and far infrared (FIR, 15-1000 m). There are various uses
of infrared radiation in the areas of military, environment, industry, astronomy, climatology
and many more. For example, SWIR is extensively used in fiber-optic communication
wherein pulses of SWIR light are sent though an optical fiber. MWIR is of main interest in
gas sensing areas since many molecules and trace gasses have strong absorption lines in
this band. One of the most useful applications of LWIR is thermal imaging that translates
thermal energy into image in order to analyze an object or scene. A specific example of
thermal imaging is shown in Figure 1-1(a) in which an infrared camera is used to screen
passengers in the airport to prevent virus spread [2]. To implement these applications, one
essential component is the infrared detector. One focus of this dissertation is a special type
of semiconductor infrared detector. The other focus of this dissertation is a
thermophotovoltaic (TPV) cell that is the core element in a TPV system [3]. As shown in
Figure 1-1(b), a complete TPV system includes a heat source, radiator, emitter, set of TPV
cells and cooling system. TPV technology [4-5] has been proposed for applications such
as portable power sources, heat conversion of concentrated solar energy and cogeneration
in remote locations.
1
Figure 1-1: (a) Infrared thermography is applied for virus screening in an airport [2],
(b) Schematic illustration of a TPV system consisting of a heat source, radiator,
emitter, set of TPV cells and cooling system. Figure is from [3].
According to thermodynamic laws, all objects with temperatures higher than
absolute zero emit electromagnetic radiation. Ideally, if the object is a perfect blackbody,
the spectral radiance follows Planck’s law. In this case, the power emitted per unit area,
per unit solid angle and per unit frequency of a blackbody is given by:
2ℎ𝑐 2 1
𝐵𝜆 (𝜆, 𝑇) = ℎ𝑐 , (1-1)
𝜆5 𝑒𝑥𝑝( )−1
𝜆𝑘𝑏 𝑇
where h is the Planck’s constant, c is the speed of light, 𝜆 is wavelength, kb is Boltzmann
constant, and T is temperature. The net power per unit area radiated outward from an ideal
blackbody, considering the temperature difference with the ambient, can be obtained by
integrating Planck’s radiation formula:
𝑃 ∞ 𝑑𝜆 ∞ 𝑑𝜆
= 2ℎ𝑐 2 [∫0 ℎ𝑐 − ∫0 ℎ𝑐
] (1-2)
𝐴 𝜆5 𝑒𝑥𝑝( )−1 𝜆5 𝑒𝑥𝑝( )−1
𝜆𝑘𝑏 𝑇 𝜆𝑘𝑏 𝑇𝑎𝑚𝑏
where A is the surface area and Tamb is the ambient temperature. This integration gives the
final form of Stefan-Boltzmann law that is written as:
𝑃 𝑇
= 𝜎(𝑇 4 − 𝑇𝑎𝑚𝑏 ) (1-3)
𝐴
where  is the Stefan-Boltzmann constant, equal to 5.6704×10-8 W·m-2·K-4.
2
Illustrations of blackbody spectral radiation at various temperatures are shown in
Figure 1-2. The marked regions are linked with several specific technologies: solar cells,
thermophotovoltaics and infrared detectors. The surface temperature of the Sun is around
5800 K; the strongest output of the solar radiation spectrum is in the visible range.
Therefore, the semiconductor materials used in solar cells typically have a wide bandgap
(Eg) such as 1.1 eV for Si, the most common material for commercial solar cells [6-7]. By
comparison, the temperature of the heat source in a TPV system is in a lower temperature
regime, ranging from 1000-2000 K [4-5]. The radiation of the heat source mainly falls in
the NIR and SWIR spectra. On this account, narrower bandgap materials are preferred for
TPV cells. For example, the most prevalent material for TPV cells is GaSb with a 0.7 eV
bandgap [4-5]. Thermal imaging targets usually have a temperature approaching the
ambient; the radiation is mainly distributed over the MWIR and LWIR bands. Hence, the
infrared photodetectors fitted in infrared cameras are typically made of semiconductors
whose bandgaps are lower than 0.4 eV, e.g. InSb with a bandgap of 0.18 eV [8-9].
Photon energy (eV)

8 10 1 0.1
10
Spectral radiance (W.m-2.sr-1.m-1)
106
K
800
TPV
104
T=5
K
000
102
K
T=2
000
T=1
100
0K
30
T=
10-2
MWIR
LWIR
10-4
10-6
0.1 1 10 100
Wavelength (m)
Figure 1-2: Spectral radiation for blackbodies at various temperatures. The shaded
regions are of interest for applications such as solar cell, thermophotovoltaics and
thermal imaging.
3
An important feature of infrared radiation is that it is mostly blocked out by the
atmosphere. The two natural greenhouse gases in Earth’s atmosphere ─ water vapor and
carbon dioxide, absorb most of the infrared light. Only a few infrared wavelength ranges
are likely to travel through the atmospheric window, as shown in Figure 1-3 [10]. Hence,
the better view on the infrared world from ground-based infrared cameras is at infrared
wavelengths with a high atmospheric transmittance. The atmospheric window is also an
important consideration in free space optical communication (FSO) [11]. Because of this,
unlike the earlier mentioned division scheme, a more commonly recognized categorization
framework in the detector community is [10]: NIR (0.7-1 m), SWIR (1-3 m), MWIR (3-
5 m), LWIR (8-14 m), very long wavelength IR (VLWIR, 14-30 m), and far IR (FIR,
30-100 m) bands.
Figure 1-3: Atmospheric transmittance spectrum of infrared radiation. The figure is

from [10].
4
1.2 Overview of infrared thermophotovoltaic energy conversion
1.2.1 Background
In modern society, the overuse of diminishing fossil fuels has driven humanity to
develop alternative non-fossil energy source as well as ways of efficient use of fossil fuels.
TPV is a promising technology that can generate electricity from non-fuel resources such
as radioactive energy and concentrated sunlight. Potentially, it is also a more efficient way
to convert fossil fuel combustions with the ultimate efficiency approaching the Carnot limit
[4-5]. Although the expected high efficiency has not been fulfilled at the current stage, fuel
versatility still motivates further pursuit of this approach.
Early efforts on TPV were dedicated to developing military portable power sources
until the 1970s [12]. After the US Army decided to choose thermoelectrics as the priority
development project, TPV technology experienced a slow pace of development. However,
it still significantly profited from the progress of solar photovoltaics (PVs), particularly
from the rapid development of solar cells. Two examples are GaSb and InGaAs diodes that
are now the two prevalent TPV cells, while they were originally explored as the subcells
in multi-junction solar cells [13-14]. Besides, the experience in controlling the incident
radiation gathered from concentrated solar PV also promotes the development of TPV.
There was a regenerated interest in TPV in the 1990s for space, industry and military
applications. In industry, the use of TPV for waste heat recovery was conceived as a
prospective market niche. Over the same period, the near-field TPV concept started to
emerge, which utilized a sub-micron vacuum gap between the radiator and TPV cells [15-
17]. This method can appreciably improve the heat transfer between the radiator (or
emitter) and TPV cell. Another benefit of this displacement is enhanced incident power
5
density and the resulting higher conversion efficiency.
Until now, TPV is still in a research and development phase, and has not reached
commercial maturity, as it has been impeded by some research barriers. For example, in
the past, the lack of suitable high efficiency TPV cells was the main obstacle. Currently,
the main difficulty is the involvement of various areas of applied science. Unlike solar PVs,
the realization of a TPV system relies on experience in various aspects including optics
with filters, heat transfer over a small scale and materials tolerant of high temperature.
Despite these obstacles, some prototype TPV system demonstrations were reported, as
briefly summarized in Table 1-1.
6
Propane Propane Propane Butane Combined Radioisotope
Heat source JP8 combustion combustor- Sunlight Sunlight
combustion combustion combustion combustion module
emitter
Si/SiO2 tungsten
Emitter planar
SiC SixNy photonic Yb2O3 tungsten on SiC SiC tungsten photonic
material tungsten
crystal crystal
Emitter 1200 ℃ 770 ℃ 700 ℃ 1462 ℃ 1275 ℃ 1309 ℃ 1007 ℃ 1500 ℃ 1200 ℃
temperature
dielectric selective emitter, dielectric surface
Spectral selective selective surface selective
filter on TPV N/A dielectric filter on filter on TPV reflective
control emitter emitter reflective filter emitter
cell TPV cell cell filter
TPV cell GaSb GaSb GaInAsSb Si GaSb InGaAs InGaAs Ge GaSb
Cell
7
0.7 eV 0.7 eV 0.55 eV 1.4 eV 0.7 eV 0.6 eV 0.6 eV 0.66 eV 0.7 eV
bandgap
Cell 75 ℃ 25 ℃ water cooled 14 ℃ 25 ℃ 25 ℃ 50 ℃ 120 ℃ water cooled
temperature
Output
80 W 1 mW 344 mW 48 W 700 W 3.16 W 100 W 415 mW 9.2 W
power
Power 67 6.24
0.4 W/cm2 32 mW/cm2 344 mW/cm2 0.1 W/cm2 1.5 W/cm2 0.79 W/cm2 0.5 W/cm2
density mW/cm2 W/cm2
System emitter/module 20%

2.0% 0.08% 2.5%- 2.4% 16% projected 0.8% 6.2%
Efficiency 23.6% projected
Institution JX Crystal MIT MIT UNSW JX Crystals Inc. Bechtel Bettis Emcore Barcelona UVA
Table 1-1: Summary of some demonstrated TPV system performance.
Inc. Inc. University

Reference [18] [19] [20] [21] [22] [23] [24] [25] [26]
1.2.2 Active components in a TPV system
Solar PV and TPV are similar technologies as they both use PV cells to generate
electricity from high temperature radiation sources. One of the main differences between
the two is the geometry. A TPV system typically consists of a heat source, absorber and
emitter (or radiator), filter and TPV cells. Sometimes a cooling fan is included in the system
to prevent overheating of the TPV cells. The general operating principle of a TPV system
is illustrated in Figure 1-4. The radiation produced from the heat source (either
radioisotope, or fuel combustion or concentrated sunlight) is absorbed by the absorber and
subsequently radiated by the emitter. The filter then converts the broadband radiation
spectrum into a narrowband emission spectrum tuned to the response of the TPV cell.
Afterwards, the radiation is captured by the TPV cell and converted into electricity. In some
cases, the absorber is coupled with a selective emitter with a narrow range of wavelength
emission, thus the filter is no longer needed. Besides the filter, the other approach of
spectral control is to reflect out-of-band photons back to the emitter via reflectors in front
of or behind the TPV cell.
Figure 1-4: Schematic illustration of a TPV system.
The system efficiency is affected by the performance of the individual components
as well as the interaction between them. To build a reliable TPV system, the operations of
8
the components need to be optimized. For example, since the heat source in a TPV system
is generally at 1000-2000 K, the emitter should have high thermal stability. There are
several suitable materials for emitters, classified as ceramics [18-19, 23], metals [22, 24,
26-28], metal oxides [21, 27, 29-30], or other novel materials [31-33]. Conventional metals
and ceramics tend to have broadband emission. In contrast, the pure polished metal oxides
(e.g. rare-earth oxides) can have narrow-band emission. Among these materials, tungsten
is currently the most used, since its emission spectrum is well matched with the bandgap
of GaSb [22, 24, 26-27]. Novel emitters based on artificial structures such as photonic
crystals and metamaterials have the advantage of very narrow emission bands, but at the
expense of more complex structures than conventional emitters [31-33].
1.2.3 Thermophotovoltaic cells
In the early period of development, investigations of TPV cells were mainly
focused on Si [34] and Ge [35]. The low cost and mature production phase of Si made it a
competitive material. However, the bandgap of Si is too wide for efficient conversion of
IR radiation, because most of the photons possess energies lower than its bandgap and are
unable to excite electron-hole pairs. Ge has a narrower bandgap than Si, but its crystal
structure can be easily damaged at high temperatures. Also, the recombination losses in Ge
cells are very high due to the large effective mass and high carrier concentration. Current
generation of TPV cells are mainly made of GaSb [22, 36], InGaAs [23, 37-38], GaInAsSb
[39-40] and InGaSb [41-42]. Among them, GaSb is often regarded as the most suitable
choice for TPV generators. GaSb has a similar bandgap (~ 0.72 eV) with Ge, which allows
it to respond to light with longer wavelengths. Under a perfectly filtered blackbody
(T=1350 K), an efficiency of ~30% was projected for GaSb cells [36].
9
Up to now, without a filter, the best reported efficiencies for TPV cells are 24% for
a 0.6 eV InGaAs cell on InP [23, 37] and 19.7% for a 0.53 eV GaInAsSb cell on GaSb
[39]. These records were measured with a ~1000 °C broadband blackbody radiator and
with a front surface reflector for recovering unabsorbed below-bandgap photons. The
bandgap of a ternary InGaAs diode, exactly lattice matched to InP, is 0.74 eV, but it
underperforms GaSb TPV cells [38]. By changing the ratio of Ga to In, the bandgap of
InGaAs can be tuned from 0.55 to 0.6 eV with some strain from the InP substrate. The
strained InGaAs cells generally outperform GaSb cells [23, 37]. Quaternary GaInAsSb
alloys latticed-matched to GaSb have bandgaps theoretically ranging from 0.25 and 0.75
eV. The fabricated GaInAsSb cells on GaSb substrate have bandgaps from 0.5 to 0.6 eV
[39-40]. The performance of these TPV cells generally falls behind InGaAs TPV diodes.
Also, the manufacture of GaInAsSb cells is expensive and is not commercially available.
Aside from the above-mentioned materials, other TPV cell research interests are
narrow bandgap (0.4 eV) materials such as InAsSbP [43-44], InAs [45-46], InSb [47] and
InAsSb [48]. These narrow bandgap cells have a low open-circuit voltage and fill factor,
as well as a poor efficiency at room temperature as shown in Table 1-2. Even some studies
are only for proof-of-concept demonstrations of potentials. To achieve optimal efficiency,
they were cooled down to overcome some of the downsides [47]. The performance limiting
factors in narrow bandgap TPV cells are identified theoretically and experimentally in
Chapters 3 and 5, respectively. Nevertheless, theoretical calculations following the detailed
balance principle showed that the optimal choice for TPV cell bandgap energy is between
0.2-0.4 eV [49-50]. In the next subsection, a similar bandgap range is calculated from the
thermodynamic perspective. Additionally, up to now, relatively less research work has
10
InAsSbP InGaSb GaInAsSb GaInAsSb InGaAs InGAAs GaSb GaSb Ge Si
MIM
0.35 0.56 0.549 0.53 0.74 0.6 0.73 0.73 0.66 1.1
21 ℃ 27 ℃ 27 ℃ 27 ℃ 30 ℃ 25 ℃ 25 ℃ 25 ℃ 300 K 300 K
1373 K 3250 K 1039 ℃ 1350 K 1200 1100 ℃ 2300 ℃

N/A arc lamp 950 ℃ SiC
blackbody blackbody tungsten blackbody ℃ SiC tungsten radiator
types of single-absorber TPV cells.
front front front perfect front front &

without without without surface surface surface band edge surfac back N/A
filter reflection filter filter e filter surface
reflection
11
0.25 3.0 3.5 2.9 0.288 0.1 3.0 2.83 1.67 9.52
34% 61% 66% 67% 65% 66.2% 75% 73% 67% N/A
120 mV 270 mV 313 mV 306 mV 405 mV 12.5 V 500 mV 477 356 mV N/A
mV
0.024 0.49 0.723 0.58 0.08 0.79 1.26 0.98 0.4 10
0.18% N/A N/A 19.7% 12.4% 24% projected 21% 16% 26%
30%
[44] [42] [40] [39] [38] [23, 37] [36] [22] [35] [34]
Table 1-2: Summary of various TPV technologies, classified by absorbing material.
been done towards narrow bandgap cells; there is still great potential in further
development of them. Table 1-1summary some important device performances of various

Table 1-2 continued
blackbody
without
950 ℃
60 mV
20 ℃
InAs
37%
0.32
0.89
0.02
[45]
3%
blackbody
17.4 mV
without
800 ℃
0.35%
300 K
InAs
1E-3
25%
0.36
0.23
[46]
1248 K IR
without
83 mV
7.2E-3
3.8E-4
source
InSb
77 K
64%
0.23
N/A
[47]
blackbody
projected
InAsSb
without
1500 K
27 ℃
0.286
39.88
162.8
16%
N/A
N/A
[48]
Illuminati
Reference
Efficiency
on source
Material
Spectral
(W/cm2)
(A/cm2)
FF (%)
control
Eg (eV)
Cell T
Pout
Voc
Jsc
1.2.4 Thermodynamic analysis of thermophotovoltaic cell efficiency
In single-absorber TPV cells, without spectral control, the major energy loss arises
from two mechanisms. The first mechanism is that photons with energies lower than the
bandgap energy are not converted. The second mechanism is due to photons with energy
higher than Eg. These photons contribute only Eg and the excess energy is released via hot
carrier heating. Theoretically, both losses can be minimized by means of spectral control,
but this would lead to low, often not acceptable, power densities, and low system
efficiencies. Without spectral control, there is a tradeoff between the intensified below-
bandgap loss and mitigated thermalization loss as the cell bandgap increases, implying an
optimal choice of the bandgap to maximize cell efficiency. Several well-established models
exist to identify the ideal cell bandgap, as well as to predict the upper limits of TPV
efficiency and power density. The efficiencies predicted by different models are compared
12
in [51]. Some models are based on empirical values for the saturation current density [52-
54]. Some models refer specifically to solar TPV conversion [55-57]. The usual assumption
made in these models is full incident spectrum (no spectral control). Here, the ultimate
efficiency and optimal bandgap are calculated by extending Shockley and Queisser’s [58]
limit for solar cells (also known as the detailed balance limit) to the TPV case.
In TPV systems, ideally, there is no radiation lost since the radiator and emitter are
closely arranged. The solid angle subtended by TPV cell can be 4π sr compared to the
6.85×10-5 sr for conventional solar cells. Thanks to this arrangement, from the Stefan-
Boltzmann law (Equation 1-3), the radiation density can reach 16-91 W/cm2 incident on
the TPV cell for a heat temperature at 1000-2000 K, while the average solar radiation on
earth’s surface is only 0.1 W/cm2. To apply detailed balance analysis, several assumptions
need to be made to simplify the scenario. First, there are no non-radiative channels in the
TPV cell; carrier recombination and generation are exclusively radiative. Second, the
bandgap is a sharp demarcation of absorption: photons with above-bandgap energy are
completely absorbed, while below-bandgap photons are hardly absorbed. Third, when a
bias voltage (V) is applied to the TPV cell, it will emit photons as a blackbody with a
chemical potential of eV.
Under these assumptions, the current flowing in a TPV cell under a bias voltage (V)
can be given by:
2𝜋𝑞 ∞ 𝐸2 𝐸2
𝐽 (𝑉 ) = ∫ [ 𝐸 − 𝐸−𝑒𝑉
] 𝑑𝐸 (1-4)
ℎ 3 𝑐 2 𝐸𝑔𝑒𝑥𝑝( )−1 𝑒𝑥𝑝( )−1
𝑘𝑏 𝑇𝑠 𝑘𝑏 𝑇𝑐𝑒𝑙𝑙
where q is electron charge, Ts and Tcell are the temperature of the source and cell,
respectively. The first term in the integral stands for the photocurrent due to light
13
absorption. The second term represents the reverse dark current originated from electron
recombination. Based on Equation 1-4, the calculated efficiencies of TPV cells for various
source temperatures are shown in Figure 1-5. The inset within the figure is the optimal
bandgap that maximizes the efficiency as a function of the source temperature. As can be
seen, the optimal bandgap for a source temperature at 1000-2000 K is in the range of 0.18-
0.37 eV, well less than the bandgap of current mainstream TPV cells made of GaSb,
InGaAs and GaInAsSb. The corresponding maximum efficiency is between 22% and 33%,
remarkably higher than the actual efficiencies of narrow bandgap TPV cells such as
InAsSbP, InAs and InSb (See Table 1-2). This is because the detailed balance limit is a
very idealized and an overestimated limit, as the analysis buries many practical factors. For
example, in real narrow bandgap devices, non-radiative recombination such as Auger and
Shockley-Read-Hall (SRH) tend to prevail over radiative recombination. These non-ideal
factors will seriously limit overall device performance. In Chapter 3, the efficiency limits
of narrow bandgap TPV cells will be re-evaluated by acknowledging some of the practical
factors.
35
Optimum bandgap (eV)
1.2
1.0
30
Conversion efficiency (%)
0.8
0.6
25 0.4
2500 K 0.2
20 0.0
0 2000 4000 6000
2000 K Source temperature (K)
15
1500 K
10
5 1000 K
0
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Bandgap (eV)
Figure 1-5: The calculated efficiencies based on Equation 1-4 for various blackbody
temperatures. The inset shows the optimal bandgap that maximizes the efficiency.
14
1.3 Overview of infrared detectors
1.3.1 Background
The historical track record of modern infrared detectors (or systems) is shown in
Figure 1-6. Modern development of infrared detector was possible after the discovery of
lead salt family (PbSe and PbS) [59]. Thereafter, further researches launched the
development of various detecting materials (or structures) including but not limited to: Ge
[60], InSb [61], Si [62], HgCdTe [63], InGaAs [64], quantum well infrared detector
(QWIP) [65], quantum dot infrared detector (QDIP) [66], barrier photodetector [67] and
type-II superlattice (T2SL) [68], as shown in Figure 1-6. Also, there are three generations
of IR detection systems that are generally considered in civil and defense applications. The
first generation is scanning systems with single and linear units. The second generation
includes focal plane array (FPA) technology with monolithic and hybrid detectors.
Combined with the read-out circuit in the FPA, a multiplexing function can be achieved.
The third generation has orders of magnitude more pixel elements than the second
generation FPAs. In addition, a multicolor function and other superior on-chip features are
possible in the third generation.
Figure 1-6: The development history of modern infrared detectors and systems.
15
As mentioned in Section 1.1, MWIR technology finds its application mainly in gas
sensing. Specifically, there are three thriving civil application areas of mid IR gas sensors:
environmental monitoring, industrial process control and medical diagnosis. Many
molecules and gases exhibit strong absorption characteristics in the mid IR band, as shown
in Figure 1-7 [69]. In addition, thanks to the much stronger absorption, gas sensing systems
based on MWIR and LWIR optoelectronics have an inherent advantage over NIR
counterparts in terms of sensitivity (or detection limit). For example, the detection limit for
CH4 at 3.26 m is 1.7 ppb compared to 600 ppb at 1.65 m. Another more contrasting
example is CO2. The detection limit for this greenhouse gas is 0.13 ppb at 4.23 m, while
it is 3000 ppb at 1.55 m. Despite the real advantages, MWIR and LWIR optoelectronics
had received considerably much less research attention than NIR optoelectronics. The main
reason for this difference is the revolution of communication systems with the advent of
optical fiber systems, which directly lead to the rapid development of NIR optoelectronics.
Nevertheless, the impressive accomplishments in MWIR and LWIR lasers such as
quantum cascade lasers (QCLs) [70-71] and interband cascade lasers (ICLs) [72-73] will
significantly promote the research and development of MWIR detectors.
16
10
HCOOH
CH3OH
T=300 K
C2H2
C2H4
H2O
CH4
CO2
NH3
NO2
H2S
P=1atm
CO
NO
O2
O3
Absorptance (Ln(I/Io))
1
0.1
0.01
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Wavelength (m)
Figure 1-7: Mid infrared absorption spectra of some molecules and gases. Data were
collected from [69].
1.3.2 Photon detection vs thermal detection
Most infrared detectors can be classified into two categories [9, 74-76]: photon
detectors and thermal detectors. Photon detection occurs when incident photons, absorbed
by the detecting material, excite free electron-hole pairs. In most instances, the material is
a bulk semiconductor or a low dimensional material such as those mentioned in Subsection
1.3.1 (refer to Figure 1-6). The electrical signal arises from the change of electron
distribution inside the detector. Thermal detection is defined as the mechanism that change
some measurable property of the detecting material due to the temperature increase of that
material resulting from the absorption of radiation, as illustrated in Figure 1-8 [76]. Among
the various thermal mechanisms, the most important three are the thermoelectric effect, the
resistive bolometric effect, the pyroelectric effect and its modification known as the
ferroelectric bolometer [9, 74-76]. Although many other mechanisms were proposed, only
these three have been shown to be practical to date. The electrical output in a resistive
bolometer (typically made of VOx) arises from the change of its electrical resistance as the
17
temperature rises. The pyroelectric effect is demonstrated with certain materials which
could generate electrical polarization that can be measured as an electrical charge on the
opposite face. The thermoelectric effect, i.e. Seeback effect, is the buildup of an electrical
potential across a temperature gradient; the resulting voltage is proportional to the
temperature difference between the hot and cold ends.
Figure 1-8: Block diagram of a thermal detector. Figure from [76].
In general, thermal detectors do not require cryogenic cooling, while the photon
detectors in MWIR and LWIR regions are cooled to suppress thermal generation of
carriers. The coolers are normally costly devices, making the detection system (e.g. an
infrared camera) more expensive than uncooled systems. Also, the coolers make the
systems bulky, and more steps are needed in manufacturing, therefore reducing the yields.
In addition, photon detectors are selective in wavelength, while thermal detectors have no
wavelength dependence. Nevertheless, cooled systems based on photon detectors are
incredibly more sensitive than uncooled thermal systems, as illustrated in Figure 1-9. As
can be seen, the image captured by a cooled infrared camera has a quality much better than
that created by an uncooled camera. In addition, the imaging speeds of cooled systems are
much higher than uncooled systems. The high-speed thermal imaging of cooled systems
18
allows capturing frame rates as high as 62000 fps.
Figure 1-9: Images created by uncooled and cooled infrared cameras. The figures are
from [77].
1.3.3 Examples of photon detectors
Photon detectors can be further subdivided into photoconductive (PC) and
photovoltaic detectors according to satisfaction or violation of symmetry in the
configuration. The simplest form of a symmetric PC photodetector consists of a slab of
semiconductor, as shown in Figure 1-10(a). By contrast, the structure of a PV photodetector
is asymmetric, in most cases, it is made of a p-n junction [See Figure 1-11]. Such an
asymmetric structure enables the separation of photo-generated carriers without applying
external bias. The resulting difference between PC and PV photodetectors is the operation
bias: PV detectors can operate at zero bias, while PC detectors require an external bias to
initiate the operation. In addition to the simplest semiconductor slab, a comparably more
complex PC photodetector structure is a QWIP [65, 78], as illustrated in Figure 1-10(b).
As can be seen, the basic elements of a QWIP are quantum wells (QWs) separated by wide
barriers. The incident light is absorbed via intersubband transitions of electrons within the
QWs. Once the electrons are optically excited into the continuous upper states, they will
be measured as a signal current. However, to collect these electrons, an external bias needs
19
to be applied and the signal current responds in an almost linear fashion to the applied bias.
Among various types of QWIPs, technology based on GaAs/AlGaAs multiple QWs is most
mature [65, 78]. QWIP detectors have relatively low quantum efficiencies, generally lower
than 10%, partially resulting from the selection rule of intersubband transitions in
conduction band [79].
Figure 1-10: Schematic diagram of (a) a photoconductive photodetector made of a

semiconductor slab, (b) a quantum well infrared photodetector based on bound-to-
continuum transitions.
The most common configuration for PV detectors is a single p-n junction as shown
in Figure 1-11. The optically excited electrons and holes are separated by the built-in
electric field in the depletion region and then contribute to the signal current. One route to
increase light absorption in a p-n junction is to sandwich a thick intrinsic layer between the
p- and n- doped layers, forming the so-called p-i-n structure. Some p-i-n detectors can use
avalanche multiplication but they must be reverse-biased [80].
20
Figure 1-11: Schematic diagram of a PV detector made of a single p-n junction
Another simple but refined PV detector technology is the barrier photodetector [67,
81]. Among various types of barrier photodetectors, the most popular one is nBn detector
as shown in Figure 1-12(a). Such a configuration is conducive to reducing majority-
electron dark current, while the signal current from minority holes is unaffected. The
barrier also takes a role to reduce the surface current, a benefit equivalent to self-
passivation. In addition, the absence of a depletion region eliminates the excess dark
current associated with the SRH process and trap-assistant tunneling. A special
modification of the nBn detector is the complementary barrier infrared detector (CBIRD)
[82] with an additional hole barrier introduced in the valance band, as shown in Figure 1-
12(b). The electron and hole barriers complement one another to impede the flow of dark
current. As with nBn detectors, the benefit of reduced dark current from elimination of a
depletion region also extends to CBIRD detectors.
Figure 1-12: Schematics of (a) an nBn barrier detector and (b) a complementary
barrier infrared detector; the biases are applied to improve carrier collection.
21
Apart from p-n junction and barrier structures, there is another more complex
photodetector operating in PV mode: the quantum cascade detector (QCD) [83-84], as
shown in Figure 1-13. As an intersubband detector, the QCD is a special variation from the
standard QWIP structure. The QCD is configured to operate in PV mode to reduce the dark
current present in a QWIP. However, despite this improvement, the dark current in QCDs
is still relatively high due to the short carrier lifetime (~ ps at 300 K) in intersubband
transitions. This fundamental problem severely undermines the ability to achieve a high
detectivity for QCDs especially at high temperatures, which will be discussed in detail in
Chapter 6. A brief summary of various photovoltaic photodetectors is presented in Table
1-3.
Figure 1-13: Schematic diagram of a quantum cascade detector.
22
Table 1-3: Summary of various photovoltaic photodetectors, classified by detecting
material.
Material or cutoff or peak Ri D*

T (K) R0A or Jd Ref
Structure (m) (A/W) (Jones)
Ge 1.55 300 10 A/cm2 0.1 N/A [60]
InGaAs 1.55 295 10 nA/cm2 0.62 1.0×1012 [85]
PbS 3.0 300 0.1 ·cm2 1.22 3.0×109 [86]
PbSe 4.0 300 6.5 ·cm2 1.6 1.0×109 [87]
InAs 3.4 295 8.1 ·cm2 0.54 1.2×1010 [88]
InSb 4.0 77 6.3E6 ·cm2 N/A 1.0×1011 [89]
InAsSb 4.0 300 0.19 ·cm2 0.76 2.6×109 [90]
HgCdTe 3.0 300 1.0 ·cm2 0.5 6.5×109 [91]
HgCdTe 5.0 300 0.01 ·cm2 1.0 2.0×109 [91]
HgCdTe 8.0 230 2E-4 ·cm2 0.8 4.0×108 [91]
HgCdTe 10.6 230 1E-4 ·cm2 0.4 2.0×108 [91]
InAs/GaSb SL 2.2 300 15 ·cm2 0.57 1.7×1010 [92]
InAs/GaSb SL 4.2 150 5.1E3 ·cm2 1.9 1.1×1012 [93]
InAs/GaSb SL 9.9 77 1.4E4 ·cm2 1.5 1.1×1011 [82]
InAs/InAsSb SL 10.0 77 119 ·cm2 4.47 2.8×1011 [94]
InAs/InAsSb SL 14.6 77 0.84 ·cm2 4.8 1.4×1010 [95]
QCD 5.4 300  ·cm2 7E-3 2.5×1010 [96]
QCD 8 300 0.028 ·cm2 1.7E-2 1.4×107 [97]
1.3.4 Performance metrics for infrared detectors
The most important performance coefficient for infrared detectors is the specific
detectivity D* that describes the smallest detectable signal. It equates to the reciprocal of
noise-equivalent power (NEP, in unit of W) that is normalized per square root of frequency
bandwidth and detector area. That is, the expression of D* is given by:
√∆𝑓𝐴
𝐷∗ = (1-5)
𝑁𝐸𝑃
23
where Δf is the bandwidth and A is the detector area. The unit of D* is cm·Hz1/2/W or more
frequently it is expressed as Jones. The noise equivalent power NEP is the incident flux
required to generate an output signal current/voltage equivalent to the noise
current/voltage. For most photon detectors, the noise current is used to define NEP:
NEP = 𝐼𝑛 /𝑅𝑖 (1-6)
where In is the noise current, and Ri is current responsivity that is equal to 1.24·QE/𝜆 (QE
is quantum efficiency). The noise sources in a photodetector include low-frequency noise,
Johnson noise, shot noise and generation-recombination (G-R) noise. In some instances,
the dominant noises are Johnson and shot noises. They occur as results of thermal
fluctuation during carrier motion (Johnson noise) and statistical fluctuation of thermal
generation of carriers (shot noise). Since the two noises are not coupled, the total mean
square noise current is the sum of both noise currents:
4𝑘𝑏 𝑇
𝑖𝑛2 = ∆𝑓 + 2𝑒𝐽𝐴∆𝑓 (1-7)
𝑅0
where R0 is zero-bias resistance and J is the dark current density. The first term in this
equation describes Johnson noise and the second term corresponds to shot noise.
Substituting Equations (1-6) and (1-7) into Equation (1-5), one can obtain the expression
of Johnson- and shot-noise limited detectivity:
𝑅𝑖
𝐷∗ = (1-8)
√4𝑘𝑏 𝑇⁄𝑅0 𝐴+2𝑒𝐽
From this equation, the D* can be improved either by reducing the noise or by increasing
the QE. The most effective way to maximize D* in conventional single-absorber detectors
is to increase the QE. In contrast, the D* can be effectively improved in multistage detectors
via noise reduction, as will be described in Chapter 2.
24
1.4 Dissertation organization
Chapter 2 concentrates on the fundamentals of the interband cascade (IC) device
family including IC lasers (ICLs), IC infrared photodetectors (ICIPs) and IC
thermophotovoltaic (ICTPV) cells. The main purpose of this chapter is to explain the
historic development, constituent materials, operation principles and basic theories of these
quantum engineered devices. It commences with the introduction of the 6.1 Å material
system: InAs, GaSb and AlSb and their unique properties. Subsequently, it presents the
attractive features of IC structures when functioning as lasers, PV cells and detectors.
Chapter 3 presents the theoretical comparison between single-absorber and
multistage ICTPV cells. The efficiency limits are calculated considering some practical
factors that apparently violate the assumptions made in the idealized thermodynamic
analysis in Subsection 1.2.4. This is in keeping with the relatively low efficiencies
demonstrated for current narrow bandgap TPV technologies. Several limiting factors are
identified, which turn out to be closely associated with short carrier lifetime, small
absorption coefficient and high dark saturation current density.
After the theoretical comparison, experimental details and comparisons between
single-absorber and multistage ICTPV cells are given in Chapter 4. A set of three TPV
cells with single-absorber and multistage architectures are characterized and analyzed in
detail. The experimental data confirmed the advantages of the multistage IC architecture
for TPV cells. It is shown that a multistage IC structure can be successful in resolving the
diffusion length limitation in single-absorber cells, and to achieve a collection efficiency
approaching 100% for photogenerated carriers.
Speculatively, the performance should be better for ICTPV cells with more stages,
25
as will be shown in Chapters 3 and 4. The initial goal of the fabricated four ICTPV devices
in Chapter 5 is to examine this speculation. However, the experimental study reaches the
opposite conclusion that significantly increasing the number of stages may penalize device
performance. Detailed device characterization and analysis are developed to explain this
contradiction, as well as to identify and quantify three factors: current mismatch, material
quality and collection efficiency.
Chapter 6 and 7 are mostly focused on the deep knowledge and strategies of IC
infrared photodetectors. Chapter 6 first describes an effective and simple approach to
extract carrier lifetime in the InAs/GaSb SLs. The developed method is applied to some
ICIP devices to extract the carrier lifetime at high temperatures. This chapter then
introduces a unified figure of merit for interband and intersubband devices, i.e. the
saturation current density J0. The significance of J0 on the performances of detectors and
PV cells is illustrated with measured D* and calculated Voc, respectively.
Chapter 7 first provides a comparative study of two sets of four ICIP devices with
current-matched and noncurrent-matched configurations. This study demonstrated the
necessity of current matching in ICIPs to maximize the utilization of absorbed photons for
an optimal responsivity. Following this study, the universally observed electrical gain in
noncurrent-matched ICIPs is explained with a unique mechanism. Furthermore, a theory is
developed to quantitatively describe the electrical gain, and the calculations agree well with
experimental data. Finally, Chapter 8 gives some prospective points for the future work
arising from these studies.
26
2 Chapter 2: Sb-based interband cascade devices
2.1 6.1 Å Semiconductor family
Interband cascade (IC) optoelectronic device is an umbrella term that refers to IC
lasers (ICLs) [72-73, 98], IC infrared photodetectors (ICIPs) [99] and ICTPV cells [100].
The materials that make up these devices are the 6.1 Å material system including InAs,
GaSb, AlSb and their related alloys. The crystal structures of the three compounds are all
zin blende. The main advantages of the three materials are small lattice constant mismatch
and similar growth windows. Specifically, the lattice constants are respectively 6.0584,
6.0959 and 6.1355 Å for InAs, GaSb and AlSb. Thus, these binary materials can be
incorperated together to the same heterostrucutre with low densities of defets and
dislocations. The bandgaps of them and the related alloys are between 0.41 eV (for InAs)
and 1.70 eV (for AlSb) as shwon in Figure 2-1(b). This bandgap range is of great interst
for the design of optoeelctronic devices in the SWIR and MWIR spectral regimes.
Figure 2-1: (a) Bandgap, lattice constant and (b) band alignment of the 6.1 Å
semiconductor materials.
The operations of IC devices are possible due to the unique properties of the 6.1 Å
materials. One of the key properties is the type-II broken-gap alignment between InAs and
27
GaSb. As shown in Figure 2-1(b), the conduction band edge of InAs is about 150 meV
lower than the valence band edge of GaSb. The benefits of this type of misaligned structure
are twofold. It enables smooth transition of electrons from valence band in GaSb layer to
conduction band in InAs layer without energy loss [101-102]. Also, due to this alignment,
the InAs/GaSb type-II SLs (T2SLs) have very flexible engineering capability [103-106]
and can cover a wide range of infrared spectra from SWIR to VLWIR. On the other hand,
the InAs/AlSb interface forms a type-II staggered alignment where the conduction band
edge of InAs is slightly above the valence band edge of AlSb. This staggered alignment,
tougher with the wide bandgap of AlSb, results in an extremely large conduction bandgap
offset of nearly 1.45 eV. This enables the realizations of very deep quantum wells and very
large tunneling barriers. Because of this feature, InAs/AlSb heterostructure has been
frequently used in resonant interband tunneling diodes (RITDs) [107-108] and short-
wavelength QCLs [109-110].
2.2 Interband cascade lasers-the historic origin
2.2.1 History and operation principle
Both ICIPs and ICTPV cells spring from ICLs, so for better understanding of their
evolutions and operations, first a brief review of ICL is given before moving on to ICIPs
and ICTPV cells. The concept of ICL was originally proposed in 1994 [98]. The main
innovation behind the concept is the capability to manipulate electron transport to form an
interband cascade scheme, whereby a single electron can generate multiple photons based
on interband transitions, as shown in Figure 2-2. Prior to the proposal of ICL, another
cascade laser, i.e. QCL, based on intersubband transitions was demonstrated in the same
28
year [70]. Both ICL and QCL consist of multiple cascade stages connected in series, and
each cascade stage ideally acts as an individual photon generator. However, unlike QCLs
in which the photons are generated via intersubband transition, ICLs use interband
transitions for active generation of photons. The injected carriers in ICLs relax to the lower
energy level at a rate much slower than in QCLs, so the threshold condition can be much
easier to establish in ICL. This is because the interband transitions in ICLs are characterized
by radiative, Auger and SRH processes, in which carrier lifetimes are on the order of
nanosecond. In contrast, the intersubband relaxation in QCLs is accompanied with
longitudinal phonon emission and has a picosecond time scale. The use of interband
transition in ICLs makes the threshold current and input power much lower than that in
QCLs. Even compared with other types of mid IR lasers such as Sb-based type-I QW diode
lasers [18-19] and II-VI lead salt lasers [20-21], the threshold current and input power of
ICLs are considerably lower. This makes them the preferred option for applications where
low power consumption is strongly prioritized.
Figure 2-2: Illustration of the photon emission and cascading effect in an interband
cascade laser. Figure from [115].
Compared to the conventional diode lasers, the cascade design requires a higher
voltage to reach threshold. This is because each cascade stage needs to consume a voltage
29
to invert the population. Nevertheless, the current required to trigger the lasing action is
significantly reduced, as multiple photons are generated for each injected electron. This
tradeoff between voltage and current is in favor of reducing Ohmic losses from the series
resistance, especially for high-power semiconductor lasers operating with high currents. In
this regard, IC structures can be beneficial to improving the overall power efficiency by
lowering the operating current.
The active core of an ICL is schematically shown in Figure 2-3. In each stage of an
ICL, the active region is sandwiched between the electron and hole injectors. The active
region, the electron injector and the hole injector are typically made of GaInSb-InAs “W”
QW, multiple InAs/AlSb QWs and multiple GaSb/AlSb QWs, respectively. Under a
forward bias, the electrons are injected from the injector into the conduction band of the
active region. The injected electrons are confined in the active region by the AlSb barriers
and transit to the valence band via photon emission. The transited electrons subsequently
enter the electron injector in the next stage via interband tunneling through the broken gap
between InAs and GaSb. This process is orders of magnitude faster than the interband
transition (~1 ns) in the active region. Therefore, the electrons relaxed to valence band in
the active region are efficiently swept out and population inversion can be readily achieved.
30
Figure 2-3: Band diagram of the active core for an interband cascade laser. Figure
from [73].
2.2.2 Current status of ICL performance
Since its first demonstration, the performance/capability of ICL has been
transformed a lot. In CW operation, ICLs can cover a broad range of wavelengths
extending from 2.8 m to 6.0 m at room temperature (RT) or above [116-120]. Further
preparation for high temperature operation with a longer wavelength is in progress [115,
121-124]. Typically, the epitaxy growth of ICL is done on either a GaSb [72-73, 116-118,
125-126] or InAs [115, 119-124] substrate. As wavelength increases, the InAs/AlSb SL
cladding layers in GaSb-based ICLs need to be thick, in order to provide strong optical
confinement. This is problematic for heat dissipation, as InAs/AlSb SLs have very low
thermal conductivity (~2.7 W/m·K). Also, thick InAs/AlSb SLs are challenging in MBE
growth due to many shutter movements. These issues can be readily resolved in InAs-based
ICLs wherein the SL cladding layers are replaced with highly doped InAs layers [115, 119-
124]. Besides, this approach offers another benefit: the low refractive index for highly
31
doped InAs layers increases the optical confinement. Figure 2-4 shows the room
temperature threshold current densities for both InAs- and GaSb-based ICLs in the
wavelength range of 2.7-7.2 m. Most of the data are collected in pulsed modes at 300 K.
As can be seen, the technology maturity for GaSb-based ICLs is well demonstrated in the
3-4 wavelength region. By comparison, InAs-based ICLs aim to cover wavelengths longer
than 4 m. In the 4-5 m wavelength region, the two types of ICLs have comparable
performances. However, as the wavelength goes beyond 6 m, InAs-based ICLs
outperform GaSb-based ICLs in terms of threshold current density.
Figure 2-4: Room temperature threshold current density for both InAs- and GaSb-
based broad-area ICLs. Figure is from [124].
2.3 Interband cascade thermophotovoltaic devices
2.3.1 InAs/GaSb type-II superlattices
The ideal of InAs/GaSb T2SLs was first introduced in 1977 [127]. Ten years later,
it was proposed for detector application [68]. Since then, it has been recognized as a
promising material for mid IR detectors due to the predicted reduction of Auger
recombination rates [128-130]. Measurements of the Auger recombination coefficient by
32
pump-probe transmission likewise showed suppressed Auger rates compared to bulk
materials [131]. Factors considered to contribute to this suppression include strain induced
splitting in valence band, quantum confinement and off-resonance positions of the spin-
orbit split-off band. On the other hand, as shown in Figure 2-5(a), the electrons and holes
are confined separately in InAs and GaSb layers, which reduces the light absorption. The
bandgap of InAs/GaSb SLs is the difference between the minibands for electrons and holes.
The miniband for holes is very narrow since the effective mass of holes is large. Moreover,
the energy level of hole is almost quasi-constant with GaSb well thickness. Hence, the
bandgap of InAs/GaSb SLs is mainly controlled by conduction band level, via the change
of InAs and GaSb layer thicknesses.
1.2 2.0 (b) Al70In30Sb

(a)
1.0
1.5
0.8
Energy (eV)
Energy (eV)
0.6 Eg 1.0
0.4 Eg
0.5
0.2
0.0 0.0
InAs GaSb InAs GaSb
0 5 10 15 20 25 30 0 5 10 15 20 25 30
Distance (nm) Distance (nm)
Figure 2-5: Band structure, minibands and wavefunctions of electrons and holes for
(a) InAs/GaSb superlattice and (b) M-shape Al(In)Sb/GaSb/InAs/GaSb/Al(In)Sb SL.
When the bandgap is wide, the binary InAs/GaSb SL is not the preferred option.
This is because a wide bandgap necessitates thin InAs layers, which can make the bandgap
very sensitive to layer variations during growth. Also, it can cause interface
mixing/roughness, as lower material and interface quality were reported in literature [132-
133]. A solution to these issues is inserting thin Al(In)Sb layer in the middle of GaSb layers,
forming the so-called M structure [104, 134-135]. The letter “M” stands for the shape of
33
the band alignment of the Al(In)Sb/GaSb/InAs/GaSb/Al(In)Sb layers, as shown in Figure
2-5(b). There are several potential advantages of the M-shape SL. First, the AlSb blocking
barrier can reduce the dark current and improve the R0A product of devices made from this
structure [104]. Second, the AlSb layer can compensate the tensile strain induced by InAs
layers. Third, it reduces the wavefunction penetration into barrier layers, thereby narrowing
the minibands and allowing a sharp increase of absorption coefficient near bandgap. In
addition to M-shape SL, there are other modifications of the normal InAs/GaSb SL,
namely, the W- [105] and N-shape SLs [106]. These various modifications manifest the
flexible heterostructure design of T2SLs based on InAs/GaSb/AlSb material system.
2.3.2 Operation principle of ICTPV cells
The photovoltaic operation of IC structures was first demonstrated with devices
that were fabricated from ICL wafers [136]. The light absorption region was simply
composed of a single pair of coupled quantum wells; small absorption was revealed by the
measured low responsivity of the fabricated PV detectors. To address this problem, it is
necessary to make some modifications to the structure. One prominent alteration is
replacing the quantum well absorber with much thicker InAs/GaSb T2SLs [99-100]. This
structural change was shown to be very effective to improve light absorption characteristics
and overall device performance [99]. Further refinement of the structure was made on the
hole injection region: additional QWs are added to better block intraband tunneling of
electrons, thus reducing the dark current density [137].
Overall, the structure of an ICTPV cell is roughly similar with that of an ICL. Each
stage of an ICTPV cell consists of an electron barrier (eB), a hole barrier (hB), and a T2SL
absorber sandwiched between the two barriers, as shown in Figure 2-6. The electron and
34
hole barriers correspond to the hole and electron injectors in an ICL structure, respectively.
They are assigned different names in ICLs and ICTPV cells to distinguish between their
functions in the two structures. In ICTPV cells, the unipolar barrier plays a function as
blocking the namesake carrier while allowing smooth transport of the otherwise carrier, as
shown in Figure 2-6. The unipolar barriers work as intended because of the proper energy
alignment at the interfaces. For example, the first electron miniband energy level of the
T2SLs lies within the bandgap of GaSb layer in the electron barrier, therefore the photo-
generated electrons can only move to the hole barrier. This provides a novel way for
constructing PV devices with perfect current rectification without appealing to p-n
junctions.
The basic operation principle of an ICTPV cell is illustrated in Figure 2-6(a). If the
concept of hole is disregarded, the electron and hole barriers serve as the tunneling and
relaxation regions for electrons, respectively. As shown, electrons optically excited in the
absorber first travel to the hole barrier by diffusion. Following the diffusion process, the
electrons then relax to the bottom state in the digitally grated QWs of the hole barrier. The
transition in this energy ladder times on the order of picosecond, much faster than the
interband excitation in the absorber region. As such, the photo-generated electrons can be
transferred to the bottom of the energy ladder with very high efficiency. This mechanism
allows efficient and quick removal of electrons in the absorber region. Finally, the electrons
return to the valence band state in the adjacent absorber through interband tunneling
facilitated by the broken gap alignment between InAs and GaSb.
35
Figure 2-6: (a) Schematic band diagram of an ICTPV cell, (b) Schematic showing the
operation of an ICTPV cell.
2.3.3 Enhancement of open-circuit voltage in ICTPV cells
The advantage of IC structure for light emission is apparent: one electron can be
reused to generate multiple photons. In the reversing situation as in light-to-electron
converting devices, generation of a single electron requires multiple photons. Given this
situation, the achievable maximum quantum efficiency (or photocurrent) for ICTPV cells
is reduced by a factor of 1/Nc, where Nc is number of stages. This seems to make it
counterintuitive to explore this type of TPV cells. To resolve this problem, one needs to
really understand the benefits provided by multistage design. One of the key benefits is
enhanced collection efficiency of photo-generated carriers. This benefit will be described
in detail in next subsection, both physically and mathematically. Another important benefit
36
is the enhanced open-circuit voltage Voc, as it is equal to the sum of the photovoltages
created in every stage. As shown in Figure 2-6(b), the unipolar barriers repeat their roles
to separate photo-generated electrons and holes in all stages. This yields an effective
photovoltage in each individual stage. The recycling of electron across the device make
them add up to the total open-circuit voltage of the device. This behavior is analogous to
that seen in extensive study of multijunction solar cells [13-14]. As will be shown in
Chapter 3, at high incident power densities, the Voc of an ICTPV cell approximately scales
with the number of stages.
Because of enhanced Voc, the conversion efficiency of ICTPV cells can be higher
than conversional single-absorber cells even though the photocurrent is lower, which will
be shown in Chapter 3 and 4 in both theory and practice. From another perspective, like
ICLs, the reduction of photocurrent can be beneficial for mitigating the Ohmic power loss
in series resistances. In practice, TPV cells may experience significant Ohmic loss in cases
such as power delivery in free space [138-139] and near-filed TPVs [15-17]. In these
instances, the TPV cell often encounter an intensive illumination condition and generate a
high photocurrent, consequently suffering a heavy Ohmic loss.
2.3.4 Improvement of carrier collection efficiency in IC structures
The QE of a TPV cell depends on both the absorption of incident photons and the
collection of photo-generated carriers. The carrier collection probability fc (x) can be found
using Green’s function solution to the diffusion equation, as described in [140-141]. Its
expression at distance x from the collection point (x=0) is given by:
cosh[(𝑑−𝑥)/𝐿]
𝑓𝑐 (𝑥) = (2-1)
cosh(𝑑/𝐿)
37
where d is the absorber thickness and L is the diffusion length. Here, the light is assumed
to be incident from the collection point and travels through the absorber in a direction
opposite to the flow of minority carriers. In the other case where light is incident opposite
the collection point, most electrons are generated far from the collection point, therefore
the QE is likely reduced [142]. In the subsequent discussion, only the regular illumination
pattern will be treated. The calculated fc (x) based on Equation 2-1 in a 3.3 m absorber
for various diffusion lengths is plotted in Figure 2-7. As shown, the fc (x) is a strong
function of diffusion length. Also, it decreases dramatically with x if the diffusion length
is shorter than the absorber thickness. For example, given L=1 m, fc (x) is even lower than
0.4 when x is longer than L. Evidently, for a single-absorber device, increasing the absorber
thickness enhances the absorption, but may fail to improve QE, especially when the
diffusion length is short.
1.0
L=5 m
0.8 L=4 m
Collection probability
L=3 m
0.6
L=2 m
0.4 L=1 m
0.2
0.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Position (m)
Figure 2-7: Collection probability of carriers as a function of the distance from the
collection point. The absorber thickness is 3.3 m. The number near the curve
indicates the diffusion length.
The mechanism that affects collection probability also affect QE. Considering
carrier collection probability, the QE of a single-absorber device is given by:
38
𝑑
𝑄𝐸 = −1 𝑞 ∫0 𝑓𝑐 (𝑥)𝑔𝑝ℎ (𝑥)𝑑𝑥 (2-2)
where  is the incident photon flux density per unit area, and gph (x) is the photon
generation rate per unit volume. Here, the top surface reflection is left aside, which is
practically possible by adding a front anti-reflection layer. Note that Equation 2-2 can be
used to calculate the effective QE in each stage of a multistage IC device as well. The gph
(x) in Equation 2-2 exponentially deceases with position following the rule:
𝑔𝑝ℎ (𝑥) = 𝛼𝑒 −𝛼𝑥 (2-3)
where  is absorption coefficient. When applied to multistage IC device, Equation 2-3
needs to be modified to reconcile the light absorption in the optically upper stages. Based
on Equations 2-2 and 2-3, the QE of a single-absorber TPV device is given as:
𝛼𝐿 𝛼𝐿𝑒 −𝛼𝑑
𝑄𝐸 = 1−(𝛼𝐿)2 × [tanh(𝑑 ⁄𝐿) + cosh(𝑑⁄𝐿) − 𝛼𝐿] (2-4)
Likewise, the effective QE in the Nth stage of a multistage IC device is given by:
𝑁−1 𝛼𝐿 𝛼𝐿𝑒 −𝛼𝑑𝑁

𝑄𝐸𝑁 = 𝑒 −𝛼 ∑𝑚=1 𝑑𝑚 1−(𝛼𝐿)2 × [tanh(𝑑𝑁 ⁄𝐿) + cosh(𝑑 − 𝛼𝐿] (2-5)
𝑁 ⁄𝐿 )
𝑁−1
where dm is the absorber thickness in the mth stage, and the term “𝑒 −𝛼 ∑𝑚=1 𝑑𝑚 ” represents
light absorption in all the upper stages.
Based on the above equations, a numerical example is provided to illustrate the
improvement of carrier collection in multistage architecture, as shown in Figure 2-8. It
presents the calculated fc (x)·gph (x) in single-absorber and four-stage IC devices for
L=0.4. The total absorber thicknesses (d) for both structures were set to be the absorption
depth. Therefore, if no absorption occurs in the barrier regions (indicated by thick grey
lines in Figure 2-8), the total absorption in the absorbers is equal in the two cases. The four-
stage IC device has identical absorber thickness in each stage, meaning that the individual
39
absorber thickness is equal to d/4. According to Equation 2-2, the QEs of the two cells are
marked by the shaded regions in Figure 2-8. As can be seen, the total effective QE of the
four-stage IC device is appreciably higher than the single-absorber device. This result can
be considered the equivalent of much higher total collection efficiency (c) in the four-
stage IC device. Here, the c is defined as the ratio of the total effective QE in any of the
stages to the total absorption of incident photons (1-e-d). The calculated c for the single-
absorber cell is only 46% due to the low collection probability at positions far from the
collection point. At the right edge of the absorber, the carrier generated over there has a
collection probability of only 16%. In contrast, since the absorbers are made thin, the
collection probability is much higher in the four-stage IC device. For example, the
collection probability is enhanced to 83% at the right edge of each individual absorber.
This enables it to achieve a total c as high as 89%.
1.0
Barriers
0.8
g
ph (x)
f
g (x)f (x) (a.u.)
(x) g gph (x)

0.6 (x)
f
ph
(x)
gp (x
h )f
0.4 (x)
gp (x
g ( h )f (x)
ph x
)f
0.2 (x)
0.0
d/4 d/4 d/4 d/4
Figure 2-8: Comparison of collection process in single- and four-stage IC devices for
a low L product (L=0.4). The thickness d of the single-stage device equates the
absorption depth. The individual absorber thickness of four-stage IC device is d/4.
It should be commented that the above analysis ignored a couple of unfavorable
factors that may affect collection efficiency. For example, TPV cells generally operate at
40
forward bias for performing power output. The applied external field may impede the
collection of photo-generated carriers. To calculate c with accounting the external bias,
it’s going to be more complex and challenging whatever method one chooses. The
experimental investigation of this subject is presented in Chapter 4, while the theoretical
aspect will continuous to be one of future research focuses. Another neglected factor is the
recombination at the absorber-electron barrier interface, characterized by surface
recombination velocity. The complete calculation with consideration of interface
recombination is described in [141].
2.4 Interband cascade infrared photodetectors
2.4.1 Operation principle of ICIPs
The configuration and operation principle of an ICIP are quite analogous to those
of an ICTPV cell. In fact, there is no essential difference between them except operating
bias voltage and light intensity encountered by them. As shown in Figure 2-9, like an
ICTPV cell, each stage of an ICIP consist of an electron barrier, a hole barrier and a T2SL
SL absorber. The constituent layers of the three components in each stage are same in the
two different types of devices. Also, electrons almost undergo the same transport path in
them. The only notable difference is the operating voltage as illustrated in Figure 2-6 and
2-9. To better differentiate them from an ICL, the detailed band profile of one stage of an
ICIP is shown in Figure 2-9(b), which differs markedly in the absorber region from an ICL.
41
Hole Barrier Electron Barrier
2.5
(b)
2.0
Energy (eV)
1.5
Absorber Absorber
1.0
 Tuneling

0.5
Relaxing
0.0
0 20 40 60 80 100 120 140
Distance (nm)
Figure 2-9: (a) schematic diagram of a multistage ICIP and (b) the band profile of
one stage under zero bias. The olive and purples lines in the absorber represent the
electron and hole minibands. The dotted olive wavefunction indicates the electron
states in hole barrier while the dotted purple wavefunction represents the hole states
in electron barrier.
Compared to ICTPV cells, ICIPs have relatively looser design requirement. For
example, the individual absorber thickness in an ICTPV cell is better adjusted to keep
current match between stages, as done elsewhere in multijunction tandem solar cells [13-
14], otherwise the photocurrent will be largely reduced. However, such a requirement does
not need to be fulfilled for ICIPs due to significant electrical gain, as will be descried in
Chapter 7. Besides, ICIPs can operate at zero bias, so the device design is not concerned
with the effect of external bias.
42
2.4.2 Noise reduction in ICIPs
As with an ICTPV cell, an ICIP also benefits from the high collection efficiency,
but suffers from the relatively low achievable maximum QE. The other profit offered by
multistage architecture in detectors is the reduced noise level. As shown in Figure 2-9(a),
a single electron must undergo Nc interband excitations in an ICIP to travel across the
contacts. This fact means that the noise is naturally reduced in ICIPs due to the averaging
process. A similar example is quantum well infrared detector (QWIP) [65, 78]. The noise
in these intersubband detectors is reduced by a factor of 1/Nw (number of quantum wells),
provided that the emission and capture of electrons are uncorrelated in each QW. Another
easy-to-understand example is the reduction of random error by increasing the sample size
and averaging over all the samples.
There are various sources of noise that can affect a photodetector’s detectivity. The
dominant noise changes with the environment and the temperature of the detector. For
example, when the signal is strong or the detector temperature is low, the dominant noise
is from either the fluctuation of signal current or the fluctuation of current induced by
background radiation. Conversely, when the signal is weak or the detector temperature is
high, the detectivity is generally regulated by shot or Johnson noise. In realistic
applications, the operation of detector is neither shot- nor Johnson-noise limited, since the
performance is poor and does not satisfy application requirement. However, for most
LWIR detectors such as MCT and T2SL detectors, the detectivity in this regime represents
an ultimate limit for the detector operating at room temperature [130]. The focus here will
only involve this situation. In addition, as mentioned before, the unipolar barriers allow
ICIPs to operate in unbiased mode. This means that shot noise can be neglected in an ICIP,
43
and the detectivity will be exclusively limited by Johnson noise. The mean square Johnson
noise current is inversely proportional to zero-bias resistance R0, as seen from Equation 1-
7. Hence, in order to proceed, the expressions of dark current and R0 needs to be derived
first.
Analogous to QE, the dark collection current (which has the same direction with
photocurrent) in the mth stage in an ICIP can be calculated as:

𝑑
𝐽0𝑚 = 𝑞 ∫0 𝑓𝑐 (𝑥)𝑔𝑡ℎ 𝑑𝑥 = 𝑞𝑔𝑡ℎ 𝐿tanh(𝑑𝑚 /𝐿) (2-6)
where gth is thermal generation rate per unit volume. Unlike the optical generation, the
thermal generation can be uniform across the device if the bandgaps of absorbers are made
equal in each stage.
In addition, there is another contribution of dark current: the injection current. It
has opposite direction with photocurrent and has a magnitude of 𝑒 𝑉𝑚 ⁄𝑘𝑏𝑇 𝐽0𝑚 (Vm is the
voltage that falls across the mth stage). Collectively, considering the two current
components, the total dark current of an ICIP can be written as:
𝑐𝑁
𝐽𝑑 (𝑉) = 𝑞𝑔𝑡ℎ 𝐿 ∑𝑚=1 tanh(𝑑𝑚 /𝐿)[𝑒𝑥𝑝(𝑞𝑉𝑚 ⁄𝑘𝑏 𝑇) − 1] (2-7)
Based on Equation 2-7, the R0A of an ICIP can be extracted and expressed as:
𝑘𝑏 𝑇 1
𝑅0 𝐴 = ∑𝑁𝑐
𝑚=1 (2-8)
𝑞2 𝑔𝑡ℎ 𝐿 tanh(𝑑𝑚 ⁄𝐿)
For an ICIP with identical stages, the expression of R0A of can be simplified to:
𝑘𝑏 𝑇 𝑁𝑐
𝑅0 𝐴 = 2
(2-9)
𝑞 𝑔𝑡ℎ 𝐿 tanh(𝑑𝑚 ⁄𝐿)
Evidently, from Equation 2-8 and 2-9, the R0A is larger for detectors with more stages and
thinner absorbers. In other words, according to Equation 1-7, the Johnson noise is
effectively reduced in ICIPs compared to single-absorber detectors.
44
2.4.3 Detectivity improvement in ICIPs
In principle, the device QE of an identical-stage ICIP is decided by the stage with
minimum effective QE. This will be the last stage due to most significant light attenuation.
However, to maintain current continuity, there is additional injection current induced to
offset the higher photocurrent in other stages. This undermines some of the benefits
provided by multistage architecture. Another design option to eliminate this downside is to
make current-matched absorbers. In this revised design, the individual absorber thicknesses
are increased from first stage to last stage to achieve equal photocurrent in each stage. In
practice, perfect current match is hard to accomplish unless the diffusion length and
absorption coefficient are accurately grasped. Nevertheless, even with inexact match in
photocurrent, the device QE in principle can still be improved. Here, only current-matched
ICIPs will be considered while ICIPs with identical absorbers will be detailed in Chapter
7.
The detectivity enhancement in ICIPs has been covered in [141], a brief review of
the calculation results is provided here. Substituting Equation 2-8 into Equation 1-8, one
can obtained the expression of Johnson-noise limited detectivity for an ICIP:
√ 𝑁𝑐
∗ λ 𝑄𝐸 ∑𝑚=11⁄𝑡𝑎𝑛ℎ(𝑑𝑚 ⁄𝐿)
𝐷 = (2-11)
ℎ𝑐 √4𝑔𝑡ℎ 𝐿
The current match condition in the ICIP is first obtained using an iterative process by
varying the thickness of each stage so that the contribution of QE is equal. The absorber
thicknesses are then determined by selecting the optimal photocurrent-matched absorber
sequence that maximizes detectivity. In this way, the calculated detectivity enhancement
as a function of L for ICIPs with two, eleven and thirty stages are shown in Figure 2-10
45
[141]. The detectivity enhancement is defined as the D* (Nc) of the optimized multistage
ICIP normalized to the value D* (1) of the optimized single-absorber detector. As can be
seen, the detectivity enhancement is pronounced when L1 for different designs. Also,
the detectivity is raised as the number of stages increases since the noise is further
suppressed, although the signal current is slightly reduced. At larger L, multistage ICIPs
do not make obvious advantage, but there is still a small advantage can be gained. For
example, for optimized ICIPs with many stages, the upper limit improvement is about 1.1
times higher than single-absorber detectors [141]. This conclusion can be derived from
Figure 2-10 where the platform value of detectivity enhancement is slightly higher than
unity at large L.
Figure 2-10: Johnson-noise limited detectivity enhancement for current-matched

ICIPs with two, eleven and thirty stages. Figure is from [141].
2.4.4 Comments on detectivity improvement in ICIP
The above calculations clearly quantify the possible detectivity enhancement when
L1 for current-matched ICIPs. In realistic, for InAs/GaSb T2SLs, the absorption
coefficient near bandgap is about 3000 and 2000 cm-1 in MWIR [143-145] and LWIR [145-
46
147] regimes, respectively. The diffusion length is shorter than 1.5 m at RT, as estimated
from the temperature or bias dependence of responsivity for the detectors made of
InAs/GaSb T2SLs [149-151]. Taken together, the product L can be smaller than unity at
high temperatures ( 200 K), especially for LWIR T2SL detectors. Hence, the prospect of
detectivity enhancement in ICIPs is real at high temperatures. At lower temperatures, the
diffusion length is appreciably increased as carrier lifetime is extended. For example, the
diffusion length can be far longer than 6 m at 77 K, as evaluated in [152]. The increased
diffusion length is very likely to make L larger than unity, therefore it will be bootless to
use ICIP structure at low temperatures. However, in applications where the response speed
is prioritized over sensitivity, ICIP is still the better option. For single-absorber detectors,
high response speed requires a thin absorber, which compromises light absorption and thus
sacrifices the detectivity. However, for ICIPs, they have been demonstrated with high
frequency operation (higher than 1.3 GHz) as well as decent detectivity [153-154].
2.5 Growth and fabrication of interband cascade devices
The IC devices are relatively complex structures; some devices even have
thousands of layers. This complexity rules out the possible growth by conventional growth
techniques as well as some epitaxy growth techniques such as chemical vapor deposition
(CVD), physical vapor deposition (PVD) and liquid phase epitaxy (LPE). The only reliable
and feasible growth method is molecular beam epitaxy (MBE) [75-76]. Up to present,
almost without exception the reported IC devices were grown by MBE systems. Compared
to other epitaxy growth techniques, MBE is better able to grow sophisticated structures
with high degree of success. This is due to its nature of utilizing atomic layer-by-layer
47
growth, which is accomplished through a good monitor of molecular or atomic beams onto
a heated substrate in ultrahigh environments. In this dissertation, all the devices involved
were grown by the two MBE systems in the University of Oklahoma as shown in Figure
2-11. The first one is an Intevac Gen II that has been operational since 1994. The system
is equipped with two Sb and As crackers, three In, Ga and Al effusion cells, as well as two
Si and Be doping cells. The second one is a new Veeco Genxplor MBE system launched
in 2015, which has many new and improved features. For example, all the group-III cells
are comprised of dual-filament heaters to generate more stable flux. This new MBE system
has ten cells including two In and two Ga cracked cells, two Al Sumo cells, one cracked
As cell, one cracked Sb cell and three Si, Te and Be doping cells.
Figure 2-11: (a) Intevac GEN II MBE system (1993) and (b) Veeco GENxplor MBE
system (2013).
Manufacture of IC devices involves various fabrication processes. The general
processing flow of IC devices (e.g. ICTPVs and ICIPs) include: (1) standard cleaning, (2)
mesa etching, (3) insulating layer deposition, (4) contact opening, (5) top contact
deposition, (6) lapping, (7) bottom contact deposition, and (8) mounting and wire bonding.
Specifically, after cleaning and standard contact photolithography, wet chemical etching is
used to define a mesa structure by etching deep down below the active region. Then, a ~
48
200 nm thick silicon nitride followed by ~ 200 nm silicon dioxide is sputter deposited as
an insulating layer. This step is followed by reactive ion etching (RIE) to open a window
on top of mesa. This window is opened to deposit 30/300 nm of Ti/Au layer by sputtering
technique as top metal contact. The schematic of a typical fabricated 3-stage ICTPV device
is shown in Figure 2-12(a). The cross-sectional scanning electron microscope image of the
3-stage ICTPV device is presented in Figure 2-11(b) [157].
InAs
InAs/GaSb SL
InAs/Al(In)Sb
InAs/GaSb SL
InAs/Al(In)Sb
Figure 2-12: (a) The schematic of a processed ICTPV or ICIP device and (b) Cross-
section scanning electron microscope image of a wet-etch ICTPV structure, the
Figure is from [157].
49
3 Chapter 3: Limiting factors and efficiencies of narrow bandgap
thermophotovoltaic cells
3.1 Background and motivation
In Chapter 1, the efficiency limits of TPV cells were calculated based on detailed
balance theory, which however tends to be overestimated due to some unrealistic
expectations. There are many theoretical works attempting to predict the efficiency limit
of TPV cells. For example, in [49, 51], a prospective efficiency exceeding 30% was pointed
out when the heat source is at 1000-2000 K, even without spectral control. For solar TPV,
even a maximum efficiency of 85% was projected with full concentration of incident
sunlight [55]. Realization of this extremely high efficiency requires that the incident light
spectrum is perfectly tailored to the cell absorption spectrum and non-absorbed is recycled
back to the heat source. At current stage, the highest reported TPV cell efficiencies at 300
K are 24% for a 0.6 eV InGaAs diode on InP [37] and 19.7% for a 0.53 eV GaInAsSb
diode on GaSb [39], which were measured using a 950 °C broadband radiator with spectral
control filters mounted on the front surface of the TPV cells. As for narrow bandgap TPV
cells (Eg 0.4 eV), the demonstrated efficiencies at 300 K are far below 10% (See table
1.2). Evidently, there is a large gap between the efficiencies of existing TPV cells and
theoretical predictions, and little work has been dedicated to narrow bandgap TPV cells to
clarify their efficiency limits. It is therefore necessary to have ongoing work to bridge the
efficiency gap and to determine the practical efficiency limits as well.
Most of previous theoretical works assumed very ideal behaviors of carrier
recombination and collection. Specifically, they assumed purely radiative recombination
and an infinite diffusion length. However, in real devices, non-radiative recombination is
often involved and even prevails, and carrier collection can be limited by a short diffusion
50
length. In this chapter, practical factors such a finite diffusion length (L) and absorption
coefficient () are considered and their effects on conversion efficiency () are inspected.
As examples, calculations are carried out for narrow bandgap InAs/GaSb T2SLs and
quaternary GaInAsSb materials in several different scenarios under monochromatic light
illumination. This narrow bandwidth light illumination can be accomplished through the
use of spectral filters or selective emitters that can be made based on nanostructured
materials and metamaterials [31-33]. The calculations start from single-absorber TPV cells
and then are performed for multistage IC architecture to show how it can be used to
improve the performance of narrow bandgap TPV cells.
3.2 Practical limitations on single-absorber TPV devices
3.2.1 Quantum efficiency and dark saturation current density
The conversion efficiency of a TPV device is intimately related to its output current
and voltage. These two quantities are characterized by quantum efficiency QE and voltage
efficiency V (defined as the ratio of open-circuit voltage eVoc to the bandgap). Both QE
and Voc are largely ruled by dark saturation current density J0, as well as minority carrier
transport and lifetime . Therefore, QE and Voc will be severely limited if the carrier
lifetime and diffusion length are short and the J0 is significant. As an example of such
limitation, InAs/GaSb SL absorber with a bandgap of 0.29 eV will be first used for
illustration purpose. At 300 K, the diffusion length and carrier lifetime are estimated to be
1.5 m and 20 ns based on the experimental results of type-II InAs/GaSb infrared detectors
[149-151, 158]. The conversion efficiency of a TPV device under monochromatic
illumination is given by:
51
𝑞𝑉𝑜𝑐
𝜂 = 𝐹𝐹 ⋅ 𝑄𝐸 ⋅ (3-1)
ℎ𝜐
where FF is the fill factor and  is the frequency of incident photons. Hence, FF, QE and
Voc are the three main performance metrics that controls the desired conversion efficiency.
Below, their respective behaviors are studied in narrow bandgap TPV devices. The
frequency of incident photons also plays a role in affecting conversion efficiency, but is
less significant than the above-mentioned three quantities, which will be described in
Subsection 3.4.
The expression of QE for a single-absorber TPV device is given by Equation 2-4.
Here the light is assumed to travel through the absorber in a direction opposite to the flow
of minority carriers. Based on this equation, the calculated QE as a function of normalized
absorber thickness (d/L) for different values of L is shown in Figure 3-1. As can be seen,
the QE peaks a at a certain value of d/L and falls off with further increasing the absorber
thickness, irrespective of the value of L. This common tendency of QE was identified due
to the reduction of collection efficiency as the absorber thickness increases [159].
Particularly, for L=0.45, the maximum QE is only 32%, which would significantly limit
the conversion efficiency as will be shown later.
52
0.30 90
0.28 80
0.26 L=4.5
Open-circuit votlage (V)
Quantum efficiency (%)

70
0.24 solid: Voc
60
0.22 dashed: QE
50
0.20 L=1.5
40
0.18
0.16 30
0.14 L=0.45 20
0.12 10
0.10 0
0.01 0.1 1 10
Normalzied absorber thickness (d/L)
Figure 3-1: Calculated open-circuit voltage (solid) and quantum efficiency (dashed)
as a function of normalized absorber thickness for different values of L. The incident
power density is assumed to be 50 W/cm2.
The dark saturation current density is the pre-factor in standard diode equation and
measures the recombination loss in PV devices. Normally, the open-circuit voltage is a
logarithmic function of the ratio between photocurrent density and J0. In solar cells, the
thermal current density is sometimes ignored because it is low when the bandgap is
relatively wide. In contrast, J0 is orders of magnitude higher in TPV devices and therefore
cannot be neglected. The value of J0 can be calculated based on Equation 2-6 for the simple
single-stage case. The thermal generation rate gth in this equation for p-type doped
absorbers can be written as: gth=n0/, where n0 is the electron concentration at thermal
equilibrium. By replacing n0 with ni2/p0, thermal generation rate can be further written as:
ni2/Na, where ni and Na are the intrinsic carrier concentration and doping concentration,
respectively. Hence, a short carrier lifetime (e.g. 20 ns) will manifest itself as a high J0,
thus severely limiting the open-circuit voltage. An increase of carrier lifetime will naturally
reconcile this issue and enhance QE as well since the diffusion length is increased with
raised carrier lifetime. For example, if carrier lifetime is extended to 200 ns, on a
53
conservative estimate, the diffusion length will be increased is 5 m, assuming the electron
mobility (43 cm2·V-1·s-1) remains the same. In this scenario, the J0 will be an order of
magnitude lower and the QE will be appreciably improved.
Nevertheless, the J0 is still much higher than the radiative limit set by the detailed
balance theory [58]. In this fundamental limit, the dark saturation current density is given
by:
2𝜋𝑞 ∞ 𝑛2 (1−𝑒 −𝛼𝑑 )𝐸 2

𝐽0 = ℎ3𝑐 2 ∫𝐸 𝑑𝐸 (3-2)
𝑔 𝑒 𝐸/𝑘𝑏 𝑇 −1
where n is refractive index. Here, several assumptions were made: the surface reflections
and photon recycling effect [160-161] are ignored, and the radiative photons are assumed
to have a single path and a solid angle of . The term (1-e-d) in Equation 3-2 describes
incomplete absorption of photons due to the finite absorber thickness, compared to the full
absorption for a blackbody. With ignoring recycling factor, the calculated radiative carrier
lifetime is about 2.3 s [See table 3-1]. As a result, the diffusion length is around 15 m,
assuming a constant electron mobility of 43 cm2·V-1·s-1. Based on Equation 2-6 and
Equation 3-2, the calculated dark saturation density is shown in Figure 3-2 for three
different carrier lifetimes. As can be seen, for  =20 ns, J0 is on the order of 0.1 A/cm2, in
agreement with the measurements for ICIPs [158]. This substantially high J0 poses a
difficulty in realizing a high open-circuit voltage. By comparison, in the radiative limit, J0
is approximately two orders of magnitude lower. This implies that there is a still plenty
room for improvement of performance for existing TPV devices based on InAs/GaSb SLs.
54
Table 3-1: Parameters used in calculation for InAs/GaSb superlattice.
Temperature and bandgap Tdevice=300 K, Eg=0.29 eV

Effective mass 𝑚𝑒 = 0.03𝑚0 , 𝑚ℎ = 0.4𝑚0
Effective density of states Nc=1.3×1017 cm-3, Nv=6.3×1018 cm-3
−𝐸𝑔
Intrinsic carrier concentration 𝑛𝑖 = √𝑁c 𝑁v exp ( )= 3.4×1015 cm-3
2𝑘𝑏 𝑇
p-type doping concentration
in the absorber Na=2.4×1016 cm-3
Refractive index n=3.5

Absorption coefficient: =3000 cm-1
𝜃=𝜋 𝜑=2𝜋 𝐸=∞
𝑛2 2𝐸 2 𝐸
Radiative 𝐵= 2 ∫ ∫ ∫ 𝛼(𝐸) 3 2
[𝑒𝑥𝑝 ( ) − 1]−1 𝑠𝑖𝑛𝜃𝑑𝜃𝑑𝜑𝑑𝐸
𝑛𝑖 ℎ 𝑐 𝑘𝑏 𝑇
recombination 𝜃=0 𝜑=0 𝐸=𝐸𝑔
coefficient [162]
B=1.75×10-11 cm-3·s-1
Actual lifetime = ns, L=1.5 m, L=0.45

Electron mobility e=43 cm2·V-1·s-1, calculated from L=1.5 m and =20 ns.
Medium lifetime = ns, L=5 m, L=1.5

Radiative lifetime 𝜏𝑟𝑎𝑑 = 1⁄𝐵𝑁a = 2.3 μs (no photon recycling), L=15 m,
L=4.5
Ultimate limit L=15 m, L=4.5, Voc=0.29 V
100
Dark saturation current density (A/cm2)
10-1
ns

10-2 ns
200
=
it
10-3 e lim
iativ
Rad
10-4
0.01 0.1 1 10
Normalized absorber thickness (d/L)
Figure 3-2: Calculated dark saturation current density as a function of normalized

absorber thickness for a carrier lifetime of 20 ns, 200 ns and the radiative limit.
55
3.2.2 Open-circuit voltage and fill factor
The illuminated J-V characteristic needs to be known prior to calculating the open-
circuit voltage and fill factor. The net current density flowing out from a TPV device under
illumination is simply the superposition of the dark current density (Jd) and the
photocurrent density (Jph):

𝑞𝑉
𝐽 = 𝐽𝑝ℎ − 𝐽0 (𝑒 𝑘𝑏𝑇 − 1) (3-3)
where Jph equates eQE0 and J0 is given by Eq. (4) or Eq. (5) (for the radiative limit). The
term J0eqV/kbT stands for the injection current density under a forward bias, which is in the
opposite direction of Jph and thus can strongly affect the fill factor. Figure 3-3 shows the
simulated J-V curves for different values of L (0.45, 1.5 and 4.5). The diffusion lengths
and carrier lifetimes are different but the absorption coefficient (~ 3000 cm-1) is the same
in the three scenarios as shown in Table 3-1. The incident power density Pinc was assumed
to be 25 and 50 W/cm2. In each case, the absorber thickness is the optimal value that
maximizes the conversion efficiency. As shown in Figure 3-3, the simulated J-V curve is
more square-like for larger L, suggesting the increase of fill factor with L. As can be
seen in Figure 3-4, the FF decreases with d/L and is lower than 55% for L=0.45, which is
significantly lower than the 85% reported for high-quality crystalline Si and thin film GaAs
solar devices. Likewise, the Voc exhibit similar trends with d/L and is low when L is small
due to relatively high J0. These two quantities (Voc and FF) both increase with L due to
the decrease of J0 as well as the increase of the QE. Raising the incident power density
from 25 W/cm2 to 50 W/cm2 led to the insignificant enhancements of FF and conversion
efficiency for each value of L. Specifically, the FF () increases from 50% (6%), 58%
(19%) and 54% (69%) to 53% (7%), 61% (23%) and 71% (59%) for L equal to 0.45, 1.5
56
and 4.5, respectively. In the following analysis, the incident power density is set at a fixed
value of 50 W/cm2. Nevertheless, the fundamental insights gained in the analysis are
expected to be applicable to lower incident power densities.
In practice, the goal of a 50 W/cm2 incident power density is difficult to achieve for
conventional TPV configurations, but is still feasible under some circumstances. For
instance, adding a concentrator in a TPV system, analogous to concentration solar cells,
can significantly enhance the incident power density. Another example is the PV device
used in power beaming as the light is sent from a high-power laser source. In this case, the
incident power density is likely to exceed 50 W/cm2 for adequate power delivery. In
addition, in the near filed transfer technology where the TPV device is placed in extreme
proximity (typically < 100 nm) to the heat source (or radiator) [15-17], the incident power
density of the device can be very high as well. On the other hand, the high incident power
density can incur the high injection effect, as observed in a GaSb p-n junction near filed
TPV cell [163]. Narrow bandgap TPV devices with low doping level may be also subject
to this effect, but this is beyond the scope of this chapter.
160
140 solid: 50 W/cm2
Current density (A/cm2)
120 dashed: 25 W/cm2

L=4.5
100
L=1.5
80
60
40 L=0.45
20
0
0.00 0.05
0.10 0.15 0.20 0.25 0.30
Voltage (V)
Figure 3-3: Simulated J-V curves for different values of L and with incident power
density of 25 and 50 W/cm2.
57
Based on Equation 2-6 and Equation 3-3, the expression of open-circuit voltage can
be written as:
𝑘𝑏 𝑇 𝛷0 𝑄𝐸
𝑉𝑜𝑐 = 𝑙𝑛( + 1) (3-4)
𝑞 𝑔𝑡ℎ 𝐿𝑡𝑎𝑛ℎ(𝑑/𝐿)
Under highly intensive illumination, the second term in the natural logarithm can be
neglected, then the open-circuit voltage can be expressed as:

𝐸𝑔
𝑘𝑏 𝑇 𝛷0 𝑄𝐸𝜏𝑝0 𝐸𝑔 𝑘𝑏 𝑇 𝛷0 𝑄𝐸𝜏𝑝0
𝑉𝑜𝑐 = 𝑙𝑛 ( 𝑒 𝑘𝑏𝑇 ) = + 𝑙𝑛 ( ) (3-5)
𝑞 𝑁𝑐 𝑁𝑣 𝐿𝑡𝑎𝑛ℎ(𝑑/𝐿) 𝑞 𝑞 𝑁𝑐 𝑁𝑣 𝐿𝑡𝑎𝑛ℎ(𝑑/𝐿)
Here, the well-known relationship for non-degenerate absorbers was used:
𝑛𝑖2 = 𝑁𝑐 𝑁𝑣 𝑒 −𝐸𝑔/𝑘𝑏𝑇 (3-6)
where Nc (Nv) is the effective density of state for the conduction (valence) band of the
absorbers (See Table 3-1). Based on Equation 3-5, the calculated open-circuit voltage for
different values of L (0.45, 1.5 and 4.5) is presented in Figure 3-1. As shown, the Voc
gradually decreases with the absorber thickness due to the sharper increase of Jo (as shown
in Figure 3-2) than QE. As an example, the Voc decreases from 0.128, 0.187 and 0.287 V
to 0.118, 0.163 and 0.266 V while the normalized absorber thickness increases from 0.01
to 10 for L of 0.45, 1.5 and 4.5, respectively. Hence, in practical device with L=0.45,
the Voc seldom exceeds 0.13 V even at high incident power density, which sets a boundary
(<0.45%) of the voltage efficiency. As the carrier lifetime increases via improvement of
material quality, the Voc can be increased substantially as shown in Figure 3-1 with a higher
L. The Voc in the radiative limit is quite close to bandgap voltage, but never allowed to
exceed it. This is because the amplified stimulated emission will be triggered when the
separation of quasi-fermi levels for electrons and holes exceeds the bandgap. Such a
process will further reduce the carrier lifetime thus increase the saturation dark current
58
density. In [164], unexpectedly, the value of Voc was evaluated to be higher than bandgap
voltage for a solar device under monochromatic light illumination. However, the
calculation did not account the reduction in carrier lifetime. Below, based on Equation 3-
5, a convincing argument is provided to support why Voc< Eg/q.
Under steady state condition, the sweep-out of photo-generated electrons needs to
be compensated by the absorption of photons. This signifies that the density of escaping
photogenerated electrons equates 0QE/v, where v=Ltanh(d/L)/ represents the average
escaping speed of photogenerated electrons. The upper limit of photo-generated electron
density is the available density of states NcNv/p0. Hence, based on Equation 3-5, Voc is
always lower than Eg/q. This implies that the carrier lifetime  reduces with increasing 0
in order to keep consistent with the upper limit.
74
72 ultimate limit
70
L=4.5
68
Fill factor (%)
66
64
62
60 L=1.5
58
56
54 L=0.45
52
0.01 0.1 1 10
Normalzied absorber thickness (d/L)
Figure 3-4: Calculated fill factor as a function of normalized absorber thickness for
different values of L. The incident power density is assumed to be 50 W/cm2 except
in the ultimate limit.
3.2.3 Conversion efficiency
The fact that Voc is always lower than Eg/q offers an effective approach to evaluate
59
the ultimate limit of conversion efficiency for single-absorber devices. To do this, one
needs to first define the ratio of the photon flux to the thermal flux as:
𝛷0
=𝑔 (3-7)
𝑡ℎ𝐿
According to Equation 3-4, the maximum value of  is exp(-Eg/kbT)·tanh(d/L)/QE to keep
Voc lower than Eg/q. When  reaches this value at sufficiently high incident power density,
the conversion efficiency will be stretched to its ultimate limit. This means the ultimate
efficiency limit of a single-absorber device can be obtained by maximizing following
equation with an optimal voltage:
𝜂 = [𝑒 𝐸𝑔/𝑘𝑏𝑇 − (𝑒 𝑞𝑉/𝑘𝑏𝑇 − 1)] ∙ 𝑉/(𝑒 𝐸𝑔 /𝑘𝑏𝑇 𝐸𝑔 ) ∙ 𝑄𝐸 (3-8)
According to this equation, the ultimate efficiency equates the quantum efficiency
multiplied by a factor of 0.71 for a 0.29 eV bandgap. The diffusion length in the ultimate
limit will be assumed to be 15 m, identical to the value in the radiative limit (See Table
3-1). In the ultimate limit, the fill factor remains constant with of d/L as shown in Figure
3-4. It should be emphasized that there are two approximations were made to derive
Equation 3-8. First, the incident photon energy is precisely matched with the bandgap.
Second, the illumination source has an ideal monochromatic spectrum with a shape of delta
function. In practice, the incident photons should possess an energy higher than bandgap
to excite electron-hole pairs. Thus, the first assumption would somewhat overestimate the
conversion efficiency. The second assumption significantly simplifies the illumination
source, which in fact does not make too much difference in conversion efficiency. For
example, provided that the incident photon has Gaussian distribution with the central
energy being 0.34 eV (50 meV higher than the bandgap) and a FWHM of 26 meV (equal
to kbT), the calculated conversion efficiency is 5.4% for L=0.45 at the power density of
60
50 W/cm2. This value of efficiency is slightly lower than the 5.6% calculated for the case
with a perfect monochromatic light (delta function) at 0.34 eV.
Figure 3-5 shows the calculated conversion efficiency of single-absorber devices
in different cases. As shown, the efficiencies in the radiative and ultimate limit are quite
close to each other, especially at smaller d/L. The peak efficiencies are 59% and 63% in
the radiative and ultimate limit, respectively. The vast gap between the radiative limit and
the practical efficiency (L=0.45) reveals a huge potential for improvement. To bridge this
gap, the material quality needs to be greatly improved. For L=0.45, the actual achievable
efficiency is less than 7% as a directly result of low Voc (Figure 3-1) and FF (Figure 3-4)
that spring from a high J0 with a short carrier lifetime (~ 20 ns). If, however, the carrier
lifetime increases by an order of magnitude, the efficiency is possible to reach up to 23%.
These results explicitly show that carrier lifetime is the key issue in narrow bandgap TPV
devices. Besides, another important issue is the relatively low QE ( 32%) due to a small
product of L. The main tendency of conversion efficiency with d/L is resembles that of
QE with d/L (Figure 3-1). That is, the conversion efficiency peaks at a certain absorber
thickness, then slowly drops, and finally reaches a plateau value with further increasing
absorber thickness. The maximum value of  occurs at an optimal d/L equal to 1.8, 1.1 and
0.7 for L value of 0.45, 1.5 and 4.5, respectively, consistent with the order of the optimal
d/L for maximum QE. Compared to the optimal d/L for maximum QE, the optimal d/L for
maximum  is slightly lower due the decrease of Voc and FF with increasing d/L.
61
70
ultimate limit
60

50 L=4.5
40
30
L=1.5
20
10 L=0.45
0
0.01 0.1 1 10
Figure 3-5: Calculated conversion efficiency vs normalized absorber thickness for
different values of L. The incident power density is assumed to be 50 W/cm2 except
for the ultimate limit.
Figure 3-6 shows the calculated conversion efficiency as a function of bandgap
within 0.2-0.4 eV for single-absorber devices. In principle, the variation of bandgap should
result in systematic changes in carrier lifetime. However, because of little relevant
experimental data and uncertainties in carrier lifetime for InAs/GaSb SLs with different
bandgaps, the carier lifetime, absorption coefficient and diffusion length are remained same
for different bandgaps as given in Table 3-1. This assumption, together with same doping
concentration, implies that the thermal generation is proportioanl to e-Eg/kbT. Hence, a
modest increase in bandgap will result in a large redcution in J0 and significant increases
in FF and votlage efficiency, eventually raising conversion efficiency sustantially as shwon
in Figure 3-6. For example, for L=0.45, the conversion efficiency is raised from 3% to
12% while the bandgap is increased from 0.2 eV to 0.4 eV.
62
0.20 0.25 0.30 0.35 0.40
70
68

(a)
66 mate
64 Ulti
62
60 L=4.5
58
30
25 L=1.5
20
15
10 L=0.45
5
0 80
100
75
90 Ultimate
Voltage efficiency (%)
L=4.5 70
80
65
Fill factor (%)

70 60
L=1.5
60 55
50 50
(b)
40 45
solid: voltage efficiency
30 40
L=0.45 dahsed: fill factor
20 35
0.20 0.25 0.30 0.35 0.40
Bandgap (eV)
Figure 3-6: Calculated (a) conversion efficiency and (b) voltage efficiency and fill
factor for L=0.45, 1.5 and 4.5 and the ultimate efficiency limit as a function of
bandgap. The incident power density is 50 W/cm2 except for the ultimate limit.
In the radiative limit, the J0 detemined by Equation 3-2 decreases with increasing
bandgap, but at a slower rate than that for for L=0.45 or 1.5. Consequently, the FF and
Voc increase gradually with bandgap, while the voltage efficiency decreases with bandgap
as shown in Figure 3-6(b). Hence, in the radiative limit, the increase of conversion
efficiency with bandgap is insignificant as it ranges between 58%-60%, as shown in Figure
3-6(a). Note that, in Equation 3-2, the absorption spectrum was assumed to have same
shape but different take-off points for different bandgaps. The diffusion length in the
radiative limit was still taken to be 1.5 m for different bandgaps. In addition, the QE at
the optimal absorber thickness is almost identical for different bandgaps. This means that
63
the maximum QE is purely decided by the value of L and insensitive to the change of
bandgap. Also, the small value of L (0.45) in narrow bandgap materials serves as an
obstacle to achieving a high conversion efficiency (15% as shown in Figure 3-6) in single-
absorber TPV devices.
3.3 Efficiency improvement in multistage TPV devices
3.3.1 Enhancement of open-circuit voltage
The structure and operation principle of ICTPV devices are described in Chapter 2.
Figure 3-7 shows the chemical potentials (designated by the flat lines) across individual
stages for an ICTPV device under illumination, which adds up to generate a high open-
circuit voltage. Each stage in a multistage ICTPV device operates in the same manner as a
single-absorber device. The equations in the preceding section can be directly applied to
the individual stages in a multistage device. The net current flowing in the mth stage is
given by:
𝑞𝑉𝑚
𝐽𝑚 = 𝛷𝑚 𝑄𝐸𝑚 − 𝑔𝑡ℎ 𝐿𝑡𝑎𝑛ℎ(𝑑𝑚 /𝐿)(𝑒 𝑘𝑏𝑇 − 1) (3-9)
where m is the incident flux on the mth stage, QEm is the effective quantum efficiency
given by Equation 2-5, Vm is the voltage across the mth stage, and dm is the absorber
thickness. The optimized multistage device is designed to have an equal photocurrent in
each stage. This current matching condition is realized with an iterative process by varying
the thickness of each stage so that the contribution of photocurrent from each is equal. The
optimal absorber thicknesses are then found by selecting the photocurrent-matched
absorber sequence that maximizes the output power.
64
Figure 3-7: Schematic of a three-stage ICTPV device under forward voltage and
illumination. Optical generation gphm, thermal generation gthm and recombination Rm,
along with the chemical potentials m in each stage are shown, where the index m
denotes the stage ordinal. The flat quasi-Fermi levels (designated with 1, 2, 3
and 4) correspond to the case where the diffusion length is infinite.
Based on Equation 3-9, the J-V characteristic of a multistage TPV device is
obtained by adding together the voltage across each stage:
𝑁
𝑐 𝑘𝑏 𝑇 𝛷𝑚 𝑄𝐸𝑚 −𝐽
𝑉 = ∑𝑚=1 𝑙𝑛[ + 1] (3-10)
𝑞 𝑔𝑡ℎ 𝐿𝑡𝑎𝑛ℎ(𝑑𝑚 /𝐿)
Then the open-circuit voltage of a multistage device can be derived by setting J=0 in
Equation 3-10. After correcting m with absorption in the upper stages, the expression of
Voc can be written as:
𝑘𝑏 𝑇 𝑁 𝑄𝐸𝑚 𝑁
𝑉𝑜𝑐 = [𝑁𝑐 𝑙𝑛() + ∑𝑚=1
𝑐
𝑙𝑛 ( 𝑐
) − ∑𝑚=2 ∑𝑚−1
𝑖=1 𝛼𝑑𝑖 ] (3-11)
𝑞 tanh(𝑑𝑚 /𝐿)
where  is the ratio of photon flux to thermal flux, defined by Equation 3-7. The third term
on the right side of Equation 3-11 represents light attenuation. According to Equation 3-
11, when  is substantially high, the Voc of a multistage device is dominated by the first
term in Equation 3-11 since the last two terms are negligible. This implies that the Voc of a
multistage device nearly scales with number stages when the photon flux to thermal flux
ratio is very high. This speculation is confirmed by the calculations for the incident power
65
density of 50 W/cm2 (corresponding to a minimum  of 305) as shown in Figure 3-8. The
open-circuit voltage enhancement in this figure is the Voc(Nc) of the optimized multistage
device normalized to the Voc(1) of the optimized single-absorber device. Note that, the
parameters used in the calculation are same as those for single-absorber devices, as
presented in Table 3-1. In different scenarios, the normalized open-circuit voltage almost
scales with Nc. The slopes are only slightly lower than unity (indicated by the dashed purple
line in Figure 3-8, i.e. Voc(Nc)/Voc(1)=Nc) due to light attenuation in the optically deeper
stages. For example, the slope is about 0.9 for L=0.45 and 0.95 for L=1.5 and 4.5. This
good consistent linear proportionality for a wide range of L will lead to a universal
enhancement of conversion efficiency in multistage ICTPV devices compared to single-
absorber devices.
Open-circuit voltage enhancement
30
Voc(Nc)/Voc(1)=Nc
25 L=0.45
L=1.5
20 L=4.5
15
10
0
0 5 10 15 20 25 30
Number of stages
Figure 3-8: Calculated open-circuit voltage enhancement Voc(Nc)/Voc(1) as a function
of number of stages. The dashed purple line indicates Voc(Nc)/Voc(1)=Nc. In the
calculations, L was set at 0.45. 1.5 and 4.5. The incident power density is 50 W/cm2.
66
3.3.2 Enhancement of conversion efficiency
Figure 3-9 shows the calculated conversion efficiency as a function of number of
stages for different values of L. The  is increased from 7%, 23% and 59% in a single-
absorber structure to 17%, 33% and 68% in a multistage IC architecture for L equal to
0.45, 1.5 and 4.5, respectively. Therefore, the  has a universal absolute increase of 9-10%
regardless of the value of L. In terms of relative change, it is more pronounced for small
value of L. For example, for L=0.45, the  of multistage devices is more than twice that
for single-stage cells. This can be explained by resorting to the preceding analysis. When
 is high enough, the following equations hold: Voc(Nc)/Voc(1)Nc (Figure 3-8) and
FF(Nc)/FF(1)1 according to Equation 3-9 and 3-11. Then efficiency enhancement in a
multi-stage structure (Nc)/(1) is approximated as:
𝜂(𝑁𝑐 ) 𝑄𝐸(𝑁𝑐 ) 𝑉𝑜𝑐 (𝑁𝑐 ) 𝐹𝐹(𝑁𝑐 ) 𝑁𝑐 ∙𝑄𝐸(𝑁𝑐 )

= ∙ ∙ ≈ (3-12)
𝜂(1) 𝑄𝐸(1) 𝑉𝑜𝑐 (1) 𝐹𝐹(1) 𝑄𝐸(1)
According to this equation, it is evident that the efficiency enhancement of a multistage
device is essentially due to its increased particle conversion efficiency 𝜂part that is defined
as Nc·QE(Nc) for current-matched IC structures. Increasing the number of stages increases
𝜂part, although it shortens the absorber thicknesses and reduces QE(Nc). This explains why
the  increases with the number of stages as shown in Figure 3-9. From Figure 3-1, QE(1)
is low for small L, hence the (Nc)/(1) can be substantial. For large L, QE(1) is
relatively high, so the (Nc)/(1) is less significant, but still exceeds unity. This manifestly
shows how the multistage structures enhance through an increased particle efficiency with
shortened individual absorbers for high collection of photo-generated carriers, which could
otherwise be lost to recombination with a long single absorber.
67
70
L=4.5

60
50
40
L=1.5
30
20 L=0.45
10
0 5 10 15 20
Number of stages
Figure 3-9: Calculated conversion efficiency for optimized multistage cells as a
function of number of stages. The calculation is done for L=0.45 1.5 and 4.5. The
incident power density is 50 W/cm2.
According to Equation 3-12, if Voc(Nc)/Voc(1)=Nc and Nc·QE(Nc)=1 (with
sufficiently large number stages), the efficiency enhancement is equal to 1/QE(1). This
maximum efficiency enhancement is calculated as a function of L and is indicated by the
solid purple curve in Figure 3-10. However, it is higher than the real efficiency
enhancement as represented by the dashed olive curve in Figure 3-10, since Voc(Nc)/Voc(1)
is slightly lower than Nc in practical case (See Figure 3-8). Also displayed in Figure 3-10
are the calculated maximum efficiencies that can be achieved by single-absorber and
multistage devices with two different bandgaps (i.e. 0.29 and 0.4 eV). The number of stages
of the multistage devices is twenty, which is large enough to reach the plateau value of
achievable efficiency (as shown in Figure 3-9). For the two different bandgaps, almost the
same improvement is observed. When the bandgap is increased to 0.4 eV, it’s possible to
achieve a conversion efficiency of 30% with a multistage IC architecture even for a small
L value of 0.45. This elucidates that multistage IC architecture is an effective strategy to
universally improve the device performance in a wide infrared spectral range.
68
3.3 50
red curve: Eg= 0.29 eV
3.0 blue curve: Eg=0.4 eV

Efficiency enhancement
40
ge
i-sta
2.5 mult
30
ber
bsor
sin gle-a
2.0
20
Eq. (
15 )
1.5 actual
10
0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

L
Figure 3-10: Calculated maximum conversion efficiency and conversion efficiency
enhancement as a function of L. The incident power density is 50 W/cm2.
3.4 Performance of TPV devices under variable illumination sources
3.4.1 Single-absorber TPV cells
In the preceding two sections, the incident photon energy is set equal to bandgap,
which inevitably overestimates the conversion efficiency to some degree. This is because,
to excite electron-hole pairs, the photon energy needs to be higher than the bandgap. On
the other hand, a high photon energy will escalate thermalization loss. Here, to evluate the
dependence of device performance on incident photon energy, an energy-dependent
absorption coefficient (E)=1.9×(hv-Eg)1/2 m-1 is used, which matches well with that for
quaternary Ga0.44In0.56As0.5Sb0.5 with a bandgap of 0.29 eV [165]. This bulk material has
been employed as the absorbers in IC detectors and the pre-factor 1.9 m-1 is assumed as
the best fit to the experiment data [165]. Table 3-2 shows all the parameters used in the
calculations for this Ga0.44In0.56As0.5Sb0.5 material, some of which are same with those for
InAs/GaSb SL in Table 3-1.
69
Table 3-2: Parameters used in calculation for bulk Ga0.44In0.56As0.5Sb0.5.
Temperature and bandgap Tdevice=300 K, Eg=0.29 eV

Effective mass 𝑚𝑒 = 0.028𝑚0 , 𝑚ℎ = 0.51𝑚0
Density of states Nc=1.2×1017 cm-3, Nv=9.2×1018 cm-3
−𝐸𝑔
Intrinsic carrier concentration 𝑛𝑖 = √𝑁c 𝑁v exp ( )= 3.8×1015 cm-3
2𝑘𝑏 𝑇
p-type doping concentration
in the absorber Na=2.8×1016 cm-3
Refractive index n=3.5

Absorption coefficient: α = 1.9 × √𝐸 − 𝐸𝑔 (m-1)
𝜃=𝜋 𝜑=2𝜋 𝐸=∞
𝑛2 2𝐸 2 𝐸
𝐵= 2 ∫ ∫ ∫ 𝛼(𝐸) [𝑒𝑥𝑝 ( ) − 1]−1 𝑠𝑖𝑛𝜃𝑑𝜃𝑑𝜑𝑑𝐸
Radiative recombination 𝑛𝑖 ℎ3 𝑐 2 𝑘𝑏 𝑇
coefficient [29] 𝜃=0 𝜑=0 𝐸=𝐸𝑔
B=2.81×10-11 cm-3·s-1
Actual lifetime = ns, L=1.5 m
Electron mobility e=43 cm2·V-1·s-1, calculated with L =1.5-m and =20-ns.
Radiative lifetime 𝜏𝑟𝑎𝑑 = 1⁄𝐵𝑁a = 1.3 μs (no photon recycling), L=12 m
Figure 3-11 shows the calculated conversion efficiency of a single-absorber device
as a function of incident wavelength for different diffusion lengths and under illumination
at 50 W/cm2. Note that the  at each wavelength and diffusion length is the maximum
value with the optimal absorber thickness. Given a constant electron mobility of 43 cm2·V-
1
·s-1, the diffusion length increases from 1.5 m to 15 m while the carrier lifetime is
enhanced from 20 ns to 2.0 s. For a long diffusion length, the QE is high (Figure 3-1) and
the reaches the maximum value at an incident photon energy that is closely matched with
the bandgap. Conversely, when the diffusion length is short, the QE is low at a photon
energy close to the bandgap, thus resulting in a low . By increasing the energy of incident
photons, the  can be improved since the absorption coefficient and QE is enhanced. This
leads to a blue shift of the peak value of  as indicated by the black arrow in Figure 3-11.
This result for a short diffusion length goes against the conventional view that the incident
70
photon energy should be very close to the bandgap for best conversion efficiency.
However, based on above analyses, it is comprehensible from the perspective of the QE
for narrow-bandgap TPV cells with small L.
40

35 m
= 15
30 L
2 m
25 L=1
m
L=8
20
L=5 
m
15
L=3 m
10
L=1.5 m
5
0
2.0 2.5 3.0 3.5 4.0
Wavelength (m)
Figure 3-11: Calculated conversion efficiency of a GaInAsSb single-absorber device
vs wavelength for various values of diffusion length. The incident power density is 50
W/cm2.
3.4.2 Multistage ICTPV devices
As for multistage TPV cells, there is more flexibility to maximize the conversion
efficiency under different incident photon energies because of the multiple adjustable
parameters. Despite more complicated than the single-absorber structure, the multistage IC
architecture offers an effective way of dealing with the diffusion length limitation and thus
to maximize the  at a photon energy close to the bandgap. One important consideration
in the design of a multistage TPV device is the photocurrent match between stages. If the
current is mismatched, the QE decreases with incident photon energy, which can be
partially caused by the light attenuation. Figure 3-12 shows the calculated  for four
multistage structures. These structures have the optimal current matched absorbers that
71
were designed based on an absorption coefficient of 0=3000 cm-1 (at a wavelength 0 of
4 m, close to the cutoff wavelength of 4.3 m) to maximize conversion efficiency. With
the same number of stages, the individual absorber thicknesses differ considerably for
different diffusion lengths. For example, for the 5-stage devices, the optimal absorber
thickness sequence (nm) is 476/562/693/923/1567 and 603/733/941/1318/2225 for a
diffusion length equal to 1.5 and 15 m, respectively. The light attenuation is significant
in the thick absorbers for the case of L=15 m, therefore, there are dramatic reductions in
the QE and  at short wavelengths. This explains why  of the 20-srage device with L=15
m is even lower than that for L=1.5 m at wavelengths shorter than 3 m. These results
illustrate the importance of retaining current match when selecting the illumination source
for multistage devices.
In addition, the  of four devices peaks at a wavelength slightly shorter than 0,
where the QE reaches its maximum with current match. This is because the open-circuit
voltage and fill factor are both somewhat higher at a wavelength slightly shorter than 0.
Alternatively, one can optimize the multistage structure based on the measured absorption
coefficient at every given wavelength such that the  at each wavelength reaches the
maximum value that is achievable by a multistage architecture. This is illustrated by the
olive curves in Figure 3-12 for two diffusion lengths. The total absorber thickness of each
optimized structure is about 8 m for wavelength near the bandgap, and the number of
stages for each structure is twenty. For example, for =4 m and L=1.5 m (represented
by the solid olive curve in Figure 3-12), the optimal absorber thickness (nm) sequence is
148/156/165/174/183/194/206/220/236/254/276/301/332/370/419/483/573/711/960/175
with a total absorber thickness of about 8.1 m. In contrast to single-absorber devices, the
72
maximum  of the optimized multistage devices always occurs at an incident photon
energy very close to the bandgap, regardless of the magnitude of the diffusion length. This
further validates the advantages and flexibility of the multistage architecture.
50
5-stage L=15 m
20-stage

40
optimized
30
20
10
L=1.5 m
0
2.0 2.5 3.0 3.5 4.0
Wavelength (m)
Figure 3-12: Calculated conversion efficiency for the 5- and 20-stage devices with
L=1.5 m (solid curves) and 15 m (dashed curves). The absorbers were adjusted to
be photocurrent matched with an absorption coefficient of 3000 cm -1, corresponding
to a wavelength of 4 m. The calculated maximum efficiencies with optimized multi-
stage structures at every wavelength are represented by the olive curves. The incident
power density is 50 W/cm2.
3.5 Summary and concluding remarks
To recapitulate, in this chapter, the efficiency limiting factors in narrow bandgap
TPV cells are identified and how they affect the device performance is discussed. These
factors are highly correlated with high dark saturation current density, short carrier lifetime,
relatively small absorption coefficient and finite diffusion length. As an example, narrow-
bandgap InAs/GaSb SLs are used to illustrate the specific impact of these factors on
conversion efficiency and how the device performance can be improved by adjusting
material parameters such as the product L. One way to increase L is to employ Ga-free
73
InAs/InAsSb SLs for absorbers with a relatively long carrier lifetime [166-167].
Furthermore, it is shown that multistage IC structure is capable to overcome the diffusion
length limitation and achieve a particle conversion efficiency approaching 100%, therefore
increasing the conversion efficiency by about 10% in a wide range of L values and
bandgaps. The enhancement of conversion efficiency with multistage IC structure is
especially impressive for small values of L, for which the conversion efficiency is more
than double that in the single-absorber TPV devices. In addition, the entire structure’s
flexibility and other advantages of multistage structure offer the possibility to achieve
maximum conversion efficiency with the incident photon energy close to the bandgap.
Nevertheless, as with single-absorber TPV devices, the issues of relatively low fill factor
and voltage efficiency (=qVoc/(NcEg) for IC structures) remain. These issues are directly
related to the high dark saturation current density in narrow bandgap materials. To resolve
them, an approach that can significantly increase the photocurrent without requiring a
higher incident power density needs to be implemented, which should be one of future
research focuses.
74
4 Chapter 4: Experimental comparison between single-absorber and
multistage IC thermophotovoltaic devices
In chapter 3, theoretical evidence and illustrated scenarios are presented to prove
the advantage of multistage ICTPV devices over single-absorber TPV devices.
Specifically, IC structures are shown to be capable to enhance the conversion efficiency by
promoting the collection of photo-generated carriers. In this chapter, broad experimental
proof is furnished to support the advantage of IC devices, especially in concerns of
enhanced collection efficiency. Aside from InAs/GaSb T2SLs that are treated in Chapter
3, the advantage of IC structures is also true for other narrow bandgap materials since their
diffusion length and absorption coefficient are limited as well. For example, the bulk InAs
and InSb (either intrinsic or lightly doped) typically have  in the range of 1000-3000 cm-
1
near bandgap. Their L can be several microns at room temperature but may be shortened
significantly under strong illumination due to the high concentration of excess carriers.
The effects of small  and short L on single-absorber TPV performance are
illustrated in Figure 4-1, where the calculated QE and collection efficiency (c) are plotted
as functions of normalized absorber thickness (d/L). The calculation of QE is carried out
based on Equation 2-4 without considering the surface reflection of light. The collection
efficiency is defined as the ratio of collected carriers to absorbed photons and is equal to
QE/[1-exp(-d)]. For single-absorber devices, adequate absorption of incident light
necessities a thick absorber, especially with a small . However, if the diffusion length is
short, QE will not increase further with absorber thickness after d≈L as shown in Figure 4-
1(a). This is because some photogenerated carriers recombine before being collected and
75
the collection efficiency is reduced with absorber thickness. The reduction of collection
efficiency with increasing d is more significant when L<1, as shown in Figure 4-1(a).
Also, for L1, the QE peaks at a certain finite absorber thickness, because the collection
probability (defined by Equation 2-1) of photogenerated carriers is reduced with absorber
thickness. A high collection efficiency (>90%) can be obtained only when the absorber is
thinner than the diffusion length (or thinner than 0.6L for L<1) as shown in Figure 4-1(a).
In addition, the open-circuit voltage, defined by Equation 3-4, is reduced with a limited
collection efficiency. This is illustrated by the open-circuit voltage factor VF=
ln[QE/tanh(d/L)] in Figure 4-1(b), where the dotted curves are calculated assuming
complete collection of carriers while solid curves are based on the calculated QE in Figure
4-1(a) with a limited collection efficiency. As can be seen, comparatively, VF is decreased
considerably with a limited collection efficiency especially when L<1 and d>L. For
instance, for L=0.35 and d=3L, VF is decreased by 0.91, resulting in a reduction of Voc by
24 mV at 300 K. Hence, the considerably reduced VF coupled with the limited QE due to
the finite diffusion length will result in a poor conversion efficiency when L is less than
unity.
In this chapter, a comparative study of three TPV devices is presented to
experimentally confirm the advantage of multistage architecture, as well as to examine how
different configurations affect device performance. One of the three devices has single-
absorber structure while the others are three- and five-stage IC devices. The bandgap of the
InAs/GaSb T2SLs in these devices is about 0.2 eV at 300 K, which is the narrowest
bandgap ever reported so far in TPV cells.
76
0.1 0.5 1 10
1.0 1.0
0.9 L=5.1 0.9
(a)
0.8 0.8
Quantum efficiency
Collection efficiency
0.7 0.7
0.6 L=1.1 0.6
0.5 0.5
0.4 0.4
0.3 L=0.35 0.3
0.2 0.2
0.1 0.1
0.0 0.0
Solid: L-limited collection
1.0 L=5.1 Dotted: 100% collected
Normalized Voc factor
(b)
0.5
L=1.1
0.0
-0.5
-1.0 L=0.35
-1.5
0.1 0.5 1 10
Figure 4-1: (a) Calculated quantum efficiency and collection efficiency, and (b) open-
circuit voltage factor as a function of normalized absorber thickness for several values
of L. VF initially decreases with increasing d/L due to the nearly linear increase of
dark current when d/L is small.
4.2 Device structure, growth and fabrication
The three TPV structures are grown by GENxplor MBE system (Figure 2-11) on
nominally undoped p-type GaSb (001) substrates. In the three structures, each period of
the SL absorber is composed of four layers: InSb (1.2 Å), InAs (20.5 Å), InSb (1.2 Å) and
GaSb (25.1 Å). The two thin InSb layers were inserted to balance the tensile strain of the
InAs layer [168]. The absorbers in the three structures are p-type doped to 2.6×1016 cm-3.
In the two multistage structures, the individual absorber thickness was increased in the
optically deeper stages to achieve current match between stages by compensating for light
77
attenuation. The current-matched absorbers were deigned based on the absorption
coefficient of 3000 cm-1 for a monochromatic light source and the assumption of full
collection of photo-generated carriers. The absorber thickness for the 1-stage device is 2.31
m. The 3-stage device has a total absorber thickness equal to that of the 1-stage device
with the discrete individual thicknesses of 624, 749 and 936 nm from surface to the
substrate. The individual absorber thicknesses in the 5-stage device are 360, 408, 480, 576
and 696 nm, and the total absorber thickness is 2.52 m, slightly longer than the 1- and 3-
stage devices. The electron barriers in the three devices were made of four digitally
GaSb/AlSb QWs with GaSb well thicknesses of 33/43/58/73 Å. The hole barriers consist
of eight digitally graded InAs/AlSb QWs with the InAs well thicknesses (in Å) of
32/34/36/40/45/52/60/71. The schematic layer structures of the three devices are shown
Figure 4-2. After MBE growth, square mesa devices with edge lengths ranging from 50 to
1000 m are processed by using conventional contact lithography and wet etching. For
passivation, two layers composed of Si3N4 followed by SiO2 are used for improving overall
stress management and minimizing pin holes. Finally, Ti/Au contacts are deposited by
sputtering, and then the devices are mounted on heat sinks and wire bonded for
characterization.
78
Figure 4-2: Schematic layer structures of the three TPV devices with one, three and
five stages.
4.3 Device characterizations and discussions
4.3.1 Quantum efficiency
The QEs of the three devices were measured using a FTIR spectrometer and a
calibrated blackbody radiation source with a temperature of 800 K and a 2 field of view
(FOV). The blackbody source had an aperture of 0.76 cm and was placed at 30 cm from
the device. Figure 4-3 shows the calibrated QE spectra at 300 and 340 K for the
representative 0.2×0.2 mm2 devices processed from the three wafers. Because of current
continuity in multistage IC structure, the device QE is decided by the stage with weakest
response, therefore the measured QE reflects the actual device performance and is more
meaningful than the effective QE for any individual stages. As can be seen in Figure 4-3,
at 300 K, the 1- and 3-stage devices have a 100% cutoff wavelength of 5.5 m, which
corresponds to a bandgap of 225 meV. By comparison, the 5-stage device has a slightly
79
longer 100% cutoff wavelength of 5.8 m with the SL absorber bandgap estimated to be
214 meV. Since the QE is roughly proportional to the individual absorber thickness, the 5-
stage device with thinnest individual absorbers has the lowest QE, while the 1-stage device
with a 2.31-m absorber has the highest QE among the three devices. For example, at 𝜆=4
m and T=300 K, the QEs are 29.5%, 12.0%, and 8.8% for the 1-, 3- and 5-stage devices,
respectively. As the temperature in increased to 340 K, the QEs of the 1- and 3-stage
devices were decreased, while the QE of the 5-stage device was nearly unchanged. Also,
the decline of QE with temperature for the 1-stage device is more pronounced than the 3-
stage device. For example, at 𝜆=4 m, the QE was reduced to 23.6% for the 1-stage device,
compared to a small reduction to 11.3% for the 3-stage device at 340 K. The QEs were
reduced because the diffusion length was shorter at a higher temperature, leading to a
smaller collection efficiency as illustrated in Figure 4-1. This speculation is further proved
by the bias dependence of the QE at =4 m for the three devices as shown in Figure 4-4.
60
50
solid: 300 K
dashed: 340 K
40
QE (%)
30 1-stage
3-stage
20
10 5-stage
0
2 3 4 5 6
Wavelength (m)
Figure 4-3: Measured QE spectra of 1-, 3- and 5-stage devices at 300 and 340 K.
80
As can be seen in Figure 4-4, for the 1-stage and 3-stage devices, a reverse bias is
required to achieve the saturation (or maximum) value of QE with complete collection of
photo-generated carriers at 300 K. This is because the diffusion length is either shorter than
or comparable to the absorber thicknesses in the 1- and 3-stage devices. Hence, at zero
bias, some of the photo-generated carrier recombine during transport paths and do not
contribute to photocurrent. At higher temperature (e.g. 340 K), the diffusion length is even
shorter, consequently, a larger reverse bias is required to saturate the QE for the 1- and 3-
stage devices. By comparison, the diffusion length has much less impact on the 5-stage
device since its individual absorbers are much thinner. Also, the saturation values of QE
for all the devices are higher at 340 K since the absorption coefficient is enhanced due to
the bandgap narrowing with rising temperature. Thanks to the thickest absorber, the 1-stage
device has the highest QE among the three devices. However, this highest QE does not
necessarily result in the best performance among the three devices when they operate at a
forward bias voltage.
45
40
1-stage
35
solid: 300 K
30 open: 340 K
= m
25
QE (%)
3-stage
14
12
10 5-stage
8
0 -100 -200 -300 -400 -500 -600 -700
Bias (mV)
Figure 4-4: Voltage dependent QE at 4 m for the three devices, where different
vertical scales are used in the top and bottom portions to better show variations.
81
4.3.2 Particle conversion efficiency
As pointed out in Chapter 3, instead of QE, a more proper figure of merit for
multistage TPV device is the particle conversion efficiency PCE [169-170]. It is defined
as the sum of effective QEs in individual absorbers and is equal to Nc×QE for a current-
matched configuration. At 𝜆=4 m and T=300 K, current match condition is nearly
fulfilled based on the measured absorption coefficient (3159 cm-1 for 1- and 3-stage devices
and 3470 cm-1 for the 5-stage device) from the transmission measurement. Hence, the PCE
at zero bias is 29.5%, 36.0%, and 44% for the 1-, 3- and 3-stage devices at 300 K,
respectively. The highest PCE for the 5-stage device among them agrees with the projected
high collection efficiency due to thin individual absorbers. In principle, the value of PCE
can be increased up to maximum 69% (estimated by subtracting the 31% reflection loss
from the top surface) by adding more stages to fully absorb the incident photons. Also,
adding an anti-reflection coating onto the surface can raise the PCE beyond 69%.
In theory, the effective QE in the Nth stage of a multistage ICTPV device can be
calculated based on Equation 2-5. Based on Equation 2-5, together with the measured
absorption coefficient and QE, the diffusion length was extracted to be about 1.5 m at 300
K for the three devices. Evidently, at 𝜆=4 m, the product of absorption coefficient and
diffusion length (L) is smaller than unity in the three devices. Consequently, according to
Figure 4-1, the individual absorber thicknesses need to be shorter than 0.6L in order to
achieve a collection efficiency higher than 90%. The 1-stage device has an absorber
thickness that is about 1.5 times of the diffusion length and thus it has the lowest collection
efficiency at zero bias (~60% as illustrated in Figure 4-1). In comparison, the individual
absorbers in the 5-stage device are thinner than 0.6L, thus resulting in a collection
82
efficiency over 90% and the highest PCE at zero bias as discussed above.
4.3.3 Illuminated J-V curve and open-circuit voltage
In the lighted current density-voltage (J-V) measurement, a type-II IC laser (ICL)
was employed to illuminate the three devices. The narrow emission spectrum of the ICL
reproduced the characteristics of a selective emitter (or a narrow-band filter), which is
usually included in a TPV system to minimize the thermalization and below-bandgap
losses. Both experimental and theoretical efforts were devoted to nanostructured materials
for efficient narrowband emissivity near 4 m or longer wavelengths [32-33]. These
studies reinforce the feasibility and applicability of narrow bandgap TPV devices. During
the lighted J-V measurement, the IC laser was cooled down to ~80 K and continuously
delivered high output power at an emission wavelength near 4.2 μm (See inset in Figure 4-
5(b)). This emission wavelength corresponds to a photon energy of 295 meV that is 70-80
meV higher than the bandgap of the three TPV devices at 300 K. Hence, there is some
thermalization loss (20-27%) from above-bandgap photons. Nevertheless, at laser emission
wavelength, current match was almost satisfied in the 3- and 5-stage devices. The PV
characteristics of the three devices were studied at different incident power densities simply
by adjusting the injection current of the laser. The measured J-V curves at 300 K under a
medium level of illumination from the ICL are shown in Figure 4-5(a). The incident power
density Pinc was about 19 W/cm2, which was assessed through the connection between QE
and Jsc as expressed by the following equation:
1.24𝐽𝑠𝑐
𝑃𝑖𝑛𝑐 = (4-1)
𝜆𝑙𝑎𝑠𝑒𝑟 𝑄𝐸
where laser is the laser emission wavelength. This simple and effective method to estimate
83
incident power density allows to circumvent the difficulties associated with the nonuniform
and divergent beam of the edge emitting ICL laser.
Also displayed in Figure 4-5(a) are the series resistance (Rs) corrected J-V curves
and the ideal curves that were plotted in the same manner with [171]. Or rather, the ideal
J-V curve is the superposition of dark current density and the maximum photocurrent
density (Jphmax), where the photo-generated carriers are completely collected. The
magnitude of Jphmax is the difference between the saturated current densities at a reverse
bias under dark and illuminated conditions. For example, at T=300 K and Pinc=19 W/cm2,
the saturation value of current density under illuminated (dark) condition was 25.3 (2.9),
9.1 (1.1) and 5.9 (0.9) A/cm2 for the 1-, 3- and 5-stage devices, respectively. Therefore, the
corresponding Jphmax is 22.4 (1-stage), 8.0 (3-stage) and 5.0 A/cm2 (5-stage), proportional
to their individual absorber thicknesses. At the same incident power density, the Jsc values
are 9.2 A/cm2, 6.7 A/cm2, and 4.9 A/cm2 for the 1-, 3- and 5-stage devices, respectively.
These values of Jsc are higher than Jphmax values for the three devices, primarily due to
incomplete collection of photo-generated carriers particularly in the 1-stage device. Even
though the Jsc is highest in the 1-stage device, its PCE and collection efficiency are lowest,
which results in the lowest conversion efficiency described in next subsection. The high
current in the 1-stage device also results in a significant Ohmic loss in series resistance, as
reflected by the notable shift between the Rs-corrected and measured J-V curves. Instead,
the Rs-corrected J-V curves for the 3- and 5-stage devices almost coincide with the
measured J-V curves due to the relatively lower currents.
84
25
1-stage 1-stage ICL
emmision
20 (a) 15 spectrum

T=300 K (b)
solid: measured
15 dotted: Rs corrected
T=200 K
3.5 4.0 4.5 5.0
10 Wavelength (m)
dashed: 100% collected
10
3-stage 3-stage
5
5 5-stage 5-stage
0 0
-0.4 -0.2 0.0 0.2 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8
Voltage (V) Voltage (V)
Figure 4-5: (a) Current-voltage characteristics of the three devices at 300 K under a
medium illumination level where the incident power density was about 19 W/cm2. The
solid, dotted and dashed curves correspond to the measured, Rs corrected and ideal
cases, respectively. (b) Current-voltage characteristics of the three devices at 200 K
under the same level of illumination as in (a). The inset shows the emission spectrum
of the ICL.
The primary reason for the low collection efficiency in the 1-stage device at 300K
was because the diffusion length was shorter than absorber thickness. This can be further
confirmed by examining the behaviors at a low temperature where the diffusion length
should be longer. Figure 4-5(b) shows the measured J-V curves of the three devices at 200
K under the same illumination level as in Figure 4-5(a) from the ICL. As shown, for the 3-
and 5-stage devices, the onset of current saturation occurs at a certain forward voltage
rather than a reverse voltage. This suggests that complete collection of photogenerated
carriers was achieved under a forward voltage and the diffusion length was increased
significantly beyond the absorber thicknesses in the 3-and 5-stage devices. The increased
diffusion length also improved the collection efficiency (~72% at zero bias) in the 1-stage
device, although it was still below 100% since the diffusion length was shorter than the
absorber thickness (2.31 m). Also, because of the reduced dark saturation current (orders
of magnitude lower than the photocurrent), the Voc was appreciably higher for the three
85
devices at 200 K. On the other hand, at 200 K, the Jphmax under this illumination level
dropped to 18.5, 6.9 and 4.4 A/cm2 for the 1-, 3- and 5-stage devices, respectively. This is
because the absorption coefficient decreased due to bandgap widening at lower
temperatures.
Aside from a higher collection efficiency compared to the single-stage device, the
multistage IC structure can also create a Voc far exceeding the individual absorber bandgap.
For example, at T=200 K and Pinc=19 W/cm2, the measured Voc was 170 (1-stage), 513 (3-
stage) and 745 meV (5-stage), corresponding to a voltage efficiency of 67%, 68% and 63%,
respectively. As the temperature increased to 300 K, the Voc at the same illumination level
dropped to 72 (1-stage), 223 (3-stage) and 287 meV (5-stage) with a corresponding voltage
efficiency of 32%, 33% and 27%, respectively. Presumably, the slightly lower voltage
efficiency in the 5-stage device was due to the narrower bandgap and poorer material
quality, which collectively resulted in a much higher thermal generation rate (about two
times higher as estimated in Subsection 4.4.2) than in the 3-stage devices at 300 K.
Specifically, the Voc could be reduced by ~90 mV (amplified by about 5 times with five
cascade stages [169-170]) due to the doubling of the thermal generation rate. On the same
account, the Voc of the 5-stage was lower than the 3-stage device in the ideal case as well.
In addition, the Voc and voltage efficiency increased when the incident power density was
enhanced. For example, at T=300 K and Pinc=36 W/cm2 (highest illumination level
available from the ICL), the measured Voc was 85, 271 and 371 mV for the 1-, 3- and 5-
stage devices, respectively.
86
4.3.4 Fill Factor and conversion efficiency
Figure 4-6 shows the measured Voc, FF, maximum output power density (Pmax), and
conversion efficiency () as functions of incident power density at 300 K for the three
devices. At the maximum incident power density (36 W/cm2), the FF was 25%, 28% and
38% for the 1-, 3- and 5-stage devices, respectively. Throughout the whole range of
incident power density, the 1-stage device had the lowest FF due to the lowest collection
efficiency and a greater series resistance loss, while the 5-stage device had the highest FF
because of the highest collection efficiency. Under the highest illumination level, the
maximum output power was harvested at a voltage of 43, 136 and 226 meV for the 1-, 3-
and 5-stage devices, respectively. At this voltage, the extracted collection efficiencies (See
Figure 4-7) were about 29% (1-stage), 53% (3-stage) and 87% (5-stage). If, however, the
photogenerated carriers were fully collected as in the ideal case, the FF would increase to
32%, 36% and 39% for the 1-, 3- and 5-stage devices, respectively. From this point of
view, the 5-stage device with thin absorbers is nearest to the ideal case for maximum output
power. The FFs of the 1- and 3-stage devices were also observed to peak at a certain
incident power density and then fall off with further increasing the incident optical power.
This behavior was possibly related to the larger current and the resulting higher Ohmic
losses in series resistances. In contrast, the FF of the 5-stage device exhibited a monotonic
rise with increasing incident power. The FFs of the three devices were considerably lower
than the typical values (~60-70%) of TPV cells with bandgaps of 0.5-0.6 eV [5], but they
are reasonable for narrow bandgap (~0.2 eV) TPV cells with un-optimized structures.
87
38
350 one-stage one-stage
three-stage three-stage 36
300 five-stage five-stage
34
250
32
Voc (mV)
FF (%)
200
150 (a) (b) 30
100 28
50 26
0
0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35
Pinc (W/cm2) Pinc (W/cm2)
one-stage one-stage 3.5

1.2
three-stage three-stage
3.0
1.0 five-stage five-stage
2.5
Pmax (W/cm2)
0.8
2.0
 ()
0.6
(c) (d) 1.5
0.4
1.0
0.2 0.5
0.0 0.0
0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35
Pinc (W/cm2) Pinc (W/cm2)
Figure 4-6: (a) Open-circuit voltage, (b) fill factor, (c) maximum output power density
and (d) conversion efficiency as a function of incident power density for the three
devices at 300K.
The maximum conversion efficiencies at 300 K are 0.9% (1-stage), 2.5% (3-stage)
and 3.6% (5-stage) as shown in Figure 4-6(d). The 5-stage device attained the highest
power efficiency thanks largely to the efficient collection of photogenerated carriers. This
unambiguously verifies the advantage of multistage IC structures with thin individual
absorbers for narrow bandgap TPV cells. The main reason for the relatively low conversion
efficiency in the three devices was because the dark current was significant in such a
narrow band gap (~0.2 eV) structure. Other factors include the contact resistances, some
thermalization loss (20-27%), surface reflection (31%), as well as incomplete absorption
88
(~50%) due to insufficient thick total absorber (≤2.52 m). At lower illumination levels
(Pinc<5 W/cm2), the conversion efficiency of the 5-stage device was slightly lower than the
3-stage device due to the narrower bandgap and the higher thermal generation rate, as will
be given in Subsection 4.4.2. For example, at Pinc=3.5 W/cm2, the conversion efficiency
was respectively 0.94% and 0.88% for the 3- and 5-stage devices, although the Voc of the
5-stage device was somewhat higher than the 3-stage device (103 vs. 95 mV). In fact, the
conversion efficiencies of the two multistage devices can be further enhanced by increasing
the incident power, as the conversion efficiencies have not yet saturated even at 36 W/cm2.
This can be accomplished with built-in lenses on the device surface and by exploring the
photonic structure or metamaterial. In contrast, the conversion efficiency of the 1-stage
device dropped by about 16% after saturation, which is consistent with the trend of FF
with incident power. In addition to FF, the increased Ohmic losses at higher incident power
in the 1-stage device provided another mechanism for reducing the conversion efficiency
after saturation. In contrast, for the 3-stage device, the rapid increase of Voc overcame the
decrease of FF with increasing incident power, and the Ohmic loss in the 3-stage device
was lower than in the 1-stage device. Consequently, similar trends of conversion efficiency
and Voc were observed for the 3-stage device. Table 4-1 summarizes the PV performance
characteristics and related parameters for the representative devices from the three wafers.
These data collectively show the capabilities and advantages of multistage ICTPV devices,
and the limitation of the single-stage TPV devices.
89
Table 4-1: Summary of the PV performance and the related parameters of
representative devices (0.2×0.2 mm2) from the three ICTPV wafers at 300 K. The
maximum efficiencies shown in the table for the 3- and 5-stage devices are obtained
at a maximum incident power density of 36 W/cm2.
c (0) Jsc Jphmax Voc FF Pmax Maximum Rs

Device
(%) (A/cm2) (A/cm2) (mV) (%) (W/cm2)  (%) ()
1-stage 40 12.9 40.8 85 25 0.27 0.9 4.9
3-stage 76 12.2 15.7 271 28 0.91 2.5 4.6
5-stage 95 9.3 9.7 371 38 1.29 3.6 4.7
4.4 Extraction of some important performance related parameters
4.4.1 Voltage-dependent collection efficiency
In Figure 4-5(a), there is a common characteristic for the three devices, namely a
shift between the measured and ideal J-V curves. This shift is particularly striking for the
1-stage device, significantly reduces for the 3-stage device, and almost disappears for the
5-stage device. The implies that the collection efficiencies and the photocurrents in the
three devices are voltage-dependent, and the illuminated J-V curves do not comply with
the usual superposition principle [7]. This voltage-dependent characteristic has been
reported for solar cells made of Silicon [172-174], CdS/CdTe [171, 175-176], CdS/CdInSe2
[177-178] and GaAs [173]. In thses solar cells, the voltage-dependent characteristic mainly
arises from the variation of the electrical field in the depletion region when the applied
external voltage is changed. By comparison, the diffusion process plays a more important
role in ICTPV structures.
The voltage-dependent collection efficiency c (V) can be obtained through the
approach described in [171, 174, 178]. This approach relies on two assumptions: First, the
photocurrent density can be written as the Jphmax times c (V): Jph (V)= Jphmax·c (V).
90
Second, the dark current density is assumed to remain unchanged at different incident
power densities [171, 174, 178]. Applying this approach to the current three devices, the
c (V) can be expressed as:
𝐽2 (𝑉)−𝐽1 (𝑉)
𝜂𝑐 (𝑉) = (4-2)
𝐽2𝑝ℎ𝑚𝑎𝑥−𝐽1𝑝ℎ𝑚𝑎𝑥
where J1(V) and J2(V) are the current densities at two different incident power densities,
and J1phmax and J2phmax are the corresponding maximum photocurrent densities. For each
device at 300 K, four J-V curves were selected at incident power densities of 19, 13, 7
W/cm2 and the dark condition to extract c (V) as shown in Figure 4-7(a). As can be seen,
the extracted c (V) from different pairs of J-V data does not exactly overlap for the 1- and
3-stasge devices. This suggests that the dark current might change with the incident power
density, which can be partially explained by large number of photo-generated excess
carriers shortening the carrier lifetime. Another possibility was the small variation of
device temperature (<1 K according to the estimated thermal resistance for IC structures
[179] and incident power), which may affect the dark injection current contribution,
especially at high incident power densities. For this reason, the J-V pairs at relatively low
incident power densities were used to extract c (V) as shown in Figure 4-7(a). However,
this effect somehow becomes insignificant when the individual absorbers are thin, as
evidenced by the almost overlapped c (V) profiles with different pairs of incident power
densities for the 5-stage device. Another factor is the surface leakage due to imperfect
passivation and active surface stages on the etched sidewalls, which will be discussed in
Subsection 4.4.4. Note that the possible variations of the diffusion length due to the small
change of temperature (<1 K) under different incident power densities should be negligible,
since the QE would only differ by at most 0.15% with a 1 K deviation at 4.25 m as shown
91
Figure 4-3. The temperature variation for a larger size device might be larger under
intensive illumination, but still can be addressed with effective thermal dissipation through
a heat sink. For example, based on the previously extracted data for IC structures [179],
the specific thermal resistance (Rsth) for a device with side dimension of 1 mm is lower
than 100 Kcm2/kW. An incident power density of 36 W/cm2 would increase the device’s
temperature by at most 3.6 K (with effective heat conduction through the substrate to a heat
sink) compared to its temperature in the dark.
1.0 1.0
(a) (b)
0.8 0.8
5-stage 5-stage
0.6 0.6
c
c
0.4 3-stage 0.4 3-stage

19-7
19-dark
13-7 0.2
0.2 1-stage 1-stage
13-dark
0.0 0.0
-0.5 0.0 0.5 1.0 -0.5 0.0 0.5 1.0
Figure 4-7: (a) Voltage dependence of collection efficiency derived from Equation 4-
2 using four different pairs of J-V data at 300 K for the three devices. The numbers
in the legend indicate the incident power densities under different illumination levels.
(b) Average collection efficiency over the four pairs in (a).
For ease of comparison, the average of the four c (V) curves in Figure 4-7(a) is
plotted in Figure 4-7(b). As shown, the 5-stage device had the highest average c (V), while
the 1-stage device had the lowest average c (V) among the three devices. At zero bias, the
c (0) was 40%, 76% and 95% for the 1-, 3- and 5-stage devices, respectively. For the 1-
stage device, at least 80% of the photo-generated carriers were not collected at forward
bias (>0.1 V), as reflected by the small c (V) (<0.2). This small c (V) severely penalized
the fill factor and conversion efficiency as discussed in Subsection 4.3.4. The extracted c
92
(0) was substantially smaller than the theoretical projection (~60%) shown in Figure 4-
1(a), especially for the 1-stage device. This was likely caused by the shutting of surface
leakage as mentioned earlier. As shown in Figure 4-10, there is significant surface leakage
in dark condition especially in the 1-stage device. Likewise, under illuminated condition,
large number of photogenerated carriers could leak through the rough sidewalls, thus
reducing the collection efficiency. At this moment, why the 1-stage device had most
notable surface leakage is not fully understood, and it is worth exploring in the further
research.
4.4.2 Thermal generation rate and carrier lifetime
The relatively low conversion efficiencies (5%) in the three devices were
primarily due to the high dark current density associated with the high thermal generation
rate (gth) and a relatively short carrier lifetime () in narrow bandgap InAs/GaSb T2SL
absorbers. As will be described in Chapter 6, there is a simple and effective method to
extract thermal generation rate and carrier lifetime in IC structures. This method is
particularly suitable for multistage IC devices since their dark current densities usually
exhibit clear and large linear regions at reverse bias [158]. In this method, the gth is first
found from the intercept of the linear fitting of dark current at large reverse bias [158]. The
carrier lifetime then can be calculated from the gth based on the equation:
𝑛𝑖2
𝑔𝑡ℎ = (4-3)
𝑁𝑎 𝜏
where ni is the intrinsic carrier concentration and Na is the p-type doping concentration.
The intrinsic carrier concentration is given by:
93
2𝜋𝑘𝑏 𝑇 1.5
𝑛𝑖 = 2 ( ) (𝑚𝑒 𝑚ℎ )0.75 𝑇 1.5 𝑒 −𝐸𝑔⁄2𝑘𝑏𝑇 (4-4)
ℎ2
where me and mh are the electron and hole effective masses, taken to be 0.03m0 (m0 is
electron mass) and 0.4m0, respectively. Based on Equation 4-4, the calculated intrinsic
carrier concentrations at 300 K were 1.15×1016 (1- and 3-stage) and1.44×1016 (5-stage) cm-
3
. From the linear fitting of dark current density, the thermal generation rate at 300 K was
found to be 3.81×1022, 4.55×1022 and 8.35×1022 cm-3·s-1 for the 1-, 3- and 5-stage devices,
respectively. Based on Equation 4-3, the carrier lifetime at 300 K was calculated to be 134
(1-stage), 113 (3-stage) and 89 (5-stage) ns. Compared to the 1- and 3-stage devices, the
shorter carrier lifetime and higher thermal generation rate in the 5-stage device are ascribed
to its narrower bandgap (214 meV vs. 225 meV) and poorer material quality (with
somewhat more defects and larger perpendicular lattice mismatch). In addition, both gth
and  are very strong functions of temperature in the three devices, as shown in Figure 4-
8. The sharp decrease of carrier lifetime with temperature is likely due to the growing
prevalence of Auger processes linked with bandgap narrowing of the SL absorber at high
temperatures. The thermal generation rate in the three devices is many orders of magnitude
higher than those in solar cells. For example, for a crystalline Si solar cell, the Na and  at
300 K are normally in the ranges of 1015-1016 cm-3 [7] and 0.1-1 ms [180-181], respectively.
Therefore, the gth is estimated to be 2.25×107-2.25×109 cm-3·s-1, about 13-15 orders of
magnitude lower than that in the current three ICTPV devices. Evidently, reducing the gth
either by increasing carrier lifetime or cooling down the device, even by one order of
magnitude, will boost the conversion efficiency of ICTPV devices.
94
Temperature (T)
340320300 280 260 240 220 200
700 1024
550
400 1023
Carrier lifetime  (ns)
gth (cm-3s-1)
250 1022
1021
1-stage 1020
85
70 2-stage
55 3-stage 1019
3 4 5
1000/T (K-1)
Figure 4-8: The thermal generation rate and minority carrier lifetime for the 1-, 3-
and 5-stage devices at high temperatures.
4.4.3 Series resistance
As identified in Subsection 4.4.1, the photocurrents in the three devices were
voltage dependent. This voltage-dependent characteristic creates significant complexities
when extracting the series resistance Rs using illuminated J-V curves. Even with a relatively
weak voltage dependence of photocurrent, the series resistance extracted based on a
generalized Suns-Voc method could be somewhat overestimated [182]. Hence, to avoid the
complexity caused by the voltage-dependent photocurrent, the series resistance of the three
devices were extracted from the dark condition based on the following equation [174, 178]:
𝑅𝑠 = 𝑙𝑖𝑚𝑖𝑡(𝑑𝑉 ⁄𝑑𝐼 ) (4-5)

1⁄𝐼 →0
Figure 4-9 shows the plots of dV/dI under dark conditions, as well as the extracted series
resistances for the three devices. The Rs was acquired by finding the intercept of dV/dI vs.
1/I. The extracted series resistances were respectively 4.9, 4.6 and 4.7  for the 1-, 3- and
5-stag devices, which were close to each other. This implies that the series resistances in
95
the three devices were mainly from the contacts and wires, while the resistances between
cascade stages can be ignored due to the smooth carrier transport in the type-II broken-gap
heterostructure.
12
one-stage, Rs=4.9 
11
three-stage, Rs=4.6 
10 five-stage, Rs=4.7 
dV/dI () 9
4
0 5 10 15 20 25 30 35 40
I -1 (A-1)
Figure 4-9: dV/dI data to obtain series resistance at 300 K, which was found from the
intercept of dV/dI.
4.4.4 Surface leakage
Surface leakage has been a long-standing issue for III-V based, especially T2SL
based, infrared devices [183]. Various passivation techniques were developed for T2SL
detectors with varying degree of reliability and effectiveness [184]. In principle, under dark
condition, the effect of surface leakage can be quantified through the linear fitting between
P/A and 1/R0A [185]:
1 1 1 𝑃
=( ) + ( ) (4-6)
𝑅0 𝐴 𝑅0 𝐴 𝑏𝑢𝑙𝑘 𝜌𝑠𝑤 𝐴
where sw is the device sidewall resistivity, and P and A are the device area and perimeter.
Figure 4-10 shows the size dependence of R0A, along with the sw obtained through above
fitting for the three devices at 300 K. For the 200×200 m2 devices, the R0A values were
96
0.02 (1-stage), 0.11 (3-stage) and 0.18 .cm2 (5-stage). Hence, surface leakage contributed
to 74%, 62% and 48% of the total dark current for the 1-, 3- and 5-stage devices,
respectively. For devices with larger sizes, the surface leakage affects the dark current to a
lesser degree. However, the larger size device has a relatively low R0 (e.g. only 26  for
the 0.5×0.5 mm2 device from the 1-stage wafer at 300 K), which makes it difficult to
accurately extract the device QE. Hence, to optimize the tradeoff, the 0.2×0.2 mm2 devices
with comparatively high R0 in the three wafers were selected for device analysis.
14
1/R0A (−.cm-2)
70 12
10
60 8
1/R0A (−cm-2)
6
50 4
100 200 300
40 P/A (cm-1)
1-stage sw=5.1 cm
30
3-stage sw=34.5 cm
20 5-stage sw=76.9 cm
10
0
50 100 150 200 250 300 350
P/A (cm-1)
Figure 4-10: Size dependent R0A for the three devices at 300 K. The sidewall
resistivity was smallest for the one-stage device.
In this chapter, rigorous experimental justifications of the advantage of multistage
ICTPV devices over conventional single-absorber devices are presented. This is done by a
comparative study of three narrow bandgap (~0.2 eV) TPV devices with a single-absorber
and multistage IC structures. It is shown that the performance of a single-absorber TPV
cell with T2SL absorbers is mainly limited by the small collection efficiency associated
with a relatively short diffusion length (1.5 m at 300 K). Instead, multistage IC structure
97
is proven to be capable of overcoming the diffusion length limitation and achieving a
collection efficiency of about 100% for photogenerated carriers. Consequently, the open-
circuit voltage, fill factor and conversion efficiency are greatly improved compared to the
single-absorber TPV structure. At current stage, although the demonstrated room-
temperature conversion efficiency (3.6%) is relatively low, there is still great room for
further improvement. Possible ways to improve the efficiency include increasing the total
absorber thickness, adding an anti-reflection coating onto the surface, attaching a back
reflector, as well as reducing the contact resistance. The fundamental limitation of a high
dark current in narrow bandgap absorbers can be overcome by applying an even stronger
optical illumination. This will increase the conversion efficiency since the  in multistage
ICTPV devices has not yet saturated as shown in Figure 4-6(d). Alternatively, these narrow
bandgap TPV devices can be cooled down to lower temperatures with substantially reduced
dark current density and increased power efficiency for applications such as in space (e.g.
Jupiter and Saturn missions) where the environment temperature is well below 300 K.
98
5 Chapter 5: Interband cascade thermophotovoltaic devices with more
stages
Unlike the Esaki tunnel junctions routinely used in multijunction solar cells [13,
14], type-II broken-gap heterostructures are used to connect adjacent cascade stages in IC
structures so that the interband tunneling is smooth and the electrical resistances between
stages are negligible. As often implemented in ICLs, many stages (>20) can be
concatenated together without impacting carrier transport. Hence, for ICTPV cells, many
IC stages are desirable to maximize the absorption of incident light and produce a high
open-circuit voltage for optimizing power efficiency. However, in contrast to ICLs where
the light is generated inside the active cascade stages, each stage in an ICTPV cell sees a
different intensity due to the absorption in preceding stages. Consequently, to satisfy the
current match condition between cascade stages for optimized device operation, the
absorber thickness in the optically deeper stages is increased based on the absorption
coefficient. In practice, if there are many stages in an ICTPV cell, the deviation of exact
current match condition due to the variation of material parameters can be significant. Also,
ICTPV cells are relatively complex structures that are very vulnerable to the instable
growth conditions, thus the material quality may differ vastly from structure to structure.
In this chapter, the effects of current mismatch and material quality will be identified and
quantified in four ICTPV devices with different number of stages and absorber thickness.
In addition, in Chapter 4, the better device performance in the 5-stage compared to
the 1- and 3-stage devices implies that IC structure with more stages should be preferred.
This inference is also in accordance with other experimental data of ICTPV cells [157, 182,
186-188] and the theoretical projection in Chapter 3. Hence, another purpose of this chapter
99
is to examine this inference with ICTPV devices with many stages. Note that these ICTPV
cells were designed for achieving a better understanding of the underlying physics rather
than reaching optimized device performance. At current stage, the conversion efficiencies
of ICTPV cells do not reach respected levels, and they are not comparable with those
achieved from the TPV cells with relatively wide bandgaps [36-42], as shown in Table 5-
1. This is because the conversion efficiency of an ICTPV device is primarily limited by a
significantly high dark saturation current density J0 associated with the narrower bandgap
and a short carrier lifetime. In Chapter 4, it has been shown that although the IC structure
is able to overcome the limitations of a short diffusion length and low absorption
coefficient in conventional single-stage TPV cells, the issues of low fill factor and voltage
efficiency that result from the high J0, remain in narrow bandgap ICTPV cells even under
monochromatic illumination with high incident power density, as shown in Table 5-1.
Table 5-1: Summary of ICTPV devices that have been reported so far.
Temperature Illumination Pinc

Nc Eg (eV) Voc (V)  (%) Ref.
(K) Source (W/cm2)
Blackbody @
7 80 0.24 1.11 0.67 NA 100
1323 K
Blackbody @
7 80 0.31 1.68 0.23 4.3 189
1323 K
ICL emitting
7 300 0.24 0.65 19 2.1 190
@ 4.3 m
ICL emitting
3 300 0.23 0.18 7 NA 157
@ 4.3 m
ICL emitting
3 300 0.39 0.80 130 9.6 182
@ 2.81 m
ICL emitting
5 300 0.23 0.37 36 3.6 187
@ 4.2 m
ICL emitting
6 300 0.23 0.52 21 4.1 191
@ 4.2 m
100
5.2 Device structure, growth and fabrication
The four structures were grown using GENxplor MBE system on nominally
undoped p-type GaSb (001) substrates. The first two structures have six and seven stages
and were grown earlier. The other two structures have substantially increased stages
(sixteen and twenty-three) and were grown a year later after the system maintenance.
Hence, the growth conditions and material qualities can be somewhat different between the
two sets of structures. The absorbers in the four structures were made of InAs/GaSb T2SLs
and each period of the SL consist of four layers: InSb (1.2 Å), InAs (20.5 Å), InSb (1.2 Å)
and GaSb (25.1 Å). The purpose of including the two InSb layers is to balance the tensile
strain of the InAs layer [168]. The absorbers in the four structures were p-type doped to
2.6×1016 cm-3. The schematic layer diagram of the four structures are shown in Figure 5-1,
and the individual absorber thicknesses are presented in Table 5-2. As can be seen, the
individual absorbers in the 16- and 23-stage structures are much thinner than in the 6- and
7-stage devices. Conversely, the total absorber thicknesses in the 16- and 23-stage
structures are thicker compared to those in the 6- and 7-stage ones. The electron and hole
barriers in the four structures were identical to those in the three devices described in
Chapter 4. After the MBE growth, the wafers are processed into square mesa devices with
dimensions ranging from 50 to 1000 m by using standard contact UV photolithography
and wet-chemical etching. A RF-sputter deposited two-layer passivation (Si3N4 then SiO2)
is used for minimizing pin holes and improving overall stress management, and then the
Ti/Au layers are sputter deposited for top and bottom contacts. Finally, the devices were
mounted on heat sinks and wire bonded for characterization.
101
Figure 5-1: Schematic layer structure of the four TPV devices with six, seven, sixteen
and twenty-three stages.
Table 5-2: Individual and total absorber thicknesses for the four IC TPV structures.
Device Individual absorber thickness (nm) dtotal (m)
6-stage 360/403.2/456/523.2/619.2/758.4 3.12

7-stage 307.2/336/374.4/417.6/480/556.8/662.4 3.13
144/153.6/158.4/168/177.6/187.2/196.8/211.2/225.6/240/259.2/283.2
16-stage 3.90
/312/345.6/388.8/446.4
96/100.8/105.6/110.4/115.2/120/124.8/129.6/134.4/139.2/144/148.8/
23-stage 3.87
158.4/168/172.8/182.4/196.8/206.4/220.8/240/259.2/283.2/312
5.3 Energy conversion efficiency
The energy conversion efficiency  of the four TPV structures was investigated
under the illumination from an IC laser. The narrow emission spectrum of the IC laser is
analogous to a selective emitter that would be included in a TPV system to reduce the
thermalization and below-bandgap losses. During the experiment, the laser was cooled to
102
80 K and continuously emitted at a wavelength near 4.2 m (photon energy is 295 meV)
as shown in the inset within Figure 5-2(a). The output power of the laser can be controlled
by adjusting the injection current, thereby the performance of the four devices was
investigated under different incident power densities. Figure 5-2(a) shows the measured
illuminated J-V characteristics at 300 K for representative 200×200 m2 devices from the
four wafers. The incident power density of 17 W/cm2 was assessed through the connection
between quantum efficiency and short-circuit current density Jsc, as expressed by Equation
4-1. As can be seen in Figure 5-2(a), the short-circuit current density decreases with
number of stages Nc, primarily due to reduced optical absorption in individual stages with
thinner absorbers. Conversely, the open-circuit voltage increases with the number of
stages, since it is proportional to Nc when the individual stages are connected in series, as
stated by Equation 3-11. For example, at T=300 K and Pinc=17 W/cm2, the Jsc was 4.4, 3.2,
1.3 and 1.0 A/cm2, while the Voc was 350, 518, 910 and 1461 meV for the 6-, 7-, 16- and
23-stage devices, respectively. The trade-off of Jsc for Voc with increasing the number of
stages can in principle be beneficial for improving the conversion efficiency in many cases,
according to the previous experimental results [157, 182, 186-188]. However, such benefit
may not always be demonstrated, as will be discussed in the analysis of the characteristics
of the current four devices.
103
4 6-stage
4

6-stage ICL
emission 7-stage

spectrum 3 16-stage
3 7-stage 23-stage
3.5 4.0 4.5 5.0
2 Wavelength (m)
2
16-stage (b)
(a) 1
1
23-stage
0 0
-0.5 0.0 0.5 1.0 1.5 0 5 10 15 20
Voltage (V) Pinc (W/cm2)
Figure 5-2: (a) Illuminated current density-voltage characteristics for the

representative 200×200 m2 devices from the four wafers at 300 K and at an incident
power density of 17 W/cm2. The inset shows the emission spectrum of the IC laser
used as the illumination source, (b) Conversion efficiency as a function of incident
power density for the four devices at 300 K.
Figure 5-2(b) shows the energy conversion efficiencies as a function of incident
power density for the four devices at 300 K. As shown, the four devices can be arranged
as 7-, 6-, 23- and 16-stage devices according to their  values, from best to worst. For
example, at the maximum incident power density (~21 W/cm2) available from the
illumination of the IC laser, the  is 3.5%, 4.1%, 2.7% and 3.3% for the 6-, 7-, 16- and 23-
stage devices, respectively. As theoretically illustrated in Chapter 3, the efficiency of
ICTPV cells should monotonically increase with the number of stages. This is because the
particle conversion efficiency (part), a more appropriate figure of merit for ICTPV devices,
is enhanced as the number of stages increases [169-170]. However, the results of the
current four devices indicate that the device performance in terms of  is better with fewer
cascade stages (6 and 7) than with more stages (16 and 23. This goes counter with the
theoretical forecasting in Chapter 3 and the previous experimental results [157, 182, 186-
188]. Nevertheless, the  was higher with more stages for devices grown in the same
104
campaign. For example, the device performance is better for the 7-stage compared to the
6-stage, and for the 23-stage compared to the 16-stage. Give that the four devices have
nominally identical absorber and barrier structures, what causes the different device
performances between the two sets? One possible factor is that the current mismatch is
more significant in the 16- and 23-stage devices compared to the 6- and 7-stage devices.
Another possible cause is that the 16- and 23-stage devices have poorer material quality
than the 6- and 7-stage devices, since the two sets of structures were grown in different
campaigns. In the following sections, the two possible factors will be inspected and
quantified through the analysis of detailed device characteristics such as dark current
density, carrier lifetime and quantum efficiency.
5.4 Device characterization and analysis
5.4.1 Dark current density and carrier lifetime
The dark current density-voltage (Jd-V) characteristics of the four devices were
measured using a Keithley 2636A source meter. During the measurement, the device was
put in a cryostat for temperature control between 78 to 340 K, and a top copper shield was
used to block background radiation from the environment. The measured dark current
densities at 300 K for the representative 200×200 m2 devices from the four wafers are
shown in Figure 5-3(a). As shown, the Jd decreases with number of stages due to the
reduced thermal generated carriers in thinner individual absorbers [141]. Also, the Jd in the
four devices is orders of magnitude higher than in conversional solar cells made of Si and
GaAs, which severely limits the device performance of these TPV cells. This is mainly due
to their narrow bandgaps that are 0.22-0.25 eV at 300 K as estimated from the 100% cutoff
105
wavelength of the quantum efficiency spectra [see Figure 5-4(a)]. From the measured dark
current, the carrier lifetime (), an important indicator of material quality, can be extracted.
As will be described in Chapter 6, a simple and effective method to extract carrier lifetime
is to apply a linear fit of the dark current density at large reverse bias and first obtain the
thermal generation rate gth. This approach is particularly useful for multistage IC devices
since their dark current densities usually have a large linear region under reverse bias, as
shown in Figure 5-3(b) for the four TPV devices. There is an explicit linear relationship
between current density and voltage at reverse bias starting from -2 V. The linear fittings
of current density with good accuracy from -4 to -2 V are indicated by the dashed lines in
Figure 5-3(b). Based on Equation 6-4, the thermal generation rate at 300 K acquired from
the intercept of the linear fitting is 6.6×1022, 4.3×1022, 9.6×1022 and 7.9×1022 cm-3s-1 for the
6-, 7-, 16- and 23-stage devices, respectively. The shunt resistance obtained from the slope
of the linear fitting is 10547 (6-stage), 21258 (7-stage), 29294 (16-stage) and 63459  (23-
stage).
0.0
102 6-stage
-0.2 23-stage
Dark current density (A/cm2)
7-stage
101 16-stage -0.4 e
23-stage 16-stag
-0.6
100 ge
7-sta
-0.8 (b)
T=300 K
10-1 -1.0
e
(a) -1.2 tag
10-2 6-s solid: measurement
dashed: linear fitting
-1.4
10-3
-4 -3 -2 -1 0 1 2 -4 -3 -2 -1 0
Voltage (V) Votlage (V)
Figure 5-3: (a) Dark current density for the representative 200×200 m2 devices from
the four wafers at 300 K, (b) Linear fitting (dashed lines) of dark current density at
reverse voltage for the four devices at 300 K.
106
With the extracted gth, the minority carrier lifetime can be calculated according to
Equation 4-3. The carrier lifetime is determined by the comprehensive effect of the
radiative, Auger and SRH processes. Usually, based on experimental results in literature
[158, 192-193], Auger and SRH processes are dominant in InAs/GaSb T2SLs. The intrinsic
carrier concentration at 300 K is calculated to be 1.21×1016 (6-stage), 9.9×1015 (7-stage),
8.3×1015 (16-stage) and 7.6×1015 (23-stage) cm-3, according to Equation 4-4. Finally, based
on Equation 4-3 and the obtained gth values, the extracted carrier lifetime at 300 K is 86,
88, 28, 28 ns for the 6-, 7-, 16- and 23-stage devices, respectively. Compared to the 16-
and 23-stage devices, the longer carrier lifetime in the 6- and 7-stage devices suggests their
better material quality. This agrees with higher activation energies Ea (213 and 217 eV
between 200 and 340 K) for the 6- and 7-stage devices than that (204 and 207 eV) for the
16- and 23-stage devices. The activation energies were extracted from the temperature
dependence of the zero-bias resistance. These values of Ea are 50%-100% of the zero-
temperature bandgap values (~ 275-302 meV), which implies a non-negligible contribution
of the SRH process to the dark current. The variations of material quality and the
corresponding contributions to the SRH process among the four TPV wafers result in
different carrier lifetimes, which ultimately affects the TPV device performance that will
be quantified in Section 5-5.
5.4.2 Quantum efficiency and current mismatch
In the quantum efficiency measurement, a fourier transform infrared spectrometer
(FTIR) was used to measure the relative spectra response. The calibrated QE spectrum was
obtained by measuring the device’s photocurrent, while it was illuminated by chopped
radiation from a standard blackbody source (800 K). The measured QE spectra of the four
107
devices at 300 K are shown in Figure 5-4(a). The 100% cutoff wavelength where the QE
fast turns on is 5.6, 5.3, 5.1 and 5.0 m, corresponding to a bandgap of 221, 234, 243 and
248 meV at 300 K for the 6-, 7-, 16- and 23-stage devices, respectively. The bandgap
difference results from variations in MBE growth conditions, although the SL absorbers in
each device were designed to have identical compositions and period. The difference is
more outstanding between devices grown in different campaigns. As shown in Figure 5-
4(a), the QE decreases with number of stages due to the reduced optical absorption in in
thinner individual absorbers. For example, at T=300 K and =4.2 m, the QE is 6.46%,
5.41%, 2.31% and 1.57% for the 6-, 7-, 16- and 23-stage devices, respectively. Figure 5-
4(b) shows the measured bias dependence of the QE at 300 K and at the same wavelength.
As shown, the devices with more stages and thinner absorbers tend to have weaker bias
dependences of QE. The QEs of the 6-, 7- and 16-stage devices slightly increase with
reverse bias, while the QE of the 23-stage device is nearly a constant value. Specifically,
the QE changes from 6.46%, 5.41%, 2.31% and 1.57% to 7.03%, 5.66%, 2.37% and 1.58%,
while the reverse bias is increased from 0 mV to -700 meV for the 6-, 7-, 16- and 23-stage
devices, respectively. The moderate degree of bias dependence for the QEs is due to the
relatively thin individual absorbers compared to the conventional TPV structure with a
single thick absorber. This leads to the unique advantage of high collection efficiency of
photogenerated carriers, as described in Chapter 4.
108
7.5
12 6-stage 7.0
7-stage 6-stage

10 6.5 T=300 K

16-stage
6.0 =4.2 m
23-stage
8 5.5
(a) T=300 K 7-stage
zero bias 5.0
6 2.4
2.2 16-stage
4
2.0 (b)
2 1.8
23-stage
1.6
0 1.4
2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 0 100 200 300 400 500 600 700
Wavelength (m) Bias (mV)
Figure 5-4: (a) Quantum efficiency spectra of the four devices at 300 K and (b) Bias
dependence of quantum efficiency for the four devices at 300 K and at the wavelength
of 4.2 m.
In theory, provided that the absorption coefficient () and diffusion length (L) are
known, the effective QE in each stage of an IC device can be calculated from Equation 2-
5 in the diffusion limited case. At 300 K, the measured absorption coefficient at 4.2 m is
2984, 2643, 2334 and 2200 cm-1 for the 6-, 7-, 16- and 23-stage devices, respectively.
Based on Equation 2-5, the calculated effective QE at 4.2 m in each stage of the four
devices is shown in Figure 5-5(a). In the calculation, the diffusion length was assumed to
be 1.5 m for the 6- and 7-stage devices, while it was taken to be 0.7 m for the 16- and
23-stage devices. These values of L were adopted to achieve close agreement with the
experimental results. As can be seen, the calculated effective QEs of the 7-stage device are
nearly equal in each stage and are quite close to the measured device QE. Contrarily, the
calculated effective QEs of the 6-, 16- and 23-stage devices are mismatched between
stages. In this scenario, as will be described in Chapter 7, an electrical gain will be delivered
across the device to ensure current continuity and will enhance the device’s QE to the
average value over all stages [194]. On average, the effective QE is 6.65%, 2.42% and
1.63% for the 6-, 16- and 23-stage devices, respectively. These values are well matched
109
with the measured device QEs with an error less than 5%. This also indirectly verifies the
appropriateness of the values used for the diffusion lengths for these devices. Compared to
the 16- and 23-stage devices, the longer diffusion length for the 6- and 7-stage devices
agrees with their longer carrier lifetime. In addition, the mismatch of effective QE is less
significant in the 6-stage device than in the 16- and 23-stage devices. For example, the
minimum (maximum) of the effective QEs is 6.39% (6.90%), 2.20% (2.69%), 1.38%
(1.95%) in the 6-, 16- and 23-stage devices, corresponding to a mismatch of 8% (6-stage),
22% (16-stage), 41% (23-stage) in their QEs.
7.0
Incident power density (W/cm2)

6-stage 6-stage
6.5 20
7-stage 7-stage
6.0 (a) 16-stage
16-stage
Effective QE (%)
23-stage 15
5.5 23-stage
=4.2 m
5.0
10
2.5
(b)
2.0 5
1.5
1.0 0
0 5 10 15 20 0 50 100 150 200 250 300 350 400
Stage number IC laser current (mA)
Figure 5-5: (a) Calculated effective quantum efficiency based on Equation 2-5 in each
stage of the four devices, (b) Calculated incident power density vs IC laser current
based on Equation 4-1 for the four devices.
The direct result of current mismatch in these multistage devices is the reduction of
their photocurrents, which are decided by the stage with the minimum effective QE. From
Figure 5-5(a), the photocurrent was determined by the last stage in the 6-stage device, while
it was decided by the first stage in the 16- and 23-stage devices. This statement is tenable
when the photocurrent is dominant in the device under intense illumination from the IC
laser, which can be validated through the assessed incident power densities on the four
110
devices. A simple and effective method to assess Pinc is based on the relationship between
Jsc and QE (at laser emission wavelength), as expressed by Equation 4-1. Note that, the QE
in Equation 4-1 should be the minimum effective QE in the individual stages. According
to this equation, the calculated Pinc as a function of the IC laser current is shown in Figure
5-5(b). As can be seen, the calculated values of Pinc onto the four devices are close to each
other. This is anticipated since they were illuminated by the same IC laser, even with some
possible experimental uncertainties due to alignment. The good consistency of the Pinc also
validates the above-mentioned statement that there was no electrical gain in the four
devices when they were illuminated by the IC laser. Based on this commonality, the effect
of current (or effective quantum efficiency) mismatch between stages on device
performance will be quantified in Subsection 5.5.2.
5.4.3 Collection efficiency of photogenerated carriers
As described in Chapter 4, a special feature of some ICTPV devices is that the
photocurrent is voltage dependent. But this feature is likely to be less notable for devices
with thinner individual absorbers and more stages. It would be interesting to examine this
feature in the 16- and 23-stage devices which have even more stages and thinner individual
absorbers. This can be done by comparison between the 100% collected and the measured
J-V curves. At T=300 K and Pinc=17 W/cm2, the 100% collected and the measured J-V
curves for the four devices are shown in Figure 5-6(a). As mentioned in Chapter 4, the
100% collected J-V curve refers to the ideal case where the photogenerated carriers are
completely collected. It can be plotted in the same manner as in [171] and is the
superposition of the dark current density and the maximum photocurrent density Jphmax.
The magnitude of Jphmax is the difference between the saturated current densities under dark
111
and illuminated conditions. As can be seen in Figure 5-6(a), there are noticeable shifts
between the ideal and the measured J-V curves for the 6- and 7-stage devices. This means
that the photocurrents (or the collection efficiencies) in the two devices are voltage
dependent. In contrast, for the 16- and 23-stage devices, the ideal and the measured J-V
curves almost overlap with each other. This indicates that the collection efficiencies in the
two devices are close to unity as well as being voltage independent.
The collection efficiency c in the four devices can be extracted based on Equation
4-2 whose validity relies on two assumptions, as mentioned in Subsection 4.4.1. For each
of the four devices, the J-V data at four different illumination levels were chosen for
subtraction to make a fair comparison. It was found that, although not presented here, the
extracted c using different J-V data pairs overlap each other. This verifies the assumption
that the dark current density and collection efficiency remain almost unchanged at under
different illumination levels. In particular, the extracted c based on Equation 4-2 using J-
V data at incident power densities of 7 and 17 W/cm2 is shown in Figure 5-6(b). As can be
seen, the c in the 6- and 7-stage devices decreases dramatically with forward voltage. In
contrast, the c is always close to unity in the 16- and 23-stage devices throughout the
forward voltage range of interest. At this moment, this difference of c between ths two
sets of devices is not fully understood. Presumably, one factor is that the photocurrent in
the 16- and 23-stage devices is determined by the first stage [Figure 5-5(a)] with an
absorber that is much thinner than the one in the last stage of the 6- and 7-stage devices.
This factor along with more stages (to share forward voltage) could contribute to the nearly
100% collection efficiency in the 16- and 23-stage devices. This phenomenon may need
further investigation in the future.
112
1.0
4 6-stage
solid: measured

0.8
Collection efficiency
dahsed: 100% collected
3 7-stage
0.6 6-stage
7-stage
2 T=300 K 16-stage
(a) 0.4
16-stage 23-stage
1 0.2 (b)
23-stage
0 0.0
-0.5 0.0 0.5 1.0 1.5 -0.5 0.0 0.5 1.0
Figure 5-6: (a) The measured and the 100% collected J-V curves for the four devices
at 300 K and at the incident power density of 17 W/cm2, (b) Extracted collection
efficiency at 300 K based on Equation 4-2 using J-V data under incident power
densities of 7 and 17 W/cm2 for the four devices.
5.5 Quantification of the effects of the performance limiting factors
5.5.1 Effect of collection efficiency
In the preceding section, the 16- and 23-stage devices are identified to have poor
material quality and more severe current mismatch that that the 6- and 7-stage devices. On
the other hand, the collection efficiency was higher in the 16- and 23-stage devices
compared to the 6- and 7-stage devices. Table 5-3 summaries the three factors and
characteristics, and some important performance-related parameters at 300 K. In this
section, the effects of the three performance limiting factors will be quantified.
Table 5-3: Summary of device characteristics and some important performance-

related parameters for the four devices at 300 K.
Current c-Voltage
Eg (meV) ni (cm-3) gth (cm-3s-1) Rshunt ()  (ns) L (m) 
mismatch dependence
6-stage 221 1.21×1016 6.6×1022 10547 86 1.5 3.5% mild substantial
7-stage 234 9.9×1015 4.3×1022 21258 88 1.5 4.1% none substantial
16-stage 243 8.3×1015 9.6×1023 29294 28 0.7 2.7% severe insensitive
23-stage 248 7.6×1015 7.9×1023 63459 28 0.7 3.3% severe insensitive
113
Among the three factors, the effect of voltage dependent collection efficiency is
simplest to quantify. This can be done through a comparison between the measured  and
the ideally collected case, as shown in Figure 5-7. As shown, at the maximum incident
power density, the  was 4.4% and 4.6% in the ideal case for the 6- and 7-stage devices,
respectively. This corresponds to a 0.9% (6-stage) and 0.5% (7-stage) increase relative to
the actual measured values. The more significant increase for the 6-stage device is due to
the lower collection efficiency than in the 7-stage device. Also, the increase of  was less
appreciable at the lower incident power density. This occurs because the operating voltage
at the maximum output power was smaller at the lower incident power density. From
Figure 5-6(b), the collection efficiency at the operating voltage is higher for the lower
incident power density. For example, at Pinc=17 W/cm2, the  was increased from the
measured 3.1% and 3.7% to the ideal 3.8% and 4.1%, corresponding to a 0.7% and 0.4%
increase for the 6- and 7-stage devices, respectively.
5
6-stage
4 7-stage
3
 (%)
1 solid symbol: measured

open symbol: 100% collected
0
0 5 10 15 20
Pinc (W/cm2)
Figure 5-7: Comparison of the measured  and the ideal  in the 100% collected case
at 300 K for the 6- and 7-stage devices.
114
5.5.2 Effect of current mismatch
As for the current mismatch, it is commonly recognized as a serious problem in PV
arrays. For example, it can even cause localized heating of the cell and possible cell
damage, which is known as hot-spot heating [195-196]. By comparison, although current
mismatch between stages is significant in the 16- and 23-stage devices, but far from being
able to cause any substantial damage or heating issues in a single stage when under intense
illumination. The direct negative impact of current mismatch in ICTPV devices is the
reduction of photocurrent. According to Equation 2-5, current mismatch in an IC structure
can result from the deviation of either the absorption coefficient or diffusion length from
the original reference values that were used to design current-matched absorbers.
Comparatively, the deviation of  is more prone to occur in practice and has a greater
impact on the calculated effective QE. Hence, here only the deviation of  will be
considered. In addition, the voltage dependence of collection efficiency in the 6- and 7-
stage devices should not be ignored. In this regard, the effect of current mismatch can be
quantified by decoupling the photocurrent and dark current densities. Proceeding in this
way, the illuminated J-V relation can be expressed as:
𝐽 (𝑉) = 𝐽𝑠𝑐 𝜂𝑐 ⁄𝜂𝑐 (0) − 𝐽𝑑 (𝑉) = 𝑃𝑖𝑛𝑐 𝑄𝐸 𝜂𝑐 ⁄𝜂𝑐 (0) − 𝐽𝑑 (𝑉) (5-1)
where c is shown in Figure 5-6(b) and c (0) is the collection efficiency at zero voltage.
As previously emphasized, the QE in Equation 5-1 should be the minimum effective QE
in individual stages and can be calculated from Equation 2-5. For direct connection to
actual devices, the Jd (V) in Equation 5-1 was replaced by the experimental data for the
four devices. With these specifications, the effect of the deviation of  and consequential
current mismatch will only be embodied in Jsc and QE in Equation 5-1.
115
The calculated Jsc and  as functions of  based on Equation 5-1 are shown in
Figure 5-8. In the calculation, the incident power density was taken to be 17 W/cm2, and
the diffusion length was assumed to be 1.5 m for the 6- and 7-stage devices and 0.7 m
for the 16- and 23-stage devices. The kinks in the calculated Jsc and  curves correspond
to the condition where the effective QE is perfectly matched between stages. This occurs
at an  of 2687 (6-stage), 2721 (7-stage), 2849 (16-stage) and 3061 cm-1 (23-stage). As can
be seen in Figure 5-8, the Jsc and  of the 16- and 23-stage devices peak at the current-
matched condition, while the Jsc and  in the 6- and 7-stage devices slightly increase when
 passes the current-matched condition with further increases. This is because the total
absorbers in the 6- and 7-stage devices are relatively thin so that the higher absorption
coefficient will increase absorption of photons and enhance the photocurrent. In contrast,
the total absorbers of the 16-and 23-stage devices are much thicker than the 6- and 7-stage
devices, so the light attenuation (and thus the current-mismatch) is more dominant in the
optically deeper stages. The circles in Figure 5-8 represent the calculated Jsc and  with the
measured . As can be seen, the 16- and 23-stage devices depart far more from the current-
matched condition than the 6- and 7-stage devices. At the current-matched condition, the
calculated  is 3.0%, 3.9%, 3.4% and 4.5% for the 6-, 7-, 16- and 23-stage devices,
respectively. This corresponds to a difference of 0.1% (6-stage), 0.2% (7-stage), 1.0% (16-
stage) and 1.7% (23-stage) compared to the actual measured . The impact of current
mismatch is comparable at different incident power densities. For example, at Pinc=21
W/cm2, the calculated  at the current-matched condition is 3.43%, 4.29%, 3.85%, 5.08%,
corresponding to a difference of 0.11%, 0.21%, 1.1%, 1.84% compared to the actual
obtained  for the 6-, 7-, 16- and 23-stage devices, respectively.
116
 (cm-1)
2000 2500 3000 3500 4000
6-stage
Jsc (A/cm2)
3
7-stage
16-stage
23-stage
1.5
1.0 (a)
4.5
Pinc=17 W/cm2
4.0
3.5
 (%)
3.0
6-stage
2.5 7-stage
16-stage
2.0 23-stage (b)
2000 2500 3000 3500 4000

 (cm-1)
Figure 5-8: Calculated (a) short-circuit current density and (b) conversion efficiency
based on Equation 5-1 as a function of absorption coefficient at incident power density
of 17 W/cm2 for the four devices.
5.5.3 Effect of material quality
Lastly, regarding the effect of material quality, it can be quantified through the variation of
carrier lifetime , an important parameter for material quality. The variation of  brings
corresponding variations of thermal generation and dark saturation current density [197],
which can significantly affect the fill factor and open-circuit voltage [197], consequently
making a substantial impact on conversion efficiency. The effect of material quality can be
evaluated based on a diffusion limited model as described in detail in Chapter 3. In this
model, the J-V characteristic of the device is given by Equation 3-10. Based on Equation
3-10, the calculated conversion efficiency as well as the measurement are shown in Figure
117
5-9. In the calculation, the carrier lifetime was assumed to be 28 and 87 ns, close to the
extracted values shown in Table 5-3. As can be seen, the calculated  using the extracted
carrier lifetime was higher than the measured value for all the four devices. This is mainly
because the extracted lifetime was somewhat overestimated due to the occurrence of the
SRH process. For the 6- and 7-stage devices, this is also due to the voltage dependence of
collection efficiency that was instead ignored in the calculation. Nevertheless, the
calculations based on Equation 2-5 evidently indicate the considerable impact of carrier
lifetime on device performance. As shown in Figure 5-9, there is a distinct gap between
the calculated conversion efficiencies with different values of carrier lifetime. For example,
for =28 ns and Pinc=17 W/cm2, the calculated  was 2.2% (6-stage), 2.6% (7-stage), 3.1%
(16-stage) and 3.3% (23-stage). However, as the carrier lifetime increased to 87 ns, the
calculated  at the same Pinc was 4.1%, 4.6%, 5.3% and 5.4% for the 6-, 7-, 16- and 23-
stage devices, respectively. This corresponds to an efficiency increase of 1.9% (6-stage),
2.0% (7-stage), 2.2% (16-stage) and 2.1% (23-stage). Clearly, this increase is much more
significant than those due to the eliminations of voltage-dependent collection efficiency
and current mismatch. Therefore, the material quality plays the most important role among
the three factors. If carrier lifetime is kept the same, the  is higher in the 16- and 23-stage
devices than in the 6- and 7-stage devices, even though the current mismatch is more
significant in the 16- and 23-stage devices. In this respect, given comparable material
quality, ICTPV devices with more stages and thinner absorbers are advantageous,
consistent with previous experimental results [157, 182, 186-188]. When the current
mismatch is minimized, ICTPV devices will have further conversion efficiency with more
stages.
118
6 6
measured measured
5 calculated-28 ns calculated-28 ns 5
calculated-87 ns calculated-87 ns
4 4
 (%)
 (%)
3 3
2 2
1 6-stage 7-stage 1
6 6
measured measured
5 5
4 4
 (%)
 (%)
3 3
2 2
1 16-stage 23-stage 1
0 0
0 5 10 15 20 0 5 10 15 20
2 2
Pinc (W/cm ) Pinc (W/cm )
Figure 5-9: Calculated conversion efficiency based on Equation 3-10, along with
measurement for the four devices. For each of the four devices, the carrier lifetime
used in the calculation was 27 and 87 ns.
This chapter deals with detailed characterization and performance analysis of two
sets of four narrow bandgap (~0.22-0.25 eV at 300 K) ICTPV devices. The four ICTPV
devices have increased number of stages compared to the three devices in Chapter 4. With
different numbers of stages and individual absorber thicknesses, it was shown that current
mismatch between stages could be significant with more stages due to the variation of
absorption coefficient. On the other hand, the collection efficiency of photogenerated
carriers can be much improved with thinner individual absorbers and more stages. Also,
the carrier lifetime was extracted from dark current density to evaluate the material quality.
119
The extracted shorter carrier lifetime, together with substantial current mismatch, explains
the lower conversion efficiencies in the 16- and 23-stage devices compared to that in the
6- and 7-stage devices. Furthermore, the effects of material quality, current mismatch and
collection efficiency on device performance are quantified. The quantitative analysis shows
that the material quality has the most significant impact on the device performance among
the three factors. This indicates the importance of good material quality and its consistency
for realizing efficient IC TPV devices. This conclusion also challenges the inference put
forward in Section 5.1 as more cascade stages may not succeed to improve device
performance if the material quality is poor.
120
6 Chapter 6: Carrier lifetime in mid wavelength interband cascade
devices
6.1 Introduction
Starting from this chapter, experimental studies of IC structure for infrared detector
will be presented. The operation principle and theoretical background of IC infrared
photodetectors (ICIPs) are reviewed in Chapter 2. Specifically, the noise reduction and
detectivity enhancement in multistage detectors compared to single-absorber detectors are
detailed in Chapter 2. These advantages enable ICIPs to operate at high temperatures with
decent detectivity, as has been manifested in experiment [99, 137, 151, 199]. Nevertheless,
at the current stage, ICIPs does not outperform the state-of-art HgCdTe detectors in the
MWIR regime. For example, at 300 K, the detectivity of an ICIP with a cutoff wavelength
of 4.3 m is close to 1×109 Jones [151], slightly lower than the claimed ≥ 3.0×109 Jones
for an uncooled photovoltaic HgCdTe detector with similar cutoff wavelength (~4 m)
[91]. This is partially because the carrier lifetime in InAs/GaSb T2SLs is lower than in the
HgCdTe materials, although the Auger reduction is theoretically projected to be suppressed
in T2SLs [128-130]. For example, the reported lifetimes are 30-100 ns in MWIR T2SLs
[200-203], and 10-55 ns for LWIR T2SLs [192-193, 201, 204], which are mainly limited
by SRH recombination. Speculatively, the origin of the recombination centers is ascribed
to the presence of gallium, as the gallium-free InAs/InAsSb SLs possess much longer
radiative-dominated lifetimes (e.g. >400 ns or 9 s at 77 K) [166-167]. Because of the
shorter lifetime, the dark current densities in InAs/Ga(In)Sb T2SLs detectors are generally
higher than the benchmark known as “Rule 07” [205] for MCT materials.
In this chapter, a simple and effective electrical method is developed to the extract
121
carrier lifetime in InAs/GaSb T2SLs. This method differs from the frequently used optical
methods based on time- or frequency-domain photoluminescence (PL) measurements [192,
200-201, 204]. These optical methods are mainly focused on low temperatures (<200 K),
while the developed method can extract lifetime in a wide range of temperature, especially
at high temperatures (e.g. 300 K and above). There have been a few studies on carrier
lifetime using different approaches, such as measuring photoconductive response and
modeling dark current characteristics of T2SL detectors [206-209]. However, as with the
optical methods, these approaches fail to work at high temperatures. Sometimes, a more
meaningful carrier lifetime that is different from the recombination lifetime needs to be
realized and extracted. For example, for a photodiode that is operated under a reverse bias,
the generation lifetime is more relevant to the device performance and could be far longer
than the recombination lifetime, depending on the defect energy level as discussed for Si-
based devices [210]. In practical devices, carrier lifetime is often a mixture of various
mechanisms (See Figure 6-1), which are challenging to separate.
Figure 6-1: Radiative and non-radiative recombination processes in semiconductors.
The carrier lifetime in IC devices (QCDs) is lower than MCT materials. However,
compared to the other cascade device family ─ quantum cascade (QC) devices, it can be
much longer. QC devices (QCDs) operate based on intersubband transitions within the
122
same band (e.g. the conduction band). This contrasts to IC devices (ICDs) that are based
on the interband transitions between the conduction and valence band. This fundamental
difference in carrier transport results in distinct carrier lifetimes and device performances,
especially at high temperatures. For example, the lifetime in QCDs is in the picosecond
range due to fast phonon scattering, while ICDs have a nanosecond lifetime scale due to
Auger and SRH recombination. Like IC devices, QC family include QC lasers and QC
detectors. Although QC structures were also proposed and simulated theoretically for PV
cells [211-212], none have been reported experimentally. The two families of devices are
both based on quantum-engineered layer structures, and they nearly went through a parallel
rapid evolution, especially in lasers [70-73]. However, they were often discussed and
presented separately but seldom compared with their counterparts. There is particularly no
evaluation or comparison based on a unified figure of merit to fairly describe their
characteristics with different device functionalities. In this chapter, the saturation current
density J0 is identified as the common figure of merit. A semi-empirical model is employed
to extract the J0 from many QCDs and ICDs published in literature and some of
unpublished ICDs.
6.2 Carrier lifetime in mid-wavelength ICIPs
6.2.1 Device structure, growth and fabrication
The seven devices presented in this section have ICIP structures with different numbers
of stages (Nc) and absorber thicknesses. They were grown using a GENxplor MBE system
on nominally undoped p-type GaSb (001) substrates. Table 6-1 presents the individual
absorber thicknesses of the seven ICIPs in order from the surface to substrate. For
123
convenience, they are denoted as 1S-1040, 1S-2340, M3S-312, M6S-312, N8S-312,
M12S-156 and N16S-156, where “M” and “N” stand for current-matched and noncurrent-
matched configurations, respectively. As mentioned in Chapter 2, the individual absorbers
in current-matched ICIPs are designed thicker in the optically deeper stages to ensure equal
photocurrent in each stage. In contrast, the individual absorber thicknesses in a non-
current-matched ICIP are made identical. For the current-matched ICIPs studied in the
section, the individual absorber thicknesses were designed based on the absorption
coefficient of 3000 cm-1 and the assumption of complete collection of photogenerated
carriers. 1S-1040, 1S-2340, M3S-312, M6S-312 and N8S-312 were grown earlier as
descried in [151], while M12S-156 and N16S-156 were grown in a later growth campaign
(just after system maintenance) with possibly varied conditions and material qualities. The
seven detectors have identical electron and hole barriers as described in [151]. The
absorbers in the seven detectors consist of InAs/GaSb/Al(In)Sb/GaSb M-shape SLs [104,
134-135] with layer thicknesses of 27/15/815 Å, respectively. The GaSb layers in the SLs
were p-type doped to 5.1×1016 cm-3 for all the seven detector structures. The average
doping concentration in the SLs is estimated to be 2.4×1016 cm-3 according to the ratio of
the GaSb thickness over the SL period. Upon this doping level, the carrier transport in the
absorbers is expected to be determined by the dynamics of minority electrons. The bandgap
of the absorbers was designed with a cutoff wavelength (c) near 4.3 µm at 300 K, which
closely matched the observed 100% cutoff wavelengths for devices made from the seven
wafers, implying good control of layer thicknesses and alloy compositions during MBE
growth.
124
The important design and material parameters such as surface defect density and
perpendicular (⊥) lattice mismatch of the seven wafers are summarized in Table 6-1. After
the MBE growth, the wafers were processed into square mesa devices with dimensions
from 50 to 1000 m using standard contact UV photolithography followed by wet-
chemical etching. A two-layer passivation (Si3N4 then SiO2) was RF sputter deposited to
improve overall stress management and minimize pin holes. Sputter deposited Ti/Au layers
provided top and bottom contacts. Finally, the devices were mounted on heat sinks and
wire bonded for characterization.
Table 6-1: Summary of the design and material parameters of the seven wafers.
Absorber thickness # of dtotal Doping c Defect Lattice

Wafer
(nm) stage (m) (cm3) (m) (cm-2) mismatch
1S-1040 1040 1 1.04 2.4×1016 4.4 6.0×103 -0.09%
1S-2340 2340 1 2.34 2.4×1016 4.4 5.0×104 ~0
M3S-312 312/344.5/383.5 3 1.04 2.4×1016 4.3 2.0×104 -0.027%

312/344.5/383.5/435
M6S-312 6 2.59 2.4×1016 4.3 2.0×104 -0.10%
.5/507/604.5
N8S-312 312×8 8 2.50 2.4×1016 4.3 5.0×104 -0.08%
156/169/182/195/20
M12S-156 8/227.5/247/273/299 12 3.08 2.4×1016 4.3 4.4×104 0.051%
/331.5/370.5/422.5
N16S-156 156×16 16 2.49 2.4×1016 4.3 4.3×104 0.065%
6.2.2 Dark current density
The dark current density-voltage (Jd-V) characteristics of the seven ICIPs were
measured at various temperatures. Figure 6-2 (a) and (b) shows the measured Jd at 250 and
300 K for the representative 400×400 (1S-1040 and 1S-2340) and 500×500 (other five
wafers) m2 devices made from the seven wafers. As shown, at reverse voltage, the seven
125
devices in the ascending order of Jd are N16S-156, M12S-156, N8S-312, M6S-312, M3S-
312, 1S-1040 and 1S-2340. This sequence is precisely in the descending order of number
of stages or increasing order of absorber thickness. This is because ICIPs with more stages
and thinner individual absorbers are better able to suppress the dark current. Given carrier
transport is diffusion limited, according to Equation 2-6 and 2-7, the dark current density
in the mth stage of an ICIP can be written as:
𝐽𝑑,𝑚 = 𝑒𝑔𝑡ℎ 𝐿𝑡𝑎𝑛ℎ(𝑑𝑚 ⁄𝐿)(𝑒 𝑒𝑉𝑚 ⁄𝑘𝑏𝑇 − 1) (6-1)
where Vm is the applied voltage across the mth stage and dm is the individual absorber
thickness of the mth stage. Here, the parasitic series resistance Rs and shunt resistance Rshunt
are ignored. The voltage drop across each stage equates V/Nc in a noncurrent-matched ICIP
with identical absorbers. However, in a current-matched ICIP, to ensure dark current
continuity, the Vm will be smaller in an optically deeper stage with a thicker individual
absorber. Based on Equation 6-1, given a similar cutoff wavelength and minority carrier
lifetime, the dark current density at the same voltage will be lower in ICIPs with more
stages and thinner individual absorbers. This essentially agrees with the measured Jd-V
characteristics of the seven ICIPs as shown in Figure 6-2 (a) and (b).
However, at large reverse voltage where all the carriers are swept out from the
absorbers [213-214], a more appropriate equation for dark current density is given by:
𝑉−𝐽𝑑 𝑅𝑠 𝐴
𝐽𝑑 = 𝑒𝑔𝑡ℎ 𝑑1 + (6-2)
𝑅𝑠ℎ𝑢𝑛𝑡𝐴
Because the cascade stages are connected in series, the dark current density is decided by
the stage with the thinnest individual absorber (i.e. the first stage). The second term on the
right side of Equation 6-2 represents the average leakage current density with a constant
shunt resistance. Hence, from Equation 6-2, there is a liner relationship between current
126
density and voltage at large reverse voltage, which forms the important basis to extract
thermal generation rate and carrier lifetime.
101 101
M3S-312

M6S-312 1S-2340
0 N8S-312 0
1S-1040
10 10
1S-1 1S- M12S-156
040 234
0 N16S-156
10-1 10-1
M3S-312
-2 -2 M6S-312
10 10 N8S-312
T=250 K T=300 K M12S-156
-3 (a) -3 (b) N16S-156
10 10
-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5
Figure 6-2: Dark current density versus applied voltage for the seven devices at (a)
250 K and (b) 300 K.
6.2.3 Contribution of SRH process to dark current
When carrier transport is affected by the SRH process, the description based on
Equation 6-1 is prone to errors. In contrast, Equation 6-2 can account for combined effects
of various mechanisms. Inclusion of Auger and SRH mechanisms gives a thermal
generation rate that is expressed as [213-214]:
𝑛𝑖2 𝑛𝑖2 𝑛𝑖2

𝑔𝑡ℎ = + (𝑁 = (6-3 a)
𝑁𝑎 𝜏𝐴 𝑎 +𝑛𝑖 )𝜏𝑆𝑅𝐻 𝑁𝑎 𝜏
1 1 𝑁𝑎 1 1 1
= + (𝑁 ≈ + (6-3 b)
𝜏 𝜏𝐴 𝑎 +𝑛𝑖 ) 𝜏𝑆𝑅𝐻 𝜏𝐴 𝜏𝑆𝑅𝐻
where A represents the carrier lifetime due to the Auger mechanism and SRH is the SRH
carrier lifetime. The approximation made in Equation 6-3(b) is valid if the doping
concentration Na is much higher than the intrinsic carrier concentration ni. Therefore, one
can first extract gth from Equation 6-2 and then calculate the carrier lifetime  from
127
Equation 6-3, which covers various transport mechanisms and is more accurate than
Equation 6-1.
The contribution of SRH process in the seven devices can be indirectly assessed by
the activation energy Ea. Based on the temperature dependence of R0A [See Figure 6-3(a)],
the Ea in a temperature range of 200-340 K was 256, 252, 258, 254, 249, 256, 253 meV for
1S-1040, 1S-2340, M3S-312, M6S-312, N8S-312, M12S-156 and N16S-156, respectively.
These values of Ea were smaller than their bandgaps (~288 meV) at room temperature and
about 75% of the zero-temperature bandgap Eg (0) (~329 meV). This means that the SRH
processes were involved in the carrier transport besides the diffusion process [215]. The
bandgaps of the seven devices were estimated from the 100% cutoff wavelengths in their
responsivity spectra, which were very close at every temperature of interest and two were
presented in [151]. Particularly, the temperature dependence of the bandgap for M3S-312,
as well as the Varshni fitting, are presented in Figure 6-3(b).
T (K)
340320 300 280 260 240 220 200
103 330
(a)
2 320 (b)
10
310
R0A (.cm2)
101
Eg (meV)
1S-1040 300
100 1S-2340 Vashni parameters
M3S-312 290
-1 M6S-312 Eg (T=0)=329 meV
10
N8S-312
280 =0.364 meV/K
M12S-156 =241 K
10-2 N16S-156
270
3.0 3.5 4.0 4.5 5.0 100 150 200 250 300 350
1000/T (K-1) T (K)
Figure 6-3: (a) R0A of the seven devices in the temperature range of 200-340 K. (b)
Temperature dependence of bandgap for M3S-312. The fitting Varshni parameters
for the device are shown.
128
6.2.4 Linear fitting of dark current density
Since the carrier transport is affected by the SRH process, Equation 6-2 is
preferably used to extract gth for the seven devices at higher temperatures, which is simpler
with assuming constant parasitic resistances. The feasibility and validity of constant
parasitic resistances are supported by the observed linear relationship of current density
with voltage as shown in Figure 6-4. There are obvious linear regions of Jd for the five
multi-stage devices at large reverse bias starting from -1.5 V. This behavior was also
observed at other higher temperatures for the five devices. For the two single-stage devices,
their current density-voltage curves exhibited linear characteristics between about -1.5 and
-0.3 V as well. However, the current density increased sharply with reverse bias voltage
after -1.5 V, which was likely triggered by a substantial electric field in the absorber region
and the consequential tunneling of carriers through the bandgap. This is because the entire
voltage is applied exclusively on the single stage, while the multistage ICIPs have multiple
unipolar barriers to share and withstand the voltage. In this sense, this method of extracting
the thermal generation rate is particularly well suited for multistage ICIPs where the
linearity can be ensured in a wide range of reverse voltage.
Based on Equation 6-2, the thermal generation rate for the seven devices can be
extracted by linearly fitting the dark current density at larger reverse voltages with the
rearranged equation:
𝑉 𝑅𝑠
𝐽𝑑 = (−𝑒𝑔𝑡ℎ 𝑑1 + )⁄(1 + ) (6-4)
𝑅𝑠ℎ𝑢𝑛𝑡𝐴 𝑅𝑠ℎ𝑢𝑛𝑡
The lines that were linearly fit to the experimental data for the seven devices at 300 K are
shown in Figure 6-4. The linear fits were performed between -3 and -1.5 V for the five
multistage devices for good accuracy. By comparison, the linear fits for the two single-
129
stage devices were done in the voltage range of -1.5 to -0.3 V to circumvent the effect of
substantial tunneling of carriers as previously mentioned.
0.0
156
16S-
T=300 K N
-0.1
-0.2 M12S-156
Jd (A/cm2) -0.3
-312 0.0
M6S
-0.4 -0.5 40
-312 1S-10
Jd (A/cm2)
N8S -1.0
340
-0.5 12
-1.5 1S-2
S-3
M3 -2.0
-2.5
-0.6 -2.0 -1.5 -1.0 -0.5 0.0
Voltage (V)
-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0

Voltage (V)
Figure 6-4: Linear fitting (dashed) and experimental measurements (solid) of the
dark current density at reverse bias voltage for the five multistage devices at 300 K.
The inset shows the corresponding results of the two single-stage devices at 300 K.
6.2.5 Estimated thermal generation rate and carrier lifetime
Based on Equation 6-4, the thermal generation rate at 300 K found from the
intercept of the fitted line with the vertical axis was 3.1×1022 (1S-1040), 3.2×1022 (1S-
2340), 3.2×1022 (M3S-312), 3.6×1022 (M6S-312) and 4.0×1022 cm-3/s (N8S-312, M12S-
156 and N16S-156). Simultaneously, the shunt resistance obtained from slope of a fitted
curve was 1449, 1192, 3338, 5639, 5054, 13343 and 13361  for 1S-1040, 1S-2340, M3S-
312, M6S-312, N8S-312, M12S-156 and N16S-156, respectively. The Rs was extracted
from the differential resistance at large forward voltage, and was less than 10  at 300 K.
Since Rs was at least two orders of magnitude smaller than Rshunt, the term Rs/Rshunt in
Equation 6-4 can be ignored when extracting the thermal generation rate in the seven
devices.
130
With the extracted gth, the minority carrier lifetime can then be calculated from
Equation 6-3 in which the intrinsic carrier concentration is given by Equation 4-4. At 300
K, the calculated electron and hole effective masses of the T2SLs using a two-band k·p
model were 0.049m0 and 0.48m0, respectively. Note that the electron effective mass scales
linearly with the temperature-dependent bandgap according to Kane’s model [216]. At 300
K, the calculated intrinsic carrier concentration was 4.1×1015 cm-3, one order of magnitude
lower than the doping concentration in the absorbers. At a lower temperature (e.g. 200 K),
the calculated ni was 7.8×1013 cm-3 and the Fermi energy EF was 4.5 kbT higher than the
valence band edge Ev, implying that Equation 4-4 was still valid for the seven devices.
Hence, the extraction of carrier lifetime was carried out at 200-340 K.
Based on Equation 4-4 and 6-3, along with the extracted thermal generation rate,
the minority carrier lifetime at 300 K was estimated to be 22.9 (1S-1040), 22.1 (1S-2340),
22.3 (M3S-312) 19.7 (M6S-312), 17.8 (N8S-312), 17.8 (M12S-156) and 17.8 ns (N16S-
156). In the same manner with 300 K, the carrier lifetimes and thermal generation rates at
other higher temperatures were also obtaine as shown in Figure 6-5. For the seven devices
at 200-340 K, the extracted  was ranges between 167 and 8.5 ns depending on the material
quality, and monotonically decreased with increasing temperature. For example, compared
to M12S-312 and N16S-312 (which were grown later in a different growth campaign), the
longer  in M3S- is due to the better material and crystal structure quality (Table 6-1). For
the same reason, the lifetime of 1S-1040 was longer than that of 1S-2340. Also, the
extracted carrier lifetimes were similar between the two single-stage devices and the five
multistage devices. This supports the validity and feasibility of the developed method for
non-cascade photodetectors. At temperatures higher than 200 K, the extracted carrier
131
lifetime was somehow shorter than the values (of 135-108 ns between 200 and 300 K) that
were stated in [217] for T2SL ICIPs (with a cutoff wavelength near 5 m) based on the
fitting of the Jd-V curve to an equation similar to Equation 6-1. Also, the carrier lifetimes
exhibited a rapid decrease with increasing temperature, which was close to an exponential
relationship especially in the temperature range of 250-340 K. For instance, for M6S-312,
the carrier lifetime decreased from 132 ns to 10.6 ns while the temperature was increased
from 200 to 340 K. This dependence of lifetime on temperature was quite different from
the previous results obtained by optical and other electrical methods [192-193, 208], which
follow a T-1/2 law determined by the SRH mechanism [218]. Analogous to R0A, an effective
“activation energy” of ~150 meV was extracted for the seven devices at 250-340 K,
confirming an exponential relationship with inverse temperature (1/T). The sharp decrease
of the carrier lifetime with increasing temperature can be attributed to the growing
dominance of the Auger processes associated with the bandgap narrowing of the SL
absorber at high temperatures. The similar effect of Auger process has been analyzed by
others for InAs/InAsSb T2SLs [219-220]. Overall, the developed method to extract carrier
lifetime include contributions from various transport mechanisms such as Auger and SRH
processes as indicated in Equation 6-3, which should be effective in broader contexts and
closer to actual devices.
132
Temperature T (K)
340 320 300 280 260 240 220 200
1024
Thermal generation rate gth (s-1cm-3)

1023
100
85
70 1S-1040 1022
Lifetime  (ns)
55 1S-2340
M3S-312
40 M6S-312 1021
N8S-312
25 M12S-156
N16S-156 1020
1019
10
8.5
7 1018
3.0 3.5 4.0 4.5 5.0
1000/T (K-1)
Figure 6-5: The thermal generation rate and minority carrier lifetime for the five
multistage and two single-stage devices at high temperatures.
6.3 Interband cascade devices vs quantum cascade devices
6.3.1 Device structures
As estimated in the preceding section, the lifetime in IC devices (ICDs) has a tens
of nanosecond timescale at 300 K. This should be much longer than the intersubband
transitions occurring on a time scale of picosecond in QC devices (QCDs). It is generally
known that the relatively much longer carrier lifetime in ICDs has resulted in a significantly
lower threshold current density (Jth) and power consumption in ICLs at room temperature
(RT) compared to in QCLs. This has been demonstrated for a wide IR spectral region (2.7-
6 m) [73, 221]. Since the lasers normally operate under forward bias, the J-V
characteristics under reverse bias for extracting J0 are not readily available for QCLs.
Hence, the analysis of QCDs is mainly concentrated on RT QC detectors reported in the
literature [83-84, 96, 222-224]. Some ICDs included here are IC laser structures that were
reported previously [115, 120, 179, 225-226], while the others are IC light emitting devices
133
(LEDs). The active regions of all these ICDs consist of an asymmetric “W” quantum well
(QW) [227] with two InAs electron QW layers on both sides of the GaInSb hole QW layer.
The ICDs have numbers of cascade stages (Nc) ranging from 6 to 15. Besides, ICDs with
InAs/Ga(In)Sb T2SL absorbers that were designed as detectors and TPV cells are also
included here [137, 151, 159, 199, 228-231]. They will be denoted by “ICD_SL” to
differentiate from those having QWs in the active regions. Most of the ICDs were
processed into square mesa type devices as well as several broad area IC lasers.
6.3.2 Semi-empirical model for dark current density
In cascade devices, there is a potential barrier region formed between two ends of
adjacent cascade stages, since the electronic states near the two ends lie at a low energy
level on one end and a high energy level on the other. If a forward bias (positive on the
high energy end) is applied to a cascade stage, the number of available carriers being able
to overcome the potential barrier from the low energy end to the high energy end is
increased exponentially with the bias voltage. Consequently, the forward current density
will have an exponential increase with the bias voltage. Conversely, at reverse voltage, the
current density approximates to a constant (J0) value since the number of carriers that can
move from the high energy end does not increase with the reverse bias voltage. Hence,
semi-empirically, the current density-voltage (Jd-V) characteristic in a cascade device with
identical stages can be described by:
𝐽𝑑 (𝑉) = 𝐽0 (𝑒 𝑞𝑉⁄𝑁𝑐𝑘𝑏 𝑇 − 1) (6-5)
Qualitatively, this expression resembles the standard diode equation for a p-n junction.
Equation 6-5 can be derived from a fundamental level with lengthy mathematical
134
manipulations, as described in detail in [141] for ICDs and in [232-234] for QCDs. The
approach offered here grasps the main feature in cascade devices and offers a simple way
to derive Equation 6-5 for current-voltage characteristics in complicated cascade structures.
This approach has not been documented before should be beneficial in helping promote a
better understanding of complex cascade devices.
It has been shown that the value of J0 is proportional to the carrier concentration
and inversely proportional to carrier lifetime that can be affected by various scattering
mechanisms such as defects, doping, phonons and Auger recombination. This relationship
has been explored to extracted carrier lifetime in ICIPs as described in the preceding
section. From Equation 6-5, the R0A of a cascade device can be obtained as:
𝑁𝑐 𝑘𝑏 𝑇
𝑅0 𝐴 = (6-6)
𝑞𝐽0
In theory, the values of J0 for ICDs and QCDs can be extracted by fitting the measured Jd-
V curves to Equation 6-5. However, in an actual device, the parasitic series and shunt
resistance (Rs and Rshunt) are often presented. Considering these factors, the Jd-V curve of a
cascade device should be fitted to a modified equation:

𝑉−𝑅𝑠 𝐴𝐽𝑑
𝐽𝑑 (𝑉) = 𝐽0 (𝑒 𝑞(𝑉−𝑅𝑠 𝐴𝐽𝑑 )⁄𝑁𝑐𝑘𝑏𝑇 − 1) + (6-7)
𝑅𝑠ℎ𝑢𝑛𝑡 𝐴
6.3.3 Saturation current densities for cascade devices
From Equation 6-7, the three parameters, J0, Rshunt and Rs, can be extracted through
the least-square fitting method. In the fits, the values of Rshunt and Rs were kept in the range
of 103-104 and 1-10 , respectively. As an example, Figure 6-6 shows the measured Jd-V
curves and fitting results for a large area (400 m×400 m) eight-stage ICD (wafer R083)
[115] and a fifty-stage QCD (110 m×110 m) [96] at 300 K. The two devices have the
135
identical transition energy E of 0.23 eV in the active region at 300 K, which was the
bandgap for the ICD or the energy separation of the two involved conduction subbands for
the QCD. As shown in Figure 6-6, the magnitude of Jd is at least an order of magnitude
lower in the ICD than in the QCD. This difference is ascribed to the comparatively much
longer carrier lifetimes in the ICD. Also, the least-square fittings based on Equation 6-7
were in excellent agreement with measurements, supporting the validity of the semi-
empirical model. Specifically, the extracted J0 (Rshunt) obtained from the fitting procedure
is 0.017 A/cm2 (5945 ) and 1.8 A/cm2 (6772 ) for the eight-stage ICD and fifty-stage
QCD, respectively. The other fitting parameter Rs is 5  for the ICD, and 7  for the QCD
with a smaller device area.
101
QCD
100
10-1
ICD
-2
10
10-3 E=230 meV line: simulated

circle: measured
-1.0 -0.5 0.0 0.5 1.0

Voltage (V)
Figure 6-6: The measured and fitted Jd-V curves for an 8-stage ICD and a 50-stage
QCD at 300 K. The ICD and QCD were mentioned in [115] (wafer R083) and [96],
respectively.
Aside from the two devices, the least-square fitting was also performed for other
ICDs [83-84, 96, 222-224] and QCDs [115, 120, 179, 225-226]. The extracted values of J0
at 300 K for these ICDs and QCDs are presented in Figure 6-7. As can be seen, the value
of J0 is more than one order of magnitude lower in ICDs than in QCDs with similar E.
136
This distinction of extracted J0 implies the significant effect of carrier lifetime on transport
current, consistent with threshold behavior in laser performance for a wide infrared spectral
region mentioned earlier. Also, Figure 6-6 shows that J0 tends to increase exponentially
with decreasing E for both ICDs and QCDs. It should be commented that ICDs are more
susceptible to surface leakage currents due to the existence of surface states in their
bandgap. Hence the extracted J0 in Figure 6-7 might be more overestimated for ICDs than
for QCDs. Since there is considerable variation in device area, the product of resistance
and area is a more appropriate quantity as used effectively in Equation 6-7. In general, the
value of RshuntA extracted from fitting is smaller for QCDs compared to ICDs. However,
the ratio of RshuntA to R0A is generally higher in QCDs than in ICDs, which suggests the
relatively lower percentage of surface leakage in QCDs than in ICDs. Moreover, the
material qualities and fabrication technologies may differ greatly between different groups
Overall, the extracted values of J0 are much lower in ICDs than in QCDs. This not only
manifests substantial difference of threshold current density in lasers between the two
families, but also yields considerable differences in detector and PV device performance
as will be discussed later. The vast gap of J0 between ICDs and QCDs is fundamentally
attributed to their distinctive carrier lifetimes since J0 is inversely proportional to the
lifetime. In ICDs, Auger and SRH (through defects) processes are the main scattering
mechanisms. In QCDs, longitudinal optical (LO) phonon scattering prevails and is fast (in
ps or shorter) between and within the conduction subbands. With interband transitions, the
carrier lifetime is in the nanosecond range, about three orders of magnitude slower than for
phonon scattering. The extracted J0 is much lower in ICDs than in QCDs, which
unambiguously proves the much longer lifetime in ICDs than QCDs.
137
Wavelength (m)
8 7 6 5 4
101
Saturation current density (A/cm2)

T=300 K
100 QCD
10-1
10-2 ICD
10-3
150 200 250 300 350
Transition energy (meV)
Figure 6-7: The extracted values of J0 for ICDs and QCDs at 300 K. Some ICDs have
been described previously in [83-84, 96, 222-224], while others are from our
unpublished studies. The QCDs are from [115, 120, 179, 225-226].
6.3.4 Effect of J0 on the performances of detectors
The saturation current density J0 is a measure of Johnson noise in a photodetector.
The R0A contained in Equation 6-6 is also reflected in the specific detectivity D*. As
described in Subsection 1.3.4, D* is essentially a measure of signal to noise ratio ─ the most
important figure of merit for photovoltaic photodetectors operating at zero bias. The
expression of D* is given by Equation 1-8 where Ri is the responsivity. Figure 6-8(a) shows
the measured peak Ri for ICDs and QCDs at 300 K. In addition to some of the ICDs
presented in Figure 6-7, another two ICDs (devices A and B) [136] and ICD_SLs from
[137, 151, 199, 229-231] are also included in Figure 6-8 (a) and (b). As shown in Figure
6-8(a), the peak Ri is generally higher in ICDs than in QCDs and is especially high in
ICD_SLs with enhanced absorption in SL absorbers. The lower Ri in QCDs is partly
because of the low escape probability that is proportional to the carrier lifetime [65, 83] for
QCDs, while this value is close to unity for ICDs with the much longer lifetime [99].
138
Another factor might be the polarization selection rule for intersubband transitions in
conduction band QWs [65, 79], which prohibits the absorption of normal incident light in
QCDs. This problem in QCDs is typically mitigated by making facets made by polishing
at an angle of 45o to the growth direction. In addition, an improved responsivity can be
achieved for intersubband photodetectors by using a photonic metamaterial to enhance the
light-matter interaction. This was demonstrated in a QWIP detector with photoconductive
gain near 9 m at RT [236]. in which the responsivity (~0.2 A/W) is comparable to those
in ICD_SLs as shown in Figure 6-8(a). However, due to substantial noise with a high dark
current density, its detectivity D* (~2.8×107 Jones) is about one order of magnitude lower
than that in ICD_SLs with similar E as shown in Figure 6-7(b).
Wavelength (m) Wavelength (m)

1210 8 6 4 1210 8 6 4
Peak responsivity (mA/W)
QWIP (a) (b)

Peak detectivity (Jones)
102 109
101 108
QWIP
ICD ICD
QCD QCD
100 ICD_SL 107 ICD_SL
100 150 200 250 300 350 400 450 100 150 200 250 300 350 400 450
Transition energy (meV) Transition energy (meV)
Figure 6-8: Measured peak (a) responsivities and (b) detectivities for ICDs, ICD_SLs
and QCDs at 300 K. In addition to some of the ICDs presented in Figure 6-6, two
ICDs (devices A and B) [136] and all ICD_SLs from [137, 151, 199, 229-231] are
included. One QWIP is from [236].
From Equation 1-8 and 6-6, the John-noise limited D* is inversely proportional to
the square root of J0. Figure 6-8(b) shows the measured peak D* values at 300 K for the
considered ICDs and QCDs. As can be seen, the values of D* are almost one order of
magnitude higher for ICDs than for QCDs. At 300 K, the achieved D* in most QCDs is less
139
than 3×107 Jones mainly because of a high J0, while most D* values for ICDs are higher
than 1×108 Jones and some even exceed 1×109 Jones. Also, the difference of D* between
ICDs and QCDs is more significant than the difference in Ri between the two families. This
arises from more than one order of magnitude lower Jo in ICDs than in QCDs, although
the number of cascade stages Nc (<15) in ICDs is less than in QCDs (≥30). If they had the
same Nc, the value of D* would be increasingly higher in ICDs than in QCDs.
According to Equation 1-8 and 6-6, D* is proportional to the square root of the
number of stages if Ri remains unchanged. This is roughly correct when individual
absorbers are only made of a pair QWs and kept thin, and the total absorber thickness does
not cause a substantial light attenuation [99]. Conversely, when the light absorption is
significant in individual absorbers (e.g. especially in ICD_SLs), the attenuation of light
intensity along the propagation direction needs to be considered in evaluating the Ri [141,
194, 232]. In this scenario, the D* for a non-current matched cascade device (e.g. with
identical absorbers) will reach a maximum value at a finite Nc as discussed in [141, 194].
This is particularly true for ICD_SLs where SLs are used as active absorbers to enhance
absorption and responsivity for attaining the highest value of D* among all devices, as
shown in Figure 6-8. Nevertheless, compared to ICDs, the additional increase in D* in
ICD_SLs is not as appreciable as the boost in the peak Ri. This is because the Jo is much
higher in ICD_SLs with thicker SL absorbers than in ICDs. Nevertheless, with two
adjustable parameters, the SL absorber thickness and the number of stages, ICD_SLs can
be optimized with more flexibilities to improve D* at high temperatures [141, 194].
In addition, if the detector has a voltage rather than a current output, one can define
its responsivity as the ratio of output voltage to power [9]. Analogous to p-n diodes,
140
neglecting shunt and series resistances, the net current density J in ICDs and QCDs (with
identical stages) under light illumination can be approximately written as:
𝐽 = 𝐽0 (𝑒 𝑞𝑉⁄𝑁𝑐𝑘𝑏𝑇 − 1) − 𝐽𝑝ℎ (6-8)
where the photocurrent density Jph is simply presumed to be bias independent. In an actual
device, the photocurrent may be bias dependent as described in Chapter 4 and 5 for some
ICTPV devices. Based on Equation 6-8, the open-circuit voltage Voc for a cascade device
can be expressed as:
𝑁𝑐 𝑘𝑏 𝑇 𝐽𝑝ℎ
𝑉𝑜𝑐 = 𝑙𝑛 ( + 1) (6-9)
𝑞 𝐽0
Hence from this equation one can see that the lower J0, the higher Voc would be.
Also, when the photocurrent is significantly lower than the dark current, which is
generally true in the detection of weak light at high temperatures. In this case, Equation 6-
9 can be approximated to first order as:
𝑁𝑐 𝑘𝑏 𝑇 𝐽𝑝ℎ
𝑉𝑜𝑐 = (6-10)
𝑞 𝐽0
which is linearly proportional to the number of stages and the ratio of photocurrent and
saturation current densities. Therefore, if the detector output is voltage, more stages and a
lower saturation current density will benefit the device performance. According to Figure
6-7 and 6-8, the voltage responsivity will be much higher in ICDs than in QCDs. The is
due to the higher photocurrent (proportional to responsivity) and the much lower J0 in ICDs
compared to QCDs. Overall, in terms of either current or voltage responsivity, ICDs will
maintain the advantages over QCDs.
141
6.3.5 Effect of J0 on the performances of photovoltaic cells
As for photovoltaic cells to convert light into electricity, the saturation current
density J0 remains an important parameter to evaluate device performance. As mentioned
in Chapter 1, the relatively low transition energy E in the active region makes ICDs and
QCDs more appropriate for TPV applications where the heat source temperatures are
generally at 1000-2000 K. In fact, TPV cells based on IC structures have been
experimentally demonstrated with high Voc that far exceeded the single bandgap value,
showing the cascade effect [159, 182, 190-191]. In contrast, TPV cells based on QC
structures have not been reported experimentally, possibly due to high values of J0 in
QCDs. Based on Equation 6-10 and the data in Figure 6-7 and 6-8, the open-circuit voltage
Voc can be calculated for cascade devices under light illumination at an incident power
density Pinc. Assuming Pinc=1 W/cm2, about ten times the average of solar radiation at the
surface of the earth, and the radiation peaks at the response wavelength (with spectral
control in a TPV system) for ICDs and QCDs so that Jph=Ri·Pinc, the Voc is estimated and
plotted in Figure 6-9 for the devices presented in Figure 6-8. As can be seen, the QCDs
have a very modest Voc (<3 mV) due to a high J0 even with many stages (≥30). This may
explain why QC TPV cells have not been demonstrated in experiment so far. In contrast,
the values of Voc for the ICDs are considerably higher (more than an order of magnitude in
most cases) than for QCDs. This mainly stems from the much lower J0 in ICDs than in
QCDs (Figure 6-7). Combined with the higher photocurrent density as indicated in Figure
6-8(a), the IC structure is more advantageous than the QC structure for TPV applications.
Note that, despite the much higher Ri, the Voc for ICD_SLs is similar with those for ICDs
because of the higher J0 in ICD_SLs. However, with higher Ri and Jph, ICD_SLs will have
142
a higher output power and conversion efficiency if they have the same number of cascade
stages.
Wavelength (m)
1210 8 6 4
102
Open-circuit voltage (mV)

101
100 ICD
QCD
ICD_SL
100 150 200 250 300 350 400 450

Transition energy (meV)
Figure 6-9: Estimated Voc at 300 K for the ICDs, ICD_SLs and QCDs shown in
Figure 6-8.
In this chapter, firstly, an electrical method is developed to extract thermal generation
rate and minority carrier lifetime in in T2SL-based ICIPs. This method is more general and
considers the parasitic shunt and series resistances existed in practical devices. It can also
cover various transport mechanisms such as Auger and SRH processes. Based on this
method, the carrier lifetime at high temperatures (200-340 K) was evaluated to be between
8.5 and 167 ns, depending on the material quality. The extracted carrier lifetime displayed
a different temperature dependence from those previously obtained by other methods for
T2SL detectors, especially at high temperature range. Speculatively, such a temperature
dependence may be related to the growing dominance of the Auger process at high
temperatures. This method should also be applicable to detectors with other barrier
configurations, such as nBn, XBn and CBIRD [67, 81-82].
143
Secondly, the fundamental difference in carrier lifetime between ICDs and QCDs
is manifested by the saturation current density J0. By comparing and analyzing available
ICD and QCD data, it is shown that J0 can be used as a unified figure of merit to describe
both interband and intersubband cascade structures in terms of their device functionalities.
The significance of J0 on detector and PV cell performances was illustrated by comparing
the measured detectivity and the estimated open-circuit voltage, respectively. The extracted
values of J0 are more than one order of magnitude lower in ICDs than in QCDs with similar
transition energies. This result, in combination with the discussion of the consequences of
J0 on device performance, clearly revealed the advantages of IC configurations over
intersubband QC configurations based on the same framework. The overall picture for both
QCDs and ICDs sheds light from the perspective of a united figure of merit, which will
offer instructive guidance and stimulation to the future development of both ICDs and
QCDs. It is worth pointing out that both ICDs and QCDs have their respective merits. For
example, QCDs are based on more mature material systems. The epitaxial growth and the
device processing technologies are well-established. Consequently, at the present stage,
QCDs can have better uniformity as well as less surface leakage and higher output power
for lasers. Hence, both QCDs and ICDs will coexist for various applications with different
requirements.
144
7 Chapter 7: Long wavelength interband cascade infrared
photodetectors
7.1 Introduction
In Chapter 6, a new method was developed to extract the carrier lifetime in mid-
wavelength ICIPs and a common figure of merit (closely related to carrier lifetime) was
proposed to evaluate the performances of IC and QC devices. In this chapter, further
understandings in the operations and behaviors of ICIPs are presented. All the devices
included in this chapter operate in the LWIR band. However, the fundamental principles
revealed in this chapter are also suitable to ICIPs working in other spectral regions.
Compared to conventional single-absorber structures, the multistage configuration of ICIPs
provides more degrees of freedom for optimizing device performance. On the other hand,
this also complicates the design process and requires a more comprehensive understanding
of multiple factors in order to optimize device performance. For example, ICIPs can be
divided into two groups: current-matched ICIPs [142, 231, 237-239] where the
photocurrent is designed to equal in all stages, and noncurrent-matched ICIPs [99, 137,
198-199, 240-241] with identical stages, as shown in Figure 7-1. In a current-matched ICIP,
the absorbers in the optically deeper stages are made thicker to achieve an equal
photocurrent in all stages. This relies on the precise knowledge of material absorption
coefficients, which may vary with temperature and increase the difficulty in
implementation at different operating temperatures. By comparison, in a noncurrent-
matched ICIP, the individual absorber thicknesses are designed to be identical in each
stage. It’s simpler to implement but has a possible drawback of substantially reduced
responsivity due to light attenuation, especially with relatively thick absorbers [99, 141].
145
Figure 7-1: Schematic illustration of the multi-stage ICIP with (a) regular and (b)
reverse configurations. The two configurations can be realized by reversing the
growth order of layers in one structure without changing the light illumination
direction.
Although these two groups of ICIPs have been explored independently, they have
not been studied together in the same framework. To identify and understand their specific
features and differences in device performance, a comparative study of the electrical and
optical properties of several ICIPs with both absorber designs are presented in this chapter.
Electrical gains significantly exceeding unity are observed from noncurrent-matched
ICIPs. To further examine the preliminary findings on electrical gain and to better
understand how noncurrent-matched ICIPs can be designed for optimized device
performance, additional three ICIPs with varied absorber thicknesses and number of
cascade stages are studied and a theory is developed to quantitatively explain the electrical
gain. As will be discussed in detail in the Section 7.3, a reasonable agreement is obtained
between theoretical calculations and experimental results.
146
7.2 Current matched ICIPs vs noncurrent-matched ICIPs
The two sets of four ICIP structures included in this section were designed to target
the LWIR region (8-12 m) with a reverse illumination configuration [142, 239]. The four
structures have different numbers of stages and variations of individual absorber
thicknesses, but they have identical electron and hole barriers and the same InAs/GaSb SL
composition. Each period (60 Å) of the SL absorber are made of layers: InSb (1.9 Å), InAs
(31 Å), InSb (1.9 Å) and GaSb (25.2 Å). The two thin InSb layers were inserted to balance
the strain from the InAs layer [168]. The absorbers in the four structures were p-doped to
2.6×1016 cm3 so that the electrons were the minority carriers. The electron barriers consist
of four GaSb/AlSb QWs with GaSb well thicknesses of 33/43/58/73 Å. The hole barriers
are seven digitally graded InAs/GaSb QWs and the InAs well thicknesses therein are
48/50/52/55/58/62/70 Å.
Set #1 includes two current-matched ICIP structures called Mat.-8S and Mat.-12S.
They have eight and twelve cascade stages, respectively. Mat.-8S was fabricated from
wafer S#4-8 that was described in detail in [239]. Mat.-12S is made up of 12 stages with
absorber thicknesses of 180, 192, 210, 228, 246, 264, 282, 306, 336, 366, 396, and 432 nm,
from the surface to the substrate (the direction of light illumination). Set #2 has two
noncurrent-matched ICIP structures, NMat.-16S and NMat.-20S, with sixteen and twenty
cascade stages, respectively. NMat.-16S has sixteen discrete identical stages with the
individual absorber thickness (222 nm) equal to that of the first-stage absorber in Mat.-8S.
NMat.-20S has twenty discrete identical stages with each absorber thickness (180 nm)
equal to that of the first absorber of Mat.-12S. The total absorber thickness in these four
147
ICIP structures is 2.29 m (Mat.-8S), 3.44 m (Mat.-12S), 3.55 m (NMat.-16S), and 3.60
m (NMat.-20S). Table 7-1 summarizes the design parameters, along with some key
material properties including cutoff wavelength 𝜆c, bandgap Eg and activation energy Ea
for the four ICIPs.
Table 7-1: Summary of material and design parameters for the four devices.
Total
Absorber # of 100% Eg (meV) Ea (meV) Ea (meV)
Device thickness
type stages 𝜆c (m) at 0K 78-125K 150-250K
(m)
NMat.-20S Identical 20 3.60 9.5 188 43 160
Current-
Mat.-12S 12 3.44 11.0 174 45 155
matched
NMat.-16S Identical 16 3.55 11.1 172 64 160
Current-
Mat.-8S 8 2.29 11.0 175 45 155
matched
The four ICIP structures were grown by molecular beam epitaxy (MBE) on p-type
GaSb substrates that were nominally undoped. After the MBE growth, the wafers were
processed into deep-etched square mesa devices with dimensions from 50 to 1000 m
using conventional contact UV photolithography and wet etching. A RF-sputter deposited
two-layer passivation (Si3N4 then SiO2) was used for improving overall stress management
and minimizing pin holes, and sputter deposited Ti/Au layers were used for top and bottom
contacts. Finally, the devices were mounted on heat sinks and wire bonded for
characterization.
7.2.2 Electrical properties
Electrical and optical properties of devices from these wafers were determined
through measurements of dark current density-voltage (Jd-V) characteristics and photo-
response spectra. From the measured Jd-V curves, the R0A were extracted for the four
148
representative devices as shown in Figure 7-2 at a wide temperature range. This allows to
obtain the activation energies by fitting R0A (1/T) to the following equation:
𝑅0 𝐴 = 𝐶𝑇 𝑏 𝑒 𝐸𝑎⁄𝑘𝑏 𝑇 (7-1)
where b and Ea are the two fitting parameters. In principle, the parameter b is expected to
be 1.5 if the dark current density scales with ni (SRH limited) and 3 if it scales with ni2
(diffusion limited). The extracted Ea values are shown in Table 7-1, where q=0 was used
at 78-125 K and q=2 was used at 150-250 K. From the extracted Ea, the carrier transport in
these devices at high temperatures (>150 K) is diffusion limited. This is because the
extracted Ea is nearly equal to their zero-temperature bandgaps Eg (T=0), which can be
determined by fitting Eg (T) to the Varshni formula:
𝛼𝑇 2
𝐸𝑔 (𝑇) = 𝐸𝑔 (𝑇 = 0) − (7-2)
𝛽+𝑇
where  and  are the Varshni parameters. The evaluated Eg (T=0) based on Equation 7-2
was 188, 174, 172 and 165 meV for NMat.-20S, Mat.-12S, NMat.-16S and Mat.-8S,
respectively.
The diffusion limited carrier transport can be further examined by comparing the
experimentally extracted R0A with the theoretical projections of a diffusion transport
model, which is given by Equation 2-8. According to this equation, R0A is larger for
detectors with more cascade stages, but lower for detectors with thicker absorbers. This
feature is corroborated by Figure 7-2, where the values of R0A for NMat.-20S and NMat.-
16S are higher than Mat.-12S and Mat.-8S thanks to the larger number of stages and the
thinner individual absorbers for all stages. Note that the thermal generation rate in Equation
2-8 is given by Equation 4-3, which implies that it scales with e− E g / kbT
.
149
T (K)
250 200 150 100
105 R0 A = CT − q e Ea kb T
104
103
R0A (.cm2)
102
NMat.-20S
101
Mat.-12S
100 NMat.-16S
Mat.-8S
10-1
4 6 8 10 12
-1
1000/T (K )
Figure 7-2: Extracted R0A of the four representative devices at various temperatures.
Based on Equation 2-8, the ratio of R0A between NMat.-20S (NMat.-16S) and Mat.-
12S (Mat.-8S) can be obtained from:
𝑅0 𝐴𝑁𝑀𝑎𝑡.−20𝑆 ∑𝑁𝑀𝑎𝑡.−20𝑆(tanh𝑑𝑚 ⁄𝐿 )−1

= 𝑚
∑𝑀𝑎𝑡.−12𝑆(tanh𝑑𝑚 ⁄𝐿 )−1
𝑒 ∆𝐸𝑔 ⁄𝑘𝑏𝑇 (7-3 a)
𝑅0 𝐴𝑀𝑎𝑡.−12𝑆 𝑚
𝑅0 𝐴𝑁𝑀𝑎𝑡.−16𝑆 ∑𝑁𝑀𝑎𝑡.−16𝑆(tanh𝑑𝑚 ⁄𝐿 )−1

= 𝑚
∑𝑀𝑎𝑡.8𝑆(tanh𝑑𝑚 ⁄𝐿 )−1
𝑒 ∆𝐸𝑔 ⁄𝑘𝑏𝑇 (7-3 b)
𝑅0 𝐴𝑀𝑎𝑡.−8𝑆 𝑚
where 𝛥Eg is the bandgap variation between two devices. Here, the diffusion length and
carrier lifetime were assumed to be same for the four wafers, which is reasonable because
they were designed with nominally identical SL absorber periods and grown in a close time
interval. Since the cutoff wavelength of NMat.-20S was shorter than the other three devices
that had a nearly equal bandgap, one needs to account the bandgap difference between
NMat.-20S and Mat.-12S in Equation 7-3(a), while 𝛥Eg can be neglected for NMat.-16S
and Mat.-8S in Equation 7-3(b). Based on Equation 7-3, the calculated ratios of R0A as a
function of diffusion length at 300 K are shown in Figure 7-3. As can be seen, if the
diffusion length far exceeds absorber thickness, the two R0A ratios approach a saturation
value of 6.44 and 2.50 for R0ANMat.-20S/R0AMat.-12S and R0ANMat.-16S/R0AMat.-8S, respectively.
150
7
T=300 K
5
R0A ratio
NMat.-20S/Mat.-12S
4
NMat.-16S/Mat.-8S
2
0 500 1000 1500 2000
Diffusion length (nm)
Figure 7-3: The theoretical R0A curves at T=300K. The device dark current was
dominated by the diffusion process at this temperature.
Table 7-2 shows the experimentally obtained R0A ratios and the theoretically
calculated R0A ratios by assuming the diffusion length is appreciably longer than the
individual absorber thickness (i.e. L ≫ dm). The variations in the calculated values of
R0ANMat.-20S/R0AMat.-12S with temperature resulted from the exponential term exp[Eg /(kbT)]
in Equation 7-3, where Eg was determined from the experimental data with certain
uncertainty. The experimentally obtained values used in Table 7-2 are for bulk R0A,
obtained by excluding the surface leakage contribution based on Equation 4-6. The non-
monotonic temperature dependence of the theoretical and experimentally extracted R0A
ratios may be caused by the uncertainty of Eg as mentioned above. Nevertheless, as shown
in Table 7-2, the experimentally extracted R0A ratios are in good agreement with theoretical
calculations at these high temperatures, confirming the diffusion limited carrier transport.
This also implies that the diffusion length is indeed longer than the individual absorber
thicknesses, though there may be minor inaccuracies in experimental data related to
variations of their bandgaps and parasitic series resistances. From Table 7-2 and Figure 7-
3, it can be inferred that the diffusion length in the four devices is finite, but probably longer
151
than 500 nm at 300 K.
Table 7-2: Theoretical calculated and experimental extracted values of R0A ratios at
high temperatures.
T (K) 280 300 320
(𝑹𝟎 𝑨𝑵𝑴𝒂𝒕.−𝟐𝟎𝑺 ⁄𝑹𝟎 𝑨𝑴𝒂𝒕.−𝟏𝟐𝑺 )𝒎𝒆𝒂𝒔𝒖𝒓𝒆𝒅 6.2 6.1 6.3

(𝑹𝟎 𝑨𝑵𝑴𝒂𝒕.−𝟐𝟎𝑺 ⁄𝑹𝟎 𝑨𝑴𝒂𝒕.−𝟏𝟐𝑺 )𝒕𝒉𝒆𝒐𝒓𝒚 6.3 6.4 6.4
(𝑹𝟎 𝑨𝑵𝑴𝒂𝒕.−𝟏𝟔𝑺 ⁄𝑹𝟎 𝑨𝑴𝒂𝒕.−𝟖𝑺 )𝒎𝒆𝒂𝒔𝒖𝒓𝒆𝒅 2.4 2.5 2.3
(𝑹𝟎 𝑨𝑵𝑴𝒂𝒕.−𝟏𝟔𝑺 ⁄𝑹𝟎 𝑨𝑴𝒂𝒕.−𝟖𝑺 )𝒕𝒉𝒆𝒐𝒓𝒚 2.5 2.5 2.5
7.2.3 Responsivity
The optical response of the ICIPs was collected using a FTIR spectrometer and then
calibrated with a 600 K blackbody source (aperture diameter of 0.762cm) with a 2π field
of view (FOV). Due to efficient carrier collection in these ICIPs with thin individual
absorbers, the photocurrent is insensitive to bias voltage. The zero-bias responsivity spectra
of the four representative devices at 200-300 K are shown in Figure 7-4. As can be seen,
the current-matched ICIPs have higher responsivities than the noncurrent-matched ICIPs
at all temperatures of interest. The responsivity of the noncurrent-matched ICIPs was only
about 60% of that obtained from the corresponding current-matched ICIPs with the same
absorber thickness (180 or 222 nm) in the first stage. This relation is exemplified in Table
7-3, where the value of Ri was taken at 7 m for NMat.16S, Mat.12S and Mat.8S ICIPs,
and at 5 m for NMat.-20S since its cutoff wavelength was about 2 m shorter than other
three detectors. These data clearly evidence the necessity of current match for optimal
responsivity, and substantial light attenuation in the optically deeper stages. This
conclusion can be further examined and illustrated by considering the temperature
dependence of responsivity, as shown in Figure 7-5.
152
3 4 5 6 7 8 9 10 11 12
0.20 NMat.-20S
Mat.-12S
0.15 NMat.-16S
0.10 Mat.-8S
0.05 T=200K
Zero-bias responsivity (A/W)

0.00
0.20
0.15
0.10
0.05 T=250K
0.00
0.20
0.15
0.10 T=300K
0.05
0.00
3 4 5 6 7 8 9 10 11 12
Wavelength (m)
Figure 7-4: Zero-bias responsivity spectra for the four devices at different
temperatures.
Table 7-3: Experimentally obtained ratio of responsivity for ICIPs at different

temperatures.
T (K) 200 250 280 300 320
𝑹𝟎 𝑨𝑵𝑴𝒂𝒕.−𝟐𝟎𝑺 ⁄𝑹𝟎 𝑨𝑴𝒂𝒕.−𝟏𝟐𝑺 0.66 0.62 0.63 0.61 0.63
𝑹𝟎 𝑨𝑵𝑴𝒂𝒕.−𝟏𝟔𝑺 ⁄𝑹𝟎 𝑨𝑴𝒂𝒕.−𝟖𝑺 0.63 0.61 0.62 0.59 0.57
As shown in Figure 7-5, the responsivities of the four devices exhibited similar
trends with temperature as they peaked at certain temperatures and then fell off with further
increasing temperature. The observed trends were linked with variations of absorption
coefficient, diffusion length, and current match with temperature. As discussed earlier, the
diffusion length (>500 nm at 300 K) was likely longer than or comparable to individual
absorber thicknesses throughout the entire temperature range of interest. Accordingly, the
153
collection of photogenerated carriers would not be affected in these ICIPs at various
temperatures. Hence, the temperature dependence of responsivity resulted mainly from the
increase of absorption coefficient due to bandgap narrowing at higher temperatures and the
consequential change in current match. In other words, the responsivity initially increased
with enhanced absorption as the temperature was raised, and then decreased when the more
substantial light attenuation in the optically deeper stages began to disrupt the current
match. This was more significant for devices with relatively thick absorbers. For instance,
since the first-stage absorber of Mat.-8S and NMat.-16S is thicker (222 nm) than that (180
nm) of Mat.-12S and NMat.-20S, their responsivities peaked at lower temperatures (280
and 250 K) compared to the peak locations (300 and 320 K) for Mat.-12S and NMat.-20S.
This fact once again demonstrates the existence of substantial light attenuation and the need
of current match in achieving optimal responsivity. Note that the cutoff wavelength of
NMat.-20S was much shorter than the other three devices and approached 7 m at low
temperatures. Thus, the light absorption (and attenuation) was small at this wavelength.
This yielded a relatively rapid increase of the corresponding responsivity with temperature
up to 280 K and the peak at 320 K, as shown in Figure 7-5.
0.20
=7m
Zero-bias responsivity (A/W)
0.15
0.10
NMat.-20S
0.05
Mat.-12S
NMat.-16S
Mat.-8S
0.00
150 200 250 300 350
Temperature (T)
Figure 7-5: Temperature-dependent responsivity of the four devices at 7 m.
154
7.2.4 Electrical gain
To perform a further quantitative analysis of current-matched and noncurrent-
matched ICIPs, the absorption coefficients of the SL absorbers were measured at room
temperature as shown in Figure 7-6. Based on the measured absorption coefficient, the
evaluated responsivity was much lower than the values in Figure 7-4 for noncurrent-
matched ICIPs, indicating possible electrical gain (G) exceeding unity. Theoretically, the
responsivities of current-matched and noncurrent-matched ICIPs are expressed as [242]:

1.24
𝑅𝑖 (𝜆) = (1 − 𝑅)(1 − 𝑒 −𝛼𝑑1 )𝐺 (7-4 a)
𝜆
1.24
𝑅𝑖 (𝜆) = (1 − 𝑅)𝑒 −(𝑁𝑐−1)𝛼𝑑1 (1 − 𝑒 −𝛼𝑑1 )𝐺 (7-4 b)
𝜆
where R is the from surface reflectance taken to be 0.31 for an InAs cap layer, and d1 is the
absorber thickness in the first stage. Only the first stage was considered in Equation 7-4(a)
for the current matched ICIPs owing to an equal photocurrent in every stage. All stages
were considered with Equation 7-4(b) for noncurrent-matched ICIPs because the
photocurrent is the smallest in the last stage. According to Equation 7-4, the electrical gain
can be estimated from the measured responsivities and absorption coefficients for the four
devices.
Figure 7-6 shows the estimated electrical gain at room temperature for the four
devices. As can be seen, the electrical gain for the ICIPs exceeds the unity when the
absorption coefficient is higher than a certain value (e.g. >1500 cm-1). As the absorption
coefficient further increases at the higher photon energies, G increases for noncurrent-
matched ICIPs, but remains nearly unchanged in current-matched ICIPs. This is because
the enhanced absorption at a larger photon energy attenuates the light intensity in the last
stage, which then necessities a large electrical gain to maintain current continuity. In
155
contrast, in first stage of the current-matched ICIPs, the increase of electrical gain is not
required since the photocurrent is highest among all the stages. Also, to maintain current
continuity, the electrical gain is required to be higher in ICIPs with thinner absorbers to
make up for a shorter absorption length. This is revealed in Figure 7-6, where the G is
higher in Mat.-12S than Mat.-8S, and is higher in NMat.-20S compared to NMat.-16S
when the photon energy is higher than 0.2 eV. Note that the value of G could vary greatly
in different cascade stages with substantial light attenuation. Gain exceeding unity was also
observed in single-absorber T2SL detectors (>5) [242] and in other MWIR ICIPs [151,
165], although the mechanism was not fully understood. The underlying mechanism and
the relevant theory of electrical gain in ICIPs will be described in detail in Section 7.3.
Wavelength (m)
1110 9 8 7 6 5 4
3.5
3.5 NMat.-20S
Absorption coefficient (103 cm-1)
Mat.-12S 8S 3.0
3.0 NMat.-16S at.-
,M
Mat.-8S 12S
t.-
2.5 , Ma 2.5
Electrical gain
6 S 0S
at.-1 at.-2
2.0 NM NM
2.0
1.5
1.5
1.0
0.5 1.0
0.0 0.5
0.15 0.20 0.25 0.30 0.35
Photon energy (eV)
Figure 7-6: Absorption coefficient and electrical gain at room temperature. The dips
near 4.2 m in the gain curves were due to CO2 absorption in the response spectra.
7.2.5 Johnson-noise limited detectivity
Overall, the generated electrical gain in ICIPs can partly compensate for the light
attenuation in an optically deeper stage. As such, the responsivity in noncurrent-matched
156
ICIPs can be appreciable although not as impressive as in the current-matched ICIPs. Given
much higher R0A (Figure 7-2) and suppressed noise as shown in cleaner response spectra
(Figure 7-4), noncurrent-matched ICIPs may achieve detectivities comparable to current-
matched ICIPs. Also, due to substantial electrical gain, perfect current match is not a must
in ICIPs, which offers great flexibility in design and practical implementation.
Based on the measured responsivity and R0A, the estimated Johnson-noise limited
detectivities for the four devices are presented in Figure 7-7. The general advantage
provided by ICIPs with more stages (theoretically discussed in Chapter 2) can be seen from
the maximum values of D* for NMat.-20S. For example, at 250K, the Johnson-noise-
limited D* at =7 m (with a FOV of 2) were 6.05×108, 5.12×108, 4.51×108 and 4.56×108
Jones for NMat.-20S, Mat.-12S, NMat.-16S and Mat.-8S, respectively. At a higher
temperature (e.g. 300K), the corresponding Johnson-noise limited D* are 2.40×108 (NMat.-
20S), 1.77×108 (Mat.-12S), 1.48×108 (NMat.-16S) and 1.40×108 (Mat.-8S) Jones. These
values of D* significantly exceeds the claimed value (e.g. ≥ 4.0×107 Jones with a FOV
between /2 and 2) for commercial uncooled MCT detectors [91]. The significantly
higher D* for NMat.-20S was partially due to the relatively shorter cutoff wavelength
compared to the other three devices. Nevertheless, with a similar cutoff wavelength, the D*
of NMat.-16S is slightly higher than Mat.-8S with same first-stage absorber thickness, even
though the responsivity is lower in NMat.-16S. Hence, in terms of detectivity, noncurrent-
matched ICIPs with appropriate designs can have comparable or even better performance
over current-matched ICIPs. In fact, there is still room for improvement of the performance
for noncurrent-matched ICIPs. When the stages of an ICIP are made identical, there is a
tradeoff between reduced signal and suppression of noise with increasing stages. Adding
157
more stages to a noncurrent-matched ICIP reduces the thermal noise, but also compromises
the signal current, due to light attenuation in the optically deeper stages. Hence, an
optimized number of cascade stages may exist for maximizing D* based on the absorption
coefficient and absorber thickness [141]. If, however, the electrical gain is considered, the
optimal number of stages will change as discussed in next section.
T=200K NMat.-20S
Mat.-12S
Detectivity (cm.Hz1/2/W)
NMat.-16S
Mat.-8S
109 T=250K
T=300K
108
3 4 5 6 7 8 9 10
Wavelength (m)
Figure 7-7: Johnson-noise limited D* spectra of the four devices at various
temperatures.
7.3 A comprehensive study of electrical gain in ICIPs
To fully unlock the mechanism and theory of the electrical gain observed in ICIPs,
apart from the two ICIP structures (NMat.-16S and NMat.-20S) in the preceding section,
another three noncurrent-matched structures are studied and compared in this section,.
Hence, there are in total five noncurrent-matched ICIPs quoted in this section. The three
structures were grown using GENxplor MBE system on nominally-undoped p-type GaSb
(001). The electron barriers, the hole barriers, the InAs/GaSb SL composition and the
doping concentration in them are the same with those in NMat.-16S and NMat.-20S.
158
However, they have different numbers of stages and variations of individual absorber
thicknesses. The three structures have 15, 23 and 28 cascade stages, and the corresponding
individual absorber thicknesses are 180, 180 and 150 nm, respectively. For convenience,
the three structures are denoted as I15S-180, I23S-180 and I28S-150. Also, for consistency,
NMat.-16S and NMat.-20S are designated afresh here as I16S-222 and I20S-180,
respectively. In the notations, the “I” indicates the identical-stage design. The total absorber
thicknesses are 2.70 (I15S-180), 3.55 (I16S-222), 3.60 (I20S-180), 4.14 (I23S-180) and
4.20 m (I28S-150). The absorption is insignificant in the electron and hole barriers, since
they are composed of semiconductor QWs with bandgaps that are much wider than the
absorber bandgap.
Table 7-4 summarizes key design and material parameters, including defect density
and perpendicular (⊥) lattice mismatch of the five wafers, which have comparable material
and crystal structural quality. After the MBE growth, the wafers were processed into square
mesa devices with dimensions from 50 to 1000 m using standard contact UV
photolithography followed by wet-chemical etching. A RF-sputter deposited two-layer
passivation (Si3N4 then SiO2) was used to improve overall stress management and
minimize pin holes. Sputter deposited Ti/Au layers provided top and bottom contacts.
Finally, the devices were mounted on heat sinks and wire bonded for characterization.
159
Table 7-4: Summary of the design and material parameters of the five wafers.
# of Individual SL Total Defect density ⊥ lattice

Device
stages thickness (nm) periods thickness (m) (cm-2) mismatch
I15S-180 15 180 30 2.70 5.5×104 -0.394%
I16S-222 16 222 37 3.55 5.0×104 0.043%
I20S-180 20 180 30 3.60 3.3×104 0.061%

I23S-180 23 180 30 4.14 6.4×104 -0.378%
I28S-150 28 150 25 4.20 4.7×104 -0.369%
7.3.2 Responsivity
The optical response of the ICIPs was characterized following the same procedure
described in the beginning of Subsection 7.2.23. The calibrated responsivities of
representative devices (200×200 m2) from the five wafers at 200-300 K are shown in
Figure 7-8(a). As shown, at 300 K, I15S-180, I23S-180 and I28S-150 have a nearly
identical cutoff wavelength (10.6 m), which is longer than for I20S-180 (9.5 m) but
slightly shorter than for I16S-222 (11.1 m). As descried in the Section 7.2, the
responsivities of these ICIPs are relatively small due to the thin individual absorbers,
especially for noncurrent-matched ICIPs because of light attenuation. On the other hand,
the shot and Johnson noises are suppressed for thinner individual absorbers and a larger
number of cascade stages. As shown in Figure 7-8(a), the responsivity spectra for the five
ICIPs at high temperatures are low but clear. Although the spectra were red shifted with
temperature due to bandgap narrowing, the peak responsivity was either nearly unchanged
or raised slightly (<10%) with increasing temperature. This is because the light absorption
and attenuation in multiple stages limit the maximal value of QE and increasing the
absorption coefficient beyond a certain value does not enhance QE, as shown in Figure 7-
160
8(b) for the five devices.
In general, the QE of a noncurrent-matched ICIP is determined by the last stage
with minimum number of photogenerated carriers, as expressed by Equation 7-4(b). The
calculated QEs for the five devices as a function of absorption coefficient are shown in
Figure 7-8(b). The quite small values (<1.8%) agree with the relatively low responsivities
shown in Figure 7-8(a). Also, the order of the calculated QEs of the five devices is nearly
the same as for the measured responsivities. The peak values of QEs are1.75%, 1.64%,
1.30%, 1.13% and 0.92% that occur at an absorption coefficient of 3527, 2737, 2567, 2287
and 2119 cm-1 for I15S-180, I16S-222, I20S-180, I23S-180 and I28S-150, respectively.
This is because of a tradeoff between the light absorption and attenuation in the last
individual stage. From Equation 7-4(b), for a given absorption coefficient, it is anticipated
that the device with thinner individual absorbers and thicker total absorber will have a
smaller QE, and thus a lower responsivity. For instance, with similar cutoff wavelengths,
the responsivity of I28S-150 is lower than I23S-180 and I28S-180 at each temperature of
interest. Specifically, at T=300 K and =7 m, the responsivity of I15S-180, I23S-180 and
I28S-150 is 0.098, 0.078 and 0.065 A/W, respectively. Note that the lower responsivity in
I28S-150 does not necessarily result in a lower detectivity since it also relies on the noise
as will be discussed later.
161
3 4 5 6 7 8 9 10 11 12
1.8
0.12 (a) T=200K
0.10 (b) I15S-180
I15S-180 1.6
0.08
I16S-222 I16S-222
0.06 I20S-180
1.4
Zero-bias Responsivity (A/W)
0.04 I23S-180
0.02 I28S-150
1.2 I20S-180
0.12
0.10 T=250K
I23S-180
0.08 1.0
QE(%)
0.06
0.04 0.8 I28S-150
0.02
0.12 0.6
0.10 T=300K
0.08 0.4
0.06
0.04 0.2
0.02
0.00
3 4 5 6 7 8 9 10 11 12 0 1000 2000 3000 4000 5000
Wavelength (m) Absorption coefficient (cm-1)
Figure 7-8: (a) Zero-bias responsivity spectra for the five devices at different
temperatures. (b) Theoretically calculated external quantum efficiency of the five
devices vs. absorption coefficient.
As mentioned above, there is a tradeoff between light attenuation and absorption
related to the last stage in a noncurrent-matched ICIP. This is revealed by the trends of the
calculated QE with absorption coefficient for the five devices. As can be seen in Figure 7-
8(b), the calculated QE curves of the five devices exhibit similar and nearly parallel
patterns with increasing absorption coefficient. They all peak at a certain absorption
coefficient and then fall off with further increases. Although the individual absorbers of
I16S-222 are thicker than I15S-180, the calculated QE of I16S-222 was smaller when the
absorption coefficient exceeds 2600 cm-1, due to more substantial light attenuation in the
last stage of I16S-222. This explains the measured lower responsivity of I16S-222
compared to I15S-180 at shorter wavelengths (e.g.  4 m). In the opposite case where the
light absorption had a greater effect than the attenuation in the last stage, the responsivity
162
of I16S-222 was higher than I15S-180, as manifested in the longer-wavelength region.
Note that the analyses have not accounted for the effect of electrical gain on responsivity.
In fact, in this context, the responsivity of a device follows the same sequence as the
photocurrent in the last stage, which will be discussed in the Subsection 7.3.5.
7.3.3 Electrical gain
Like the devices described in Section 7.2, the estimated responsivities with the
measured absorption coefficient for the five devices are smaller than the values shown in
Figure 7-8. This means that the electrical gain (G) exceeds unity in the five ICIPs. Based
on Equation 7-4(b), the G can be extracted from the experimentally measured absorption
coefficient and responsivities. Figure 7-9 shows the estimated G, along with the measured
absorption coefficients at room temperature. The electrical gain of the five noncurrent-
matched ICIPs exhibits a monotonic increase with absorption coefficient and when the
absorption coefficient is higher than a certain value (e.g. 1500 cm-1), the electrical gain
exceeds unity. For I23S-180 and I28S-150, G can be as high as ~4 at an absorption
coefficient of 4800 cm-1, which is expected to compensate for more significant light
attenuation when the absorption is increased. Thanks to the high G, the Johnson-noise
limited detectivity of the two devices can exceed that of I15S-180 at 300 K, as will be
discussed in Subsection 7.3.7.
Equation 7-4(b) states that the electrical gain in noncurrent-matched ICIPs is to
compensate for the attenuation of incident light in the last stage due to absorption in the
preceding stages. Hence, the G needs to be higher in ICIPs with thinner individual absorber
and thicker total absorber to make up for the shorter absorption length and larger
attenuation in the last stage. This inference from a physical viewpoint agrees with the
163
estimated G for the five devices. As shown Figure 7-9, the five devices in ascending order
of G are I15S-180, I16S-222, I20S-180, I23S-180 and I28S-150. This sequence is exactly
in ascending order of the total absorber thickness. The higher G in I28S-150 compared to
the other four devices was also partially because of a shorter absorption length with a
thinner individual absorber. In addition, the G was slightly higher in I16S-222 compared
to I15S-180 because there was more substantial light attenuation in the last stage of I16S-
222, even though the thicker individual absorbers enabled more light absorption in the last
stage. Accordingly, although both light attenuation and absorption in the last stage were
relevant, the attenuation outweighed the absorption in the five devices when determining
G. In fact, the G differs between stages in a noncurrent matched ICIP due to different light
attenuations. The optically deeper stages have higher G to compensate for the more
significant light attenuation. Consequently, the G depends on the number of cascade stages
and is not the same for all stages.
Wavelength (m)
10 8 6 4
5.5
4500 I15S-180
5.0
I16S-222
Absorption coefficient (cm-1)
4000 I20S-180 50 4.5

1
I23S-180 S- 2
3500 ,I
28 -22
I28S-150 0 I 16S 4.0
-18
Electrical gain
3000 23S 3.5

0 ,I
2500 -18 80 3.0
5S S-1
I1 I20
2000 2.5
1500 2.0
1000 1.5
500 1.0
0 0.5
0.15 0.20 0.25 0.30 0.35 0.40
Photon energy (eV)
Figure 7-9: Absorption coefficient and electrical gain at room temperature. The dips
near 4.2 μm in the gain curves were due to CO2 absorption in the response spectra.
164
7.3.4 Underlying mechanism of electrical gain
As initially proposed in Refs. [141], the electrical gain in ICIPs stems from the
adjustment of the electric potential over every cascade stage to maintain current continuity.
In a noncurrent-matched ICIP, since the light is partially absorbed in the preceding stages
and attenuates along the propagation direction, the number of photogenerated carriers (or
the photocurrent) will not be the same in each stage. To fulfil the same current flow in each
stage, the large photocurrent in the front stages (near the top surface), must be
counterbalanced by an injection current induced by a forward electric potential. Contrarily,
the small photocurrent in the back stages (near the bottom) must be supplemented by a
thermal generation current resulted from a reverse electric potential. The total electric
potential over all of stages equates zero or the external voltage if a bias is applied on the
device. At high temperatures, the thermal generation current is high and therefore
significant gain can be obtained in the back stages, as illustrated in the current five devices.
In next subsection, a theory is developed to quantitatively describe the measured
photocurrent and the electric potentials over each stage in these ICIPs.
As per Planck’s law and standard theories for barrier detectors [141, 244], the
photocurrent in the mth stage (Iphm) of a noncurrent-matched ICIP receiving the radiation
from a standard blackbody is given by:
2𝜋𝑞𝐴𝑜𝑝𝑡 𝑟𝑎 2 ∞ 𝐸2 𝐸2
𝐼𝑝ℎ = ( ) ∫𝐸 𝑄𝐸𝑚 ( 𝐸⁄𝑘𝑏𝑇𝑏𝑏 − 𝐸⁄𝑘𝑏 𝑇𝑎𝑚𝑏 ) 𝑑𝐸 (7-5 a)
ℎ3𝑐 2 𝑑𝑠𝑑 𝑔 𝑒 𝑒
𝑄𝐸𝑚 = (1 − 𝑅)𝑇𝑤𝑖𝑛 𝑒 −(𝑚−1)𝛼𝑑 𝑄𝐸𝑑 (7-5 b)
𝛼𝐿 𝛼𝐿exp(−𝛼𝑑)
𝑄𝐸𝑑 = 1−(𝛼𝐿)2 × [tanh(𝑑 ⁄𝐿) + − 𝛼𝐿] (7-5 c)
cosh(𝑑 ⁄𝐿 )
where Aopt is the optical area of the device, ra is the radius of the aperture of the blackbody
165
source, dsd is the distance between the blackbody source and the device, Eg is the bandgap
of the absorber, QEm is the effective quantum efficiency in the mth stage, Tbb is the
blackbody temperature (set to 600 K), Tamb is the ambient temperature (~297 K), E is the
photon energy, Twin (~0.7) is the transmittance of the cryostat window (ZnSe), and QEd is
the individual quantum efficiency, which is equal in each stage. The collection probability
of photogenerated carriers is imbedded in Equation 7-5(b) and Equation 7-4(b) corresponds
to the limiting case of Equation 7-5(b) where the diffusion length is much longer than the
individual absorber thickness, leading to complete collection of photo-generated carriers.
As mentioned before, the responsivities of the five devices have weak bias dependence.
This conveys that the photo-generated carriers are efficiently collected in the five devices
due to thin individual absorbers. Hence, there is no essential difference between the two
equations, and the choice of diffusion length (typically <2 m at room temperature) is
inconsequential to the calculation of QEm; here Ln was taken to be 0.7 m. The optical loss
due to the reflection of cryostat window was considered during the calibration of
responsivity, hence Equation 7-5(b) only accounts for reflectance at the top surface of the
device. Based on Equation 7-5, the calculated photocurrent in each stage of the five devices
at room temperature is shown in Figure 7-10(a). As shown, the calculated individual
photocurrent decreases with stage number, in agreement with the attenuation of light
intensity. The first stage is unaffected by light attenuation, therefore the photocurrent in
this stage only depends upon the absorption coefficient and individual absorber thickness.
Among the five devices, I16S-222 has the highest photocurrent in the first stage since it
has the thickest individual absorber. The I20S-180 device has the lowest first-stage
photocurrent because it has the largest bandgap. Additionally, the order of the five devices,
166
in ascending photocurrent in the last stage, is nearly consistent with the order according to
the responsivity spectra [Figure 7-8(a)]. As will be illustrated later, the signal current in the
context of electrical gain, follows the same sequence as well. The calculated photocurrents
of I15S-180 and I23S-180 overlap as expected, because they have the same individual
absorber thickness, cutoff wavelength, and absorption coefficient.
9
60 I15S-180
8 (a) I15S-180 (b)
I16S-222 I16S-222
I20S-180 40 I20S-180
Electric potential (nV)

7
I23S-180
Photocurrent (nA)
I23S-180
6 I28S-150 20 I28S-150
5 0
4 -20
3
-40
2
0 5 10 15 20 25 0 5 10 15 20 25
Stage number Stage number
Figure 7-10: Theoretically calculated photocurrent based on Equation 7-5 and (b)
electric potential calculated based on Equation 7-7 for each stage of the five devices
at room temperature.
7.3.5 Net effect of electrical gain
Based on the mechanism discussed above, with electrical gain, the signal current Is
can be expressed as:
𝐼𝑠 = 𝐼𝑝ℎ1 − 𝐼0 (𝑒 𝑞𝑉1⁄𝑘𝑏𝑇 − 1) = 𝐼𝑝ℎ𝑚 − 𝐼0 (𝑒 𝑞𝑉𝑚 ⁄𝑘𝑏 𝑇 − 1) (7-6)
where I0 is the saturation dark current, which is identical in each stage for a noncurrent-
matched ICIP, and Vm is the electric potential across the mth stage. At zero external bias,
the sum of the electric potential across each stage is zero: V1+V2+···+ VNc-1+ VNc=0. At high
temperatures, I0 is much higher than the photocurrent, thus the magnitude of the electric
167
potential will be quite small and a first-order approximation in Vm can be used. Equation
(7-6) plus the condition of zero total electrical potential, to the first-order approximation,
leads to the expression of Vm:
1 𝑘𝑏 𝑇 𝑐 𝑁
𝑉𝑚 = (𝑁𝑐 𝐼𝑝ℎ𝑚 − ∑𝑖=1 𝐼𝑝ℎ𝑖 ) (7-7)
𝑁𝑐 𝑞𝐼0
where i denotes the stage number. Based on this equation, the calculated electric potential
across each stage at room temperature for the five devices is shown in Figure 7-10(b). As
can be seen, the individual electric potential is very small as it ranges from several to tens
of nV. Hence, the first-order approximation is appropriate when estimating the signal
current in the five ICIPs. In a certain stage, the electric potential shifts from positive to
negative. This means that the electrical gain is above unity in the subsequent stages.
By replacing Vm with Equation 7-7, the signal current in Equation 7-6 can be
modified to:
𝑓𝑖𝑟𝑠𝑡 𝑜𝑟𝑑𝑒𝑟 𝑞𝑉𝑚

𝐼𝑠 = 𝐼𝑝ℎ𝑚 − 𝐼0 (𝑒 𝑞𝑉𝑚 ⁄𝑘𝑏 𝑇 − 1) → 𝐼𝑝ℎ𝑚 − 𝐼0
𝑘𝑏 𝑇
𝑞𝐼0 1 𝑘𝑏 𝑇 𝑐 𝑁 𝑐 𝑁 𝐼𝑝ℎ𝑖
= 𝐼𝑝ℎ𝑚 − (𝑁𝑐 𝐼𝑝ℎ𝑚 − ∑𝑖=1 𝐼𝑝ℎ𝑖 ) = ∑𝑖=1 (7-8)
𝑘𝑏 𝑇 𝑁𝑐 𝑞𝐼0 𝑁𝑐
This equation states that the signal current in a noncurrent-matched ICIP will be the
average of the photocurrents in each stage, provided that the dark current is much higher
than the photocurrent. The net effect of electrical gain is to raise the signal current from
the minimum photocurrent in the last stage to the average photocurrent over all the stages.
Figure 7-11 shows the calculated and the measured signal currents for the five devices in a
temperature range of 200-300 K. The calculations agree well with the experimental values
for the five devices, considering some inaccuracies and uncertainties in the absorption
coefficients and possible underestimates for I16S-222 at high temperatures with a small
168
resistance. Also, the device sequences according to the calculated last-stage photocurrents
[Figure 7-10(a)], and the calculated and measured signal currents have almost the same
order. The theory predicts that the photocurrent should increase with temperature, since the
number of photogenerated carriers increases due to bandgap narrowing. However, for
I16S-222 and I15S-180, the measured photocurrent slightly decreased while the device
temperature was raised from 280 to 300 K. This was probably caused by an error from the
small resistances or other factors that have not been understood yet, which deserve future
investigation.
6.0
5.5
5.0
Signal current (nA)
4.5
4.0
3.5
I15S-180
3.0 I16S-222
2.5 Solid symbol: measured I20S-180
2.0 Open symbol: calculated I23S-180
I28S-150
1.5
200 220 240 260 280 300
T (K)
Figure 7-11: Theoretically calculated and experimentally measured signal current for
the five devices.
Thanks to the electrical gain, the signal current is enlarged. Likewise, the spectral
responsivity is enhanced and can be expressed by the average value of QEm in each stage:
𝜆
𝑅𝑖 (𝜆) = 1.24 (1 − 𝑅) [𝑄𝐸𝑑 + 𝑒 −𝛼𝑑 𝑄𝐸𝑑 + ⋯ + 𝑒 −(𝑁𝑐−1)𝛼𝑑 𝑄𝐸𝑑 ]⁄𝑁𝑐
𝜆 (1−𝑅)𝑄𝐸𝑑 (1−𝑒 −𝑁𝑐 𝛼𝑑 )

= (7-9)
1.24 𝑁𝑐 (1−𝑒 −𝛼𝑑)
This expression of Ri () can be further simplified for ICIPs with thin absorbers. The QEd
in the numerator can be canceled with the term (1-e-ad) in the denominator when the
169
photogenerated carriers are fully collected. Therefore, this equation indicates that, for
noncurrent-matched ICIPs with thin absorbers, Ri () should monotonically increase with
absorption coefficient at high temperatures. This is consistent with the calculated
temperature dependence of the signal current as shown in Figure 7-11. However, when 
is large at a photon energy well above the bandgap, the exponential term exp(-Ncd) in the
numerator in Equation 7-9 is small and negligible. Consequently, the Ri () reaches its
saturation value, as observed in Figure 7-8(a) where the peak responsivities are almost
insensitive to temperature.
Based on Equation 7-9, the simulated responsivity spectra for I20S-180 and I23S-
180 at 250 K are shown in Figure 7-12. Also displayed are the calculations without
considering the gain, experimental results with the regular mode of the IR source (inside
the Nicolet 8700 FTIR spectrometer) and experimental results with a standard blackbody
radiation source (model IR-563 from Infrared Systems Development Corporation) at 800
and 1200 K. In comparison with the regular theory without the gain, the calculation based
on Equation 7-9 agrees much better with the experimental results. However, there are some
deviations from the experimental results at high photon energies. Also, the real responsivity
spectrum depends on the light source, while the calculated responsivity cannot express this
feature. The effect of the light source is significant when it radiates more photons at high
energies, which is evidenced by the higher responsivity at short wavelengths measured
with the IR source (which has more high energy photons than the 1200 K blackbody
source) and with the blackbody source at different temperatures. This means that the gain
spectrum has some dependence on the incident photon distribution and the real response
spectrum might not exactly follow with Equation 7-9, especially when the incident light
170
has a broad energy distribution with a large percentage of high energy photons. One
interpretation of this phenomenon is that larger electrical gains are required to compensate
for the increasing light attenuation at high photon energies and it turns out to be more
dominant with the increased proportion of high energy photons.
0.10 0.10
I20S-180 I23S-180
0.08 T=250K 0.08 T=250K
Responsivity (A/W)
Responsivity (A/W)
0.06 0.06
(a) (b)
0.04 800 K 0.04 800 K
1200 K 1200 K
IR Source IR Source
0.02 0.02
Theory-with gain Theory-with gain
Theory-without gain Theory-without gain
0.00 0.00
3 4 5 6 7 8 9 10 3 4 5 6 7 8 9 10
Wavelength (m) Wavelength (m)
Figure 7-12: Theoretical and experimental responsivity spectra for two devices at 250
K with the IR source and a standard blackbody radiation source at 800 and 1200 K.
7.3.6 Electrical characteristics
The electrical properties of the ICIPs were characterized at 78-340 K. The measured
dark current densities at -50 mV and the R0A of the five devices are shown in Figure 7-13.
At 300 K, the Jd at -50 mV was 0.95, 1.46, 0.32, 0.56and 0.43 A/cm2 for I15S-180, I16S-
222, I20S-180, I23S-180 and I28S-150, respectively. These values of Jd are nearly two
orders of magnitude lower than that (50-70 A/cm2) stated by the “Rule 07” for HgCdTe
detectors [244]. Table 7-5 presents the activation energies extracted from the temperature
dependence of R0A, along with the zero-temperature bandgaps for the five devices. For
I16S-222 and I20S-18, the carrier transport is diffusion limited since the activation energies
approach the zero-temperature bandgaps. In contrast, for the other three devices, the
extracted Ea is 50%-100% of zero-temperature bandgap, suggesting the involvement of
171
both the diffusion and the SRH processes in carrier transport. As can be seen in Table 7-5,
the relatively larger perpendicular lattice mismatch may lead to a somewhat poorer material
quality for these three devices compared to I16S-222 and I20S-180. Theoretically, given
diffusion-limited carrier transport, the R0A of a noncurrent-matched ICIP can be expressed
by Equation 2-9. This equation indicates that, with a similar cutoff wavelength, the
noncurrent-matched ICIP with more stages and thinner individual absorber will have a
larger R0A. This correlation is directly proved by the ascending order of R0A of I15S-180,
I23S-180 and I28S-150, although the carrier transport was partially affected by the SRH
process. With similar cutoff wavelengths at 300 K, I28S-150 had the largest R0A (1.12×10-
1
.cm2), followed by I23S-180 (8.43×10-2 .cm2) and then I15S-180 (4.78×10-2 .cm2).
The largest R0A (1.48×10-1 .cm2 at 300 K) of I20S-180 among the five devices was
ascribed to the shortest cutoff wavelength. On the same account, the R0A (3.15×10-2 .cm2
at 300 K) of I16S-222 was smallest, as a result of the longest cutoff wavelength as well as
the thickest individual absorber among the five devices.
T (K) T (K)
340 320 300 280 260 240 220 200 340 320 300 280 260 240 220 200
I15S-180 10 I15S-180
(a) I16S-222 I16S-222 (b)
1 I20S-180 I20S-180
Jd @ -50 mV (A/cm2)
I23S-180 I23S-180
R0A (.cm2)
I28S-150 1 I28S-150
0.1
0.1
0.01
0.01
3.0 3.5 4.0 4.5 5.0 3.0 3.5 4.0 4.5 5.0
1000/T (K-1) 1000/T (K-1)
Figure 7-13: Arrhenius plot of dark current density (measured at -50 mV) and R0A
of the five devices in the temperature range of 200-340 K.
172
Table 7-5: Comparison of electrical parameters of the five ICIPs.
I15S-180 I16S-222 I20S-180 I23S-180 I28S-150

R0A (cm2) @ 200 K 3.68 2.35 14.30 5.76 6.43
R0A (10-2 cm2) @ 300 K 4.78 3.15 14.8 8.43 11.2
Eg (meV) @ 0 K 176 172 188 174 174
Ea (meV) 150-250 K 132 160 160 132 102
7.3.7 Johnson-noise limited detectivity
The estimated Johnson-noise limited detectivities for the five devices are shown in
Figure 7-14. Because of significant electrical gain, in terms of detectivity, these noncurrent-
matched ICIPs can outperform the commercially viable uncooled HgCdTe detectors with
a similar cutoff wavelength. For instance, at T=250 K, the Johnson-noise limited D* values
(for 𝜆=7 m and a FOV of 2) were 5.34×108 (I15S-180), 4.41×108 (I16S-222), 5.91×108
(I20S-180), 5.28×108 (I23S-180) and 5.45×108 (I28S-150) Jones. At a higher temperature
(e.g. 300 K), the corresponding Johnson-noise limited D* were 1.66×108, 1.46×108,
2.37×108, 1.84×108 and 1.87×108 Jones, for I15S-180, I16S-222, I20S-180, I23S-180 and
I28S-150, respectively. By comparison, the stated D* (FOV between /2 and 2 ) for
commercial uncooled MCT detectors is about 4.0×107 Jones [91]. The significantly higher
D* of I20S-180 was partially due to the relatively shorter cutoff wavelength than the other
four devices. By the same token, the lowest D* of I16S-222 was partly because of the
longest cutoff wavelength among the five devices. With similar cutoff wavelengths, despite
the lower responsivities, the D* of I23S-180 and I28S-150 are slightly higher than that of
I15S-180 at 300 K, due to the larger R0As of these two devices than that of I15S-180 (Table
7-5). The Johnson-noise limited D* (𝜆=7 m) and the 100% cutoff wavelength (at 300 K)
for the five devices are summarized in Table 7-6.
173
T=200K I15S-180
I16S-222
I20S-180
I23S-180
Detectivity (Jones)
109 T=250K I28S-150
108 T=300K
3 4 5 6 7 8 9 10
Wavelength (m)
Figure 7-14: Johnson-noise limited D* spectra of the five devices at various
temperature.
Table 7-6: Comparison of D* at 𝜆=7 m, along with the 100% cutoff wavelengths at
300 K, for the five devices.
I15S-180 I16S-222 I20S-180 I23S-180 I28S-150
100% cutoff (m) @ 300 K 10.6 11.1 9.5 10.6 10.6
* 8
D (10 Jones) @ 250 K 5.34 4.41 5.91 5.28 5.45
D* (108 Jones) @ 300 K 1.66 1.46 2.37 1.84 1.87
In fact, there is still room for improvement of D* in noncurrent-matched ICIPs. As
mentioned in Section 7.2, the tradeoff between reduced signal and suppressed noise as the
number of stages increases implies that there is an optimal number of stages that maximizes
D* based on the absorption coefficient. The optimal number depends on the electrical gain
is considered or not since it alleviates the signal current compromise. If G is accounted,
according to Equation 7-9, the Ri (𝜆) will be equal to the average value of all the stages. If,
however, the gain is excluded, the Ri (𝜆) will be determined by the value of the last stage.
In [141] and [245], the optimizations of D* ignored the effect of G and consequently the
optimized D* (and corresponding Nc) was underestimated.
174
If the electrical gain is considered, based on Equation 2-9 and 7-9, the Johnson-
noise limited detectivity of a noncurrent-matched ICIP can be estimated by the following
equation:
𝜆 𝑄𝐸𝑑 [1−exp(−𝑁𝑐 𝛼𝑑)]

𝐷∗ = (7-10)
ℎ𝑐 √𝑁𝑐 [1−exp(−𝛼𝑑)]√4𝑔𝑡ℎ 𝐿 tanh(𝑑 ⁄𝐿 )
where QEd is the individual quantum efficiency and is given by Equation 7-5(c). The
calculated D* as a function of the number of stages for different individual absorber
thicknesses are shown in Figure 7-15. Both cases are considered, where the gain is included
or excluded. In the calculation, the absorption coefficient was taken to be 2000 cm-1,
closely corresponding to =7 m (Figure 7-9), and the diffusion length was assumed to 0.7
m. As can be seen in Figure 7-15, the calculated D* peaks at a certain number of stages
and then decreases with more stages, as anticipated from the tradeoff between signal and
noise mentioned above. However, with certain individual absorber thickness, the D* peaks
at a higher value and at a larger number of stages when the gain is considered. For instance,
for d=0.5L, the calculated optimal number of stages is 18 when the gain is considered,
while it is 7 when the gain is ignored. This is consistent with the previous statement that
the gain alleviates the effect of light attenuation, thus bringing an upward shift of the
optimal number of stages. It was also reflected by a modest drop of D* after the peak value,
as distinguished from the sharp decrease in the case without the gain. Adding many stages
in a noncurrent-matched ICIP could make D* approach zero if the gain is absent. However,
this could occur only at a significantly larger number of stages if the gain is included. The
peak value of D* is raised by about 40% with the gain for each given absorber thickness.
But, in both cases, the peak D* has a weak dependence on the absorber thickness, especially
when the absorber in each stage is made thin.
175
1.0 d/L=0.25
0.8 d/L=0.50
0.25 d/L=0.75
0.6
D* (a.u.)
d/L=1.00
0.50
0.4
0.75
0.2 1.00
solid: with gain
0.0 dashed: without gain
0 10 20 30 40 50
Number of stages
Figure 7-15: Detectivity derived from Equation 7-10 versus the number of stages with
various ratios of the individual absorber thickness to the diffusion length (d/L), which
are labeled near the curves in the two cases.
In this chapter, a comparative study of four LWIR ICIPs with current-matched and
noncurrent-matched configurations is presented. It is demonstrated that current match is
necessary to maximize the utilization of absorbed photons for optimal responsivity. The
reduced responsivity in noncurrent-matched ICIPs is correlated with light attenuation in
the optically deeper stages. Based on the extracted R0As for these LWIR ICIPs, the
diffusion length is evaluated to be longer or comparable to 0.5 m at various temperatures
of interest. In addition, electrical gain above unity is observed, which is more substantial
in noncurrent-matched ICIPs for maintaining current continuity. The significant electrical
gain enabled an appreciable responsivity in noncurrent-matched ICIPs, although still not
comparable with current-matched ICIPs. This, combined with the large R0A, resulted in
Johnson-noise limited detectivities (>1.4×108 Jones at 300 K) comparable to or even better
than in current-matched ICIPs.
176
To fully explain the observed electrical gain, additional three noncurrent-matched
structures are included and studied, which shows that the electrical gain commonly exists
in noncurrent-matched ICIPs. Furthermore, a theory is developed to quantitatively explain
the electrical gain in ICIPs. The calculations based on this theory exhibit good agreement
with experimental results. Also, on this basis, insights and guidance to optimize the
Johnson-noise limited detectivities in noncurrent-matched ICIPs are provided. This theory
on electrical gain should also be applicable to other types of multistage photodetectors such
as QWIPs [65, 78] and QCDs [83, 84]. This is because, even with distinctive transition
mechanisms from ICIPs, these types of multistage detectors are also limited by light
attenuation in the optically deeper stages, especially when the total absorbers are made
thick. Likewise, the electric potential across each stage in QWIPs and QCDs will be self-
adjusted to maintain current continuity and electrical gain will supplement the photocurrent
in the optically deeper stages.
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8 Chapter 8: Concluding notes and future work
8.1 Dissertation summary
The aim of this dissertation research was to identify and understand specific factors
that affect narrow bandgap TPV cell performance and investigate how interband cascade
(IC) structures can improve thermophotovoltaic (TPV) cells and infrared detectors, as well
as to gain further understanding of relevant device physics and operations. IC devices are
unique because of their multistage and multifactor nature in design, which was made
feasible largely thanks to the type-II broken gap alignment between InAs and GaSb. For
example, electron inter-stage transport profits much from this alignment as it enables the
smooth transition of electrons from the valence band in GaSb layer to the conduction band
in InAs layer without any considerable resistance. Through this process, electrons recycle
themselves between stages with a transport path that consists of a series of interband
excitation and collection events.
A consequence of the multistage strategy is the reduction of quantum efficiency (or
photocurrent) due to the fact that multiple photons are required for an electron to traverse
between the contacts. Nevertheless, the quantum efficiency is no longer an appropriate
measurement for multistage structures where the particle conversion efficiency is more
appropriate and is higher in IC devices. The multistage design uses thin absorbers in all
stages to ensure efficient collection of photogenerated carriers before they recombine;
while utilizing multiple stages to absorb incident photons to the maximal extent. This
results in advantages such as enhanced open-circuit voltage and suppressed noise in ICTPV
cells and IC infrared photodetectors (ICIPs), respectively. Ultimately, these advantages
178
enable the higher conversion efficiency and detectivity in multistage ICTPV cells and
ICIPs compared to conventional single-absorber TPV cells and detectors.
In chapter 3, compelling theoretical arguments are provided to underpin the
advantages of multistage ICTPV devices over single-absorber TPV devices. This chapter
begins with the identifications of the limiting factors that have driven low efficiencies in
single-absorber TPV devices. These factors are closely integrated with the high dark
saturation current density, short carrier lifetime, small absorption coefficient and limited
diffusion length. Their impact on conversion efficiency was illustrated in T2SL based TPV
devices in view of several scenarios with different values of L. It is shown that the
multistage IC structure can eliminate the diffusion length limitation that affects single-
absorber devices. As such, the particle conversion efficiency can approach 100%, and the
conversion efficiency can be increased by about 10% in a wide range of L values and
bandgaps.
In chapter 4, a fair amount of experimental evidence is presented to illustrate and
confirm the theoretically projected advantage of multistage ICTPV devices. This is done
by a comparative study of three narrow bandgap (~0.2 eV at 300 K) TPV devices with a
single stage, and three and five cascade stages. Based on the measured quantum efficiency
(QE), the diffusion length is extracted to be ~1.5 m at 300 K, which severely limited the
collection efficiency of photogenerated carriers in the single-absorber device (<20%).
Instead, the extracted collection efficiency in multistage devices approach 100%, thus its
conversion efficiency is greatly improved compared single-absorber TPV devices (3.6%
vs 0.9%).
179
Chapter 5 deals with the detailed characterization and performance analysis in
narrow bandgap (0.22-0.25 eV at 300 K) multistage ICTPV devices with increased number
of stages (i.e. 6, 7, 16, and 23 stages). It is found that current mismatch between stages
could be significant with more stages due to the variation of absorption coefficient. In
contrast, the collection efficiency of photogenerated carriers can be much improved with
thinner individual absorbers and more stages. Also, the carrier lifetime is extracted from
the dark current density to evaluate the material quality. Moreover, the effects of material
quality, current mismatch and collection efficiency on device performance are quantified.
The quantitative analysis shows that the material quality has the most significant impact
on the device performance among the three factors.
Starting from Chapter 6, experimental studies of IC structures for infrared
photodetection are provided. In this chapter, a novel and simple method is developed to
extract the thermal generation rate and minority carrier lifetime in in T2SL-based ICIPs.
This method is more general and can cover various transport mechanisms such as Auger
and SRH processes. Based on this method, the carrier lifetime at high temperatures (200-
340 K) is extracted to be 8.5-167 ns, which turns out to be affected by the material and
structural quality. The exponential temperature dependence of carrier lifetime was
speculated due to the growing dominance of the Auger process at high temperatures. In
addition, in this chapter, fundamental difference in carrier lifetime between IC devices
(ICDs) and quantum cascade devices (QCDs) is apparent from the saturation current
density J0. The extracted values of J0 are more than one order of magnitude lower in ICDs
than in QCDs with similar transition energies. Also, it is shown that J0 can be used as a
common figure of merit to describe cascade structures in terms of the device
180
functionalities. The significance of J0 on detector and PV cell performances was revealed
by the measured detectivity and the estimated open-circuit voltage, respectively.
Chapter 7 attempts a comparative study of four LWIR ICIPs with current-matched
and noncurrent-matched configurations. The cutoff wavelength of these ICIPs is around 11
m at 300 K. It is formally shown that current match is necessary to maximize the
utilization of absorbed photons for optimal responsivity. Also, the reduced responsivity in
noncurrent-matched ICIPs is strongly linked with the light attenuation in the optically
deeper stages. These ICIPs feature a substantial electrical gain, especially for noncurrent-
matched configurations. The significant electrical gain boosts the responsivity in
noncurrent-matched ICIPs, although it is still less than that in the current-matched ICIPs.
This, combined with the large R0A, results in Johnson-noise limited detectivities (>1.4×108
Jones at 300 K) comparable to that in current-matched ICIPs. The values of detectivity in
these LWIR ICIPs are better than that (~4.0×107 Jones) for uncooled state-of-the-art MCT
detectors with similar cutoff wavelengths. Hence, ICIPs can be positioned to be a
prospective candidate for replacing the commercially available MCT detectors in the
LWIR regime.
In Chapter 7, to gain an exhaustive understanding of the observed electrical gain,
three additional LWIR noncurrent-matched ICIPs are studied to allow a possible-in-depth
comparison. The study shows that the electrical gain universally exists in noncurrent-
matched ICIPs. Furthermore, a theory is developed to quantitatively elucidate the electrical
gain in ICIPs. The calculations based on this theory exhibit good agreement with
experimental results. On such a basis, insights and guidance to optimize the Johnson-noise
limited detectivities in noncurrent-matched ICIPs are provided.
181
8.2 Future works
As repeatedly stated in Chapter 3, 4, and 5, in the current phase, the relatively low
conversion efficiency in ICTPV devices is primarily due to the high saturation dark current
density coupled with a short carrier lifetime and narrow bandgap. Hence, grand structural
modifications or/and improvements in material quality are required. Otherwise for the
normal ICTPV structure with current InAs/GaSb SL materials, an attractive energy
efficiency would continue to be an unrealistic goal. The reduced dark current with
increased carrier lifetime will be equally beneficial for detector performance as the
dominating thermal noise is reduced. From this perspective, several means for objectively
reducing the dark current can be employed alone or in combination. For example, to
increase carrier lifetime, one feasible direction to pursue is to replace the InAs/GaSb SL
absorbers with gallium free InAs/InAsSb SLs with a relatively longer carrier lifetime. This
would be somewhat challenging with zero experience in incorporating this type of SL and
IC scheme together. The difficulty also lies in the possible substantial strain released from
the InAsSb layers in the SL.
Alternatively, one can improve the performance from the perspective of raising
photocurrent rather than reducing the dark current. This relies on a special technique to
enhance the light absorption, such as using plasmonic structures for achieving strong light
focusing at a certain wavelength [246-247]. Plasmons can create very strong local fields
around particle and can be guided along the interface in the form of traveling wave, known
as a surface plasmon-polariton. The enhanced absorption can only occur at the plasmonic
resonance wavelength, resulting in extremely narrow response spectra of the integrated IC
devices. For ICTPV cells, this would require an optimal spectral match between the
182
radiation spectrum of the selective emitter (or filter) and the plasmonic resonance.
However, for ICIPs, this feature would restrict them to applications in only very limited
areas.
In addition, other issues in IC devices are not fully resolved at this moment. From
the extracted activation of energy, the SRH process is identified to affect the dark current
in the form of G-R current, whose occurrence can only be in the depletion region. In the
quasi-neutral absorber region in IC structures, the current arising from the SRH process
essentially is still diffusion current. This goes counter to the ideal situation where depletion
regions are fully eliminated in IC devices since no p-n junction exists therein. It would be
meaningful to locate the depletion regions and remove them from IC devices, and
eventually to reduce the dark current. Another not fully appreciated problem is the
significant surface leakage, especially in IC devices with relatively small sizes as discussed
in Chapter 4. The ongoing fabrication research of IC devices is mainly dedicated to
dielectric passivation (SiO2 and SiNx) to improve the surface quality, which however seems
to be less than ideal. Other passivation techniques such as MBE regrowth of a wide-
bandgap semiconductor layer and deposition of a sulfide-based layer can be explored as
well to reduce the dark current. In addition, as raised in Chapter 4, the surface leakage tends
to cause less additional dark current in IC devices with more stages. This conflicts with the
larger resistance with more stages and consequentially more shunting current through the
parallel surface path, which needs to be understood in the future as well.
Another interesting subject of further investigation is the voltage dependent
collection efficiency of photogenerated carriers in ICTPV devices under laser illumination.
All the ICTPV devices in this dissertation have this feature in common. The remaining gap
183
about this subject is to theoretically simulate the collection efficiency while acknowledging
the effect of the applied external voltage. Specifically, one needs to build a reliable
mathematical model that can accurately describe the transport of electrons through the
diffusion process under an electric filed. In addition, future effort needs to be directed
toward explaining the observed exceptionally high collection efficiency for IC devices with
many stages (e.g. the 16- and 23-stage devices in Chapter 5). This result is intuitively not
surprising since more stages consume the applied voltage. However, it also might be that
the model used to extract collection efficiency (Equation 4-2) has limited power in ICTPV
devices with many stages as it is based on two idealized assumptions. Hence, additional
factors need to be considered in the future to improve the model’s performance.
Finally, research into improving the source and spectral shaping technology is
ongoing, but not in the MWIR regime. A good selective emitter that is able to convert the
radiation emitted from a broadband source to a narrow spectral band make the spectral
splitting approach unnecessary. However, there is a lack of effort into the development of
selective emitters whose radiation spectrum would match with the response of ICTPV
devices. Therefore, a reasonable next step in ICTPV research may be to utilize absorbers
with different bandgaps in order to achieve spectral splitting. This can be useful only if the
radiation received by the cell has a broadband spectral distribution. Because there are
already many inherent losses in a TPV system, this may be the most promising path
towards an efficient system.
184
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Willardson and A. C. Beer (ETs), Vol. 18, p. 201, Academic: New York, 1981.
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“Calculation of optimal absorber thickness in interband cascade type-II infrared
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204
10 Appendix A: Publications list
Refereed journal articles

[1] W. Huang, J. A. Massengale, Y. Lin, L. Li, R. Q. Yang, T. D. Mishima, M. B.
Santos, “Performance analysis of narrow-bandgap interband cascade
thermophotovoltaic cells”, Journal of Physics D: Applied Physics 53,175104
(2020).
[2] W. Huang, R. Q. Yang, “Limiting Factors and Efficiencies of Narrow Bandgap

Thermophotovoltaic Cells under Monochromatic Light Illumination”, Journal of
Applied Physics 126, 045714 (2019)
[3] W. Huang, S. M. Rassel, L. Li, J. A. Massengale, H. Ye, R. Q. Yang, T. D.

Mishima, M. B. Santos, “A unified figure of merit for interband and intersubband
cascade devices”, Infrared Physics and Technol. 96, 298 (2019)
[4] W. Huang, L. Lei, L. Li, J. A. Massengale, H. Ye, R. Q. Yang, T. D. Mishima, M.

B. Santos, “Enhanced collection efficiencies and performances of interband
cascade structures for narrow bandgap semiconductor thermophotovoltaic
devices”, Journal of Applied Physics 124, 023101 (2018)
[5] W. Huang, L. Li, L. Lei, J. A. Massengale, R. Q. Yang, T. D. Mishima, M. B.

Santos, “Electrical gain in interband cascade infrared photodetectors”, Journal of
Applied Physics 123, 113104 (2018)
[6] W. Huang, L. Li, L. Lei, J. A. Massengale, H. Ye, R. Q. Yang, T. D. Mishima, M.

B. Santos, “Minority carrier lifetime in mid-wavelength interband cascade infrared
photodetectors”, Applied Physics Letters 112, 251107 (2018)
[7] W. Huang, L. Lei, L. Li, J. A. Massengale, R. Q. Yang, T. D. Mishima, M. B.

Santos, “Current-matching versus non-current-matching in long wavelength
interband cascade infrared photodetectors”, Journal of Applied Physics 122,
083102 (2017)
[8] Y. Lin, J. A. Massengale, W. Huang, R. Q. Yang, T. D. Mishima, M. B. Santos,

“Examination of the durability of interband cascade lasers against structural
variations”, Journal of Infrared and Millimeter Waves, 39, 137-141, (2020)
[9] R. Q. Yang, L. Li, W. Huang, S. M. Rassel, J. A. Gupta, A. Bezinger, X. Wu, S.

G. Razavipour, G. C. Aers, “InAs-based Interband Cascade Lasers”, IEEE Journal
of Selected Topics in Quantum Electronics, 25, 1200108 (2019)
[10] L. Lei, W. Huang, J. A. Massengale, H. Ye, H. Lotfi, R. Q. Yang, T. D. Mishima,

M. B. Santos, M. B. Johnson, “Resonant tunneling and multiple differential
conductance features in long wavelength interband cascade infrared
photodetectors”, Applied Physics Letters, 111, 113504 (2017)
205
Conference presentations and proceedings
[1] W. Huang, R. Q. Yang, “Efficiencies and limiting factors of narrow bandgap

thermophotovoltaic cells”, talk 11275-36 at Physics, Simulation, and Photonic
Engineering of Photovoltaic Devices IX at SPIE. Photonics West, San Francisco,
California, Feb. 1-6, 2020

“Multistage Interband Cascade Thermophotovoltaic Devices with ~0.2 eV
Bandgap”, at Photovoltaic Specialists Conference, Chicago, Illinois, June16-21,
2019

“Investigation of narrow bandgap interband cascade thermophotovoltaic cells”,
talk 10913-42 at Physics, Simulation, and Photonic Engineering of Photovoltaic
Devices VIII at Photonics West, San Francisco, CA, Feb. 2-7, 2019 (in Proc. SPIE.
10913, 1091317)
[4] J. A. Gupta, X. Wu, G. C. Aers, Y. Li, L. Li, W. Huang, R. Q. Yang, “Low-

threshold InAs-based interband cascade lasers with room-temperature emission at
6.3 μm” (Invited), talk 10939-33 at Novel In-Plane Semiconductor Lasers XVIII
at Photonics West, San Francisco, CA, Feb. 2-7, 2019
[5] W. Huang, S. Rassel, L. Li, J. Massengale, Y. Li, R. Q. Yang, T. D. Mishima, M.

B. Santos, “A Unified Figure of Merit for Interband and Intersubband Cascade
Devices”, at 14th International Conference on Mid-IR Optoelectronics: Materials
and Devices MIOMD-XIV (MIOMD 2018), Flagstaff, AZ, Oct. 7-10, 2018
[6] W. Huang, L. Lin, L. Li, J. Massengale, R. Q. Yang, T. D. Mishima, M. B. Santos,

“Collection Efficiency and Device Performance in Narrow Bandgap
Thermophotovoltaic Cells Based on Interband Cascade Structures”, at 14th
International Conference on Mid-IR Optoelectronics: Materials and Devices
MIOMD-XIV (MIOMD 2018), Flagstaff, AZ, Oct. 7-10, 2018
[7] Y. Li, L. Li, W. Huang, R. Q. Yang, J. A. Gupta, X. Wu, G. Aers, “Low-threshold

InAs-based Interband Cascade Lasers near 6.3 μm”, at 14th International
Conference on Mid-IR Optoelectronics: Materials and Devices MIOMD-XIV
(MIOMD 2018), Flagstaff, AZ, Oct. 7-10, 2018
[8] J. A. Gupta, A. Bezinger, S.G. Razavipour, X. Wu, G. C. Aers, Y. Li, L. Li, W.

Huang, R. Q. Yang, “Long-Wavelength InAs-based Interband Cascade Lasers
Grown by MBE”, paper TuM6 at 34th North American Conference on Molecular
Beam Epitaxy (NAMBE 2018), Banff, Canada, Sept. 30-Oct. 5, 2018
[9] W. Huang, L. Li, L. Lei, J. A. Massengale, H. Ye, R. Q. Yang, T. D. Mishima, M.

B. Santos, “Carrier Lifetime in Mid-Infrared Type-II Superlattice Photodetectors”,
206
at 31th Annual Conference of the IEEE Photonics Society, Reston, VA, Sept. 30-
Oct. 4, 2018
[10] R. Q. Yang, W. Huang, L. Li, L. Lei, J. A. Massengale, T. D. Mishima, and M. B.

Santos, “Gain and resonant tunneling in interband cascade IR photodetectors”
(Invited), talk 10543-13 at Quantum Sensing and Nanophotonic Devices XV at
Photonics West, San Francisco, CA, Jan. 27- Feb.1, 2018 (in Proc. SPIE. 10540,
105400E)
207

THERMOPHOTOVOLTAIC DEVICES AND INFRARED PHOTODETECTORS BASED ON INTERBAND CASCADE STRUCTURES

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UNIVERSITY OF OKLAHOMA

THERMOPHOTOVOLTAIC DEVICES AND INFRARED PHOTODETECTORS

BASED ON INTERBAND CASCADE STRUCTURES

SUBMITTED TO THE GRADUATE FACULTY

in partial fulfillment of the requirements for the

A DISSERTATION APPROVED FOR THE

BY THE COMMITTEE CONSISTING OF

Dr. Rui Yang, Chair

Dr. Michael Santos, Co-chair

Dr. Kieran Mullen

Dr. Bruno Uchoa

Dr. Arne Schwettmann

Dr. Bin Wang

nominated me for several awards, and helped me improve my presentations.

my general exam and dissertation.

fabrication of some devices in this work.

I am also appreciative of our group’s collaborators. Particularly, I would like to

structures for our research group.

Last, but definitely not least, I am greatly indebted to my parents. It is their

during these years.

List of Tables .................................................................................................................. xii

List of Figures ................................................................................................................ xiv

Abstract ........................................................................................................................ xxiii

Chapter 1: Introduction ..................................................................................................... 1

1.1 Infrared radiation ............................................................................................ 1

1.2 Overview of infrared thermophotovoltaic energy conversion ........................ 5

1.2.1 Background ............................................................................................... 5

1.2.2 Active components in a TPV system ........................................................ 8

1.2.3 Thermophotovoltaic cells.......................................................................... 9

1.2.4 Thermodynamic analysis of thermophotovoltaic cell efficiency ............ 12

1.3 Overview of infrared detectors ..................................................................... 15

1.3.1 Background ............................................................................................. 15

1.3.2 Photon detection vs thermal detection .................................................... 17

1.3.3 Examples of photon detectors ................................................................. 19

1.3.4 Performance metrics for infrared detectors............................................. 23

1.4 Dissertation organization .............................................................................. 25

Chapter 2: Sb-based interband cascade devices.............................................................. 27

2.1 6.1 Å Semiconductor family ......................................................................... 27

2.2 Interband cascade lasers-the historic origin .................................................. 28

2.2.1 History and operation principle .............................................................. 28

2.2.2 Current status of ICL performance ......................................................... 31

2.3.1 InAs/GaSb type-II superlattices .............................................................. 32

2.3.2 Operation principle of ICTPV cells ........................................................ 34

2.3.3 Enhancement of open-circuit voltage in ICTPV cells ............................ 36

2.3.4 Improvement of carrier collection efficiency in IC structures ................ 37

2.4 Interband cascade infrared photodetectors.................................................... 41

2.4.1 Operation principle of ICIPs ................................................................... 41

2.4.2 Noise reduction in ICIPs ......................................................................... 43

2.4.3 Detectivity improvement in ICIPs .......................................................... 45

2.4.4 Comments on detectivity improvement in ICIP ..................................... 46

2.5 Growth and fabrication of interband cascade devices .................................. 47

Chapter 3: Limiting factors and efficiencies of narrow bandgap thermophotovoltaic cells

3.1 Background and motivation .......................................................................... 50

3.2 Practical limitations on single-absorber TPV devices .................................. 51

3.2.1 Quantum efficiency and dark saturation current density ........................ 51

3.2.2 Open-circuit voltage and fill factor ......................................................... 56

3.2.3 Conversion efficiency ............................................................................. 59

3.3 Efficiency improvement in multistage TPV devices .................................... 64

3.3.1 Enhancement of open-circuit voltage ..................................................... 64

3.3.2 Enhancement of conversion efficiency ................................................... 67