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Varshni parameters for InAs/GaSb strained layer superlattice infrared photodetectors
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2011 J. Phys. D: Appl. Phys. 44 075102
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IOP PUBLISHING
JOURNAL OF PHYSICS D: APPLIED PHYSICS
J. Phys. D: Appl. Phys. 44 (2011) 075102 (5pp) doi:10.1088/0022-3727/44/7/075102
Varshni parameters for InAs/GaSb
strained layer superlattice infrared
photodetectors
B Klein, E Plis, M N Kutty, N Gautam, A Albrecht, S Myers and S Krishna
Center for High Technology Materials, Department of Electrical and Computer Engineering,
University of New Mexico, Albuquerque, NM 87106, USA
Received 4 October 2010, in final form 29 November 2010
Published 28 January 2011
Online at stacks.iop.org/JPhysD/44/075102
Abstract
The temperature-dependent behaviour of the bandgap of mid- and long-wavelength as well as
dual-colour (mid-/long-wavelength) infrared detectors based on InAs/GaSb strained layer
superlattices (SLSs) with p-i-n and nBn designs has been investigated with
temperature-dependent absorption, photoluminescence and spectral response techniques.
Values of Varshni parameters, zero temperature bandgap E 0 and empirical coefficient α, were
extracted and tabulated. The MWIR and LWIR superlattice detectors showed a temperature
change of 0.325 meV K −1 and 0.282 meV K −1 , respectively. These values are a factor of two
lower than that of HgCdTe and InSb, making them attractive for higher operating temperatures.
(Some figures in this article are in colour only in the electronic version)
1. Introduction
The development of third generation infrared imagers has
led to a concerted research effort on the development of
higher operating temperature (HOT) detectors in the midwave
infrared (MWIR, 3–5 µm) and the long-wave infrared
(LWIR, 8–12 µm) range [1, 2]. The present dominant IR
technologies in the MWIR and LWIR wavelength ranges are
indium antimonide (InSb) and mercury–cadmium–telluride
(MCT) detectors, respectively. InAs/GaSb type II strainlayer
superlattices (SLS), first proposed for IR detection in the
1980s [3, 4], are good candidates for the development of HOT
detectors. Most of the InAs/GaSb SLS previously reported
are based on the p-i-n design [5, 6]. One of the major dark
current components in these devices is Shockley–Read–Hall
(SRH) generation-recombination (GR) current associated with
the depletion region of the p-i-n diode. The recently proposed
nBn heterostructure design [7] eliminates the GR component
of dark current as the nBn structure is intended to operate with
n-type layers in the flatband with little depletion. Klipstein
showed that the diffusion contribution to dark current is directly
proportional to the zero temperature semiconductor bandgap
E 0 for InAsSb-based nBn devices [8]. In order to design HOT
detectors based on superlattices, the variation of the bandgap
needs to be investigated. This is especially interesting for
the superlattice since the band structure of the superlattice
consists of minibands with a 2D density of states, unlike bulk
semiconductors with 3D density of states. In this paper, we
report on a systematic study of the temperature dependence
of the bandgap of both MWIR and LWIR superlattices using
optical absorption, photoluminescence and spectral response
measurements. The most common binary superlattices in the
literature for the MWIR and LWIR detector consists of 10
monolayers (ML) InAs/10 ML GaSb and 14 ML InAs/7 ML
GaSb [9–11], respectively. Hence, these particular thicknesses
were chosen for the study. In order to study the effect of
transport in the heterostructure, both p-i-n and nBn detectors
were included in the study. Finally, reference samples of
InAsSb were included, to serve as a quantitative comparison
with the literature. The Varshni parameters for all the samples
were obtained using these three techniques. It was found
that the bandgap in the superlattice changed on average by
0.33 meV K −1 for MWIR and 0.282 meV K −1 for LWIR. This
is about a factor of two lower than InSb (0.6 meV K −1 ) [12]
and MCT (0.5 meV K −1 ) [13].
The variation of the bandgap of a III–V semiconductor
with temperature is described by the linear-quadratic relation
proposed by Varshni [14]
E(T ) = E 0 − αT 2 /(T + β), (1)
0022-3727/11/075102+05$33.00 1 © 2011 IOP Publishing Ltd Printed in the UK & the USA

J. Phys. D: Appl. Phys. 44 (2011) 075102 B Klein et al
Table 1. Summary of investigated detector structures and extracted Varshni parameters.
Wavelength Heterostructure α E 0
Structure range design Material (eV K −1 ) (eV) Method
A MWIR nBn undoped barrier Bulk InAsSb 3.8 × 10 −4 0.344 PL
3.8 × 10 −4 0.352 Absorption
B MWIR nBn doped barrier Bulk InAsSb 3.8 × 10 −4 0.340 Absorption
C MWIR nBn doped barrier Bulk InAsSb 2.5 × 10 −4 0.350 PL
4.6 × 10 −4 0.341 Absorption
D MWIR pin 10 ML/10 ML SLS 3.1 × 10 −4 0.234 Absorption
3.0 × 10 −4 0.228 Spectral response
E LWIR pin 14 ML/7 ML SLS 3.2 × 10 −4 0.138 Absorption
F LWIR nBn 14 ML/7 ML SLS 2.5 × 10 −4 0.133 Absorption
2.8 × 10 −4 0.144 Spectral response
G MWIR nBn 10 ML/10 ML SLS 3.7 × 10 −4 0.233 Absorption
3.2 × 10 −4 0.241 Spectral response
LWIR nBn 14 ML/7 ML SLS 2.0 × 10 −4 0.118 Absorption
3.6 × 10 −4 0.159 Spectral response
Figure 1. Schematics of heterostructures used in this study. Samples A, B, C and F used the single-colour nBn architecture, samples D and
E were p-i-n, and sample G was a dual colour nBn structure.
where β is a constant (K), E 0 is the width of the semiconductor
bandgap at 0 K (eV), α is a fitting parameter (eV K −1 ) and T is
the temperature (K). The literature indicates a β of 266 K for
bulk GaSb [15], and a similar value of 270 K for InAs/GaSb
SLS [16]. Using experimentally determined temperaturedependent
bandgaps and β allows for the other two parameters
in the Varshni equation, α and E 0 , to be extracted. The value
of β chosen for this study was 270 K.
Previously, values of α equal to 2.5 × 10 −4 eV K −1 and
2.76×10 −4 eV K −1 for MWIR [17] and LWIR [16] InAs/GaSb
SLS detectors, found through photoresponse experiments,
have been reported. However, there was no correlation
between the photocurrent measurements, which represent
the convolution between the absorption and photocarrier
collection process and the absorption or photoluminescence
measurements that are insensitive to the photocarrier collection
process.
2. Experiment
The seven detector structures used in this study are summarized
in table 1; generic schematics of these structures are shown
in figure 1. All detectors were grown by solid source
molecular beam epitaxy (MBE) on n-type (Te-doped) epiready
(1 0 0) GaSb substrates. Structures A–C are nBn detectors
consisting of a 3 µm n-type (1 × 10 17 cm −3 ) absorbing layer
formed by InAs 0.91 Sb 0.09 , grown on top of a 1 µm n-type
(1 × 10 18 cm −3 ) contact layer. A 100 nm thick AlAs x Sb 1−x
barrier layer was deposited on top of an absorber layer,followed
by a 0.3 µm thick n-type InAs 0.91 Sb 0.09 (1 × 10 17 cm −3 ) top
contact. The barrier layer with an arsenic mole fraction
in AlAsSb of 15% was nominally undoped (in structure A)
and n-type with a carrier concentration of 1 × 10 17 cm −3 (in
structure B). In structure C, the composition of the barrier
layer was AlAs 0.1 Sb 0.9 with an n-type carrier concentration
of 1 × 10 17 cm −3 . The structure was terminated by a 10 nm
thick n-type (1 × 10 18 cm −3 ) InAs layer. It is to be noted that
the purpose of using the nBn-based InAsSb samples was to
validate the study by comparing the Varshni parameters with
previously reported bulk InAsSb films grown by MBE [18].
Structures D and E are p-i-n detectors designed to operate
in the MWIR and LWIR spectral regions, respectively. The
non-intentionally doped absorbing regions of these detector
structures were ∼2.5 µm thick, formed by 10 ML InAs/10 ML
GaSb SLS (D) and 14 ML InAs/7 ML GaSb SLS (E). N-type
(4 × 10 18 cm −3 ) bottom contacts with thicknesses of ∼0.6 µm
2

J. Phys. D: Appl. Phys. 44 (2011) 075102 B Klein et al
holder. A schematic of the setup is illustrated in figure 2.
Then, absorption was calculated by
Absorption(%) = I sam /I tsam − I subs /I tsub .
Figure 2. Configuration of samples in cryostat for absorption
measurements. The incident and transmitted light are (respectively)
made and detected with an FTIR system.
were formed by 10 ML InAs/10 ML GaSb SLS (D) and 8 ML
InAs/8 ML GaSb SLS (E). The top contact consisted of a p-type
(2 × 10 18 cm −3 ) GaSb layer with thicknesses of 160 nm (D)
and 100 nm (E). In order to improve carrier transport in the
detector structure, the 0.25 µm top and bottom components of
SLS absorber were doped. In addition, 10 periods of graded
layers were added between the absorber and the top contact
layer.
Structure F is an nBn detector intended to operate in the
LWIR wavelength range. The device structure consists of a
∼2 µm 14 ML InAs/7 MLs GaSb SLS absorber grown on top
of a ∼0.6 µm thick n-type contact layer (made of SLS with
the same composition and thickness but with Te-doped InAs
layers). This was followed by a 100 nm Al 0.2 Ga 0.8 Sb n-type
(1×10 16 cm −3 ) doped barrier layer. The structure was capped
by ∼0.13 µm thick top contact layer with the same superlattice
composition, thickness and doping concentration as the bottom
contact layer.
Structure G is a dual-colour detector with an nBn design.
It is composed of ∼2 µm thick MWIR and LWIR absorbing
layers formed by 10 ML InAs/10 ML GaSb SLS and 14 ML
InAs/7 ML GaSb SLS, respectively, separated by 100 nm
thick n-type (1 × 10 17 cm −3 ) Al 0.2 Ga 0.8 Sb barrier. N-type
(4 × 10 18 cm −3 ) top (120 nm thick) and bottom (0.5 µm
thick) contact layers were formed with SLSs with the same
composition as the MWIR and LWIR absorbing layers,
respectively. This sample was included to verify the validity of
the Varshni parameters since the MWIR and LWIR absorbers
were similar to those in samples D–F.
The temperature dependent changes in the bandgap of the
detector were determined by absorption, photoluminescence
(PL) and spectral response measurements. Absorption
measurements were performed within the 77–270 K range with
10 K increments using a Thermo Nicolet Nexus 870 Fourier
Transform Infrared (FT-IR) spectrometer, equipped with a
liquid nitrogen-cooled HgCdTe detector. First, single beam
transmission measurements were taken through a sample (I sam )
and a reference GaSb n-type substrate (I subs ), both mounted at
Brewster’s angle; transmission measurements were also taken
through the holes on the sample (I tsam ) and substrate (I tsub )
For PL measurements, the sample was placed in a closecycle
liquid helium cryostat and pumped with a 514 nm argon
laser, with a power of 1 W and chopping frequency of 207 Hz.
PL collection optics consisted of calcium fluoride lenses,
aluminium mirrors and a germanium filter. A monochromator
was equipped with a grating optimized for wavelengths from
2.5 to 6 µm. PL was measured from 10 to 160 K, with
increments of 10 K. It is to be noted that the cutoff wavelength
of the PL setup was 5.3 µm. Therefore, the PL was not suitable
for the LWIR samples.
The detector material was processed into single element
detectors with 410 × 410 µm 2 mesas having apertures ranging
from 25 to 300 µm. Details of p-i-n, nBn and dualcolour
detector fabrication are reported elsewhere [11, 19, 20].
Spectral response measurements were performed within
20–230 K temperature range with 10 K increments, using
a glow-bar source within the FTIR spectrometer. The
cutoff wavelength for PL measurements was defined as the
wavelength where the PL signal was at a maximum. For
absorption and spectral response measurements, the cutoff was
defined at the wavelength where the signal was reduced to 50%
of its peak value. The characterization methods utilized for
each investigated structure are summarized in table 1.
3. Results and discussion
Figure 3 shows a typical plot for the temperaturedependent
absorption, photoluminescence and spectral
response measurements. Measurements were made using
small temperature steps to obtain a meaningful fit. Varshni
fits for MWIR (A, B and C), LWIR (F) and dual-colour (G)
nBn detector structures using data extracted from absorption
(solid lines), PL (dash lines) and spectral response (dashed–
dotted line) measurements are shown in figure 4. The symbols
correspond to the values of the energy bandgap measured at
each given temperature. Varshni fits for MWIR (D) and LWIR
(E) p-i-n detectors, based on data extracted from absorption
and spectral response measurements are shown in figure 5. The
50% cutoff wavelength of the absorption spectrum corresponds
to the maximum of the PL curve, as illustrated by the inset in
figure 5.
The slight difference between values of energy bandgaps
extracted from temperature-dependent PL and absorption
measurements is possibly due to band filling effects, since
the number of carriers created by the laser is different
from the number of carriers created by the glow-bar source.
Presumably, the laser excitation promotes many carriers to
the conduction band, which fills the low-energy states within
the band so that the bandgap appears widened. This would
manifest as a blue-shift in the peak of the photoluminescence.
The samples in the absorption and spectral response do not
experience this phenomenon nearly as much, as the incident
radiation from the glow-bar is of low power compared with
that of the laser.
3

J. Phys. D: Appl. Phys. 44 (2011) 075102 B Klein et al
Figure 3. Representative plots of (a) absorption (77–270 K), (b) spectral response (20–200 K) and (c) photoluminescence (20–160 K) at
multiple temperatures. Sharp peaks and troughs in the plots are due to atmospheric absorption. For all three plots, the cutoff wavelength
increases with increasing temperature. The magnitude of spectral response and photoluminescence decreases with increasing temperature,
as indicated by the arrows.
Figure 4. Varshni fits for MWIR (A, B and C), LWIR (F) and
dual-colour (G) nBn detector structures extracted from absorption
(solid lines), PL (dash lines) and spectral response (dashed–dotted
lines) measurements. The symbols correspond to the values of
energy bandgap measured at each given temperature.
The zero temperature bandgap of InAsSb-based nBn
detectors with n-type barriers (structures B and C) is slightly
lower than one of the InAsSb-based detector with n.i.d. barrier.
We attribute this to variations in the quality of the samples.
For samples C (MWIR) and G (LWIR), α varies
significantly by the measurement used to determine it. We
believe that spectral response has the least error, as it can
be normalized with a background transmission measurement
to minimize effects from atmospheric distortion. Similarly,
a more complex normalization scheme is performed for the
absorption measurements; the only measurement that does
not have normalization is photoluminescence. However,
Figure 5. Varshni fits for MWIR (D) and LWIR (E) p-i-n detectors
extracted from absorption (solid lines) and spectral response
(dashed–dotted line) measurements. The inset shows representative
absorption and PL spectra. The λ 50%cutoff of the absorption spectrum
corresponds to the maximum on the PL curve.
the greatest advantage of photoluminescence is that the
cutoff wavelength is easily identified by the peak of the
spectra, rather than the 50% point, which is sometimes
difficult to define clearly. Therefore, photoluminescence
and absorption measurements have about an equal level of
accuracy.
Table 1 summarizes the Varshni parameters obtained for
each sample. All three characterization methods produced
results that are in good agreement with each other. Moreover,
our findings for InAs/GaSb SLS MWIR and LWIR material
compare closely with previously published data [16, 17]. A
comparison of the resulting measurements of the InAsSb
samples with already well-documented Varshni equations
shows good agreement. For a composition of InAs 0.91 Sb 0.09 ,a
0 K bandgap of 0.338 eV and α parameter of 3.4×10 −4 eV K −1
4

J. Phys. D: Appl. Phys. 44 (2011) 075102 B Klein et al
have been reported [18]. Our results are quite similar, with
average values of 0.345 eV for the 0 K bandgap and 3.7 ×
10 −4 eV K −1 for the α parameter. This similarity validates the
methods used to determine cutoff energies.
4. Conclusions
In conclusion, the temperature-dependent behaviour of
MWIR, LWIR and dual-colour (MWIR/LWIR) detectors
based on bulk InAsSb and InAs/GaSb SLS with p-i-n and nBn
designs have been investigated with conventional absorption,
PL and spectral response techniques. Values of Varshni
parameters, zero temperature bandgap E 0 and empirical
coefficient α, were extracted. All three characterization
methods produced results that were in good agreement.
To the best of our knowledge this is the first systematic
study of Varshni parameters performed on single and dual
colour InAs/GaSb SLS detectors operating in different spectral
regions.
Acknowledgment
Support from AFOSR grant FA9550-10-1-0113 is acknowledged.
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