Terahertz band-gap in InAs/GaSb type-II superlattices
L.L. Lia, W. Xua,b,?, Z. Zenga, A.R. Wrightc, C. Zhangc, J. Zhangb, Y.L. Shid, T.C. Lue
aInstitute of Solid State Physics, Chinese Academy of Sciences, Hefei 230031, China
bDepartment of Physics, Yunnan University, Kunming 650091, China
cSchool of Engineering Physics, University of Wollongong, Wollongong, NSW 2522, Australia
dKunming Institute of Physics, Kunming, China
eDepartment of Physics, Sichuan University, Chengdu 610064, China
a r t i c l e i n f o
Available online 23 January 2009
InAs/Gasb type-II superlattices
a b s t r a c t
We demonstrate theoretically that it is possible to realize terahertz (THz) fundamental band-gap in
InAs/GaSb type-II superlattices (SLs). The presence of such band-gap can result in a strong cut-off of
optical absorption at THz bandwidth. This study is pertinent to the application of InAs/GaSb type-II SLs
as THz photodetectors.
& 2008 Elsevier Ltd. All rights reserved.
Terahertz (1012Hz or THz) region is the most scientifically rich
area of the electromagnetic (EM) spectrum . The THz wave (or
T-ray) technology is of great potential to impact many inter-
disciplinary fields such as telecommunication, biological science,
pharmaceutical technology, anti-terrorist, nanotechnology, to
mention but few. The realization of T-ray sources and sensors
has been an important field of research in optics and optoelec-
tronics since 1980s . From a physics point of view, for
the generation and detection of THz radiation it is necessary to
realize a material system in which the fundamental energy gap is
around THz photon energy. Thus, THz generation and detection
can be achieved through electronic transition accompanied by
the emission and absorption of THz photons. In this paper, we
propose to employ InAs/GaSb based type-II superlattice (SL)
systems as THz band-gap materials. In an InAs/GaSb based type-II
SL, the electrons and holes are separated spatially in different
material layers  so that the energy gap between the confined
electron states in the InAs layer and the confined hole states in the
GaSb layer can be tuned artificially by simply varying the sample
growth parameters such as the widths of the InAs and GaSb layers.
Thus, by band-gap engineering, we can realize an SL system in
which the fundamental energy gap between the valence miniband
in the GaSb layer and the conduction miniband in the InAs layer is
at THz. On the basis of such structures, THz optoelectronic devices
can be designed and realized.
2. THz miniband structure
Here we generalize the usual Kronig–Penney model  to
calculate the electronic miniband structure of InAs/GaSb based
type-II SLs. From this calculation, we can obtain the wavefunction
hole (j ¼ h) in the nth miniband in the SL, with kz being the
SL wavevector along the growth direction (or the z-axis). The
effective masses for carriers (electrons and holes) in InAs/GaSb SLs
are taken as me
InAs¼ 0:038m0 with m0 being the rest electron
calculation, we take the conduction- and valence-band offsets
at the InAs/GaSb interfaces to be DEC¼ 960MeV and DEV¼
450meV and the conduction- and valence-band overlap energy
is D ¼ 150meV. These band parameters have led to a good
agreement between the experimental and theoretical results in
InAs/GaSb based type-II quantum well systems .
In Fig. 1, we show the band-gap energy between the bottom of
the lowest electron miniband in the InAs layer and the top of the
highest heavy-hole miniband in the GaSb layer as a function of the
InAs (GaSb) layer width at a fixed GaSb (InAs) well thickness. It is
found that there are two sets of growth parameters which can
be used to reach THz band-gap in InAs/GaSb SLs. When the InAs/
GaSb layer widths are about 8.5/2.8 or 6.1/7.9nm, the funda-
mental band-gap Eg¼ ee
be tuned by adjusting the InAs/GaSb layer widths. The band-gap
energy Eg decreases with increasing the InAs and/or GaSb layer
thickness, because the energy of the electron miniband in the InAs
layer decreases with increasing LInAsand that of the heavy-hole
miniband in the GaSb layer increases with LGaSb. We also find that
in these sample structures, the energy separations among the
electron and hole minibands in different layers are larger than
100meV, i.e., they are in the mid-infrared bandwidth.
nkzðzÞ and energy ej
nðkzÞ for an electron (j ¼ e) or a heavy-
InAs¼ 0:40m0, me
GaSb¼ 0:04m0and mh
GaSb¼ 0:33m0. In the
0ð0Þ is of the order of THz and can
ARTICLE IN PRESS
Contents lists available at ScienceDirect
journal homepage: www.elsevier.com/locate/mejo
0026-2692/$-see front matter & 2008 Elsevier Ltd. All rights reserved.
?Corresponding author at: Institute of Solid State Physics, Chinese Academy of
Sciences, Hefei 230031, China.
E-mail address: firstname.lastname@example.org (W. Xu).
Microelectronics Journal 40 (2009) 812–814
3. Optical absorption spectrum
In this study we consider that an EM field, which is polarized
linearly along the growth-direction of a SL, is applied to the SL
system. In such a case, the electronic transition rate induced
by direct carrier interactions with the radiation field via absorp-
tion scattering can be obtained by using the Fermi’s golden rule.
Thus, we can employ the semi-classic Boltzmann equation as the
governing transport equation to study the response of the carriers
in a SL to the applied radiation field. For the first moment, the
energy-balance equation  can be derived on the basis of the
Boltzmann equation. We then can obtain two energy-balance
equations, respectively, for an electron and a hole and, from them,
the total electronic energy transfer rate due to electron/
hole-photon coupling. With the total electronic energy transfer
rate, the optical absorption coefficient induced by electron and
hole interactions with the radiation field can be calculated through
(i.e., jaj0) transitions, we have
j;j0ajj0, where ajj0 is the absorption coefficient induced by
transition from layer j to layer j0. For intra- (i.e., j ¼ j0) and inter-layer
nðKÞÞ½1 ? fðEj
n0ðkzÞ þ _o?, (1)
ajj0 ¼ a0gjðM?=m?
where a0¼ e2=ð_?0CÞ, kjand ?0 are, respectively, the dielectric
constants of the material j and the free space, C is the velocity
of the light in vacuum, cj¼ 16p_3=o
effective mass for an electron or a hole, o is the radiation
frequency, 1=M?¼ 1=m?
n0ðkzÞ ? _o?
j0 Þ½1 ? fðxþ
h, gj¼ 8_=ðm?
oÞ and x?
nðkzÞ þ m?
n0ðkzÞ ? m?
hÞ. Moreover, n is the index
for the nth miniband along the growth-direction, K ¼ ðk;kzÞ
with k ¼ ðkx;kyÞ being the electron/hole wavevector along the
foranelectron(j ¼ 2)
electron/hole minibands in the InAs/GaSb layers are much larger
than the THz energy. As a result, the THz optical absorption is
achieved mainly via type-II transition channel, namely through
the inter-layer transition between the electron miniband in the
InAs layer and the heavy-hole miniband in the GaSb layers. The
dependence of the optical absorption spectrum on the InAs/GaSb
layer widths is shown in Fig. 2 at T ¼ 77K. Because of a strong
type-II optical transition in an InAs/GaSb SL, a sharp absorption
cut-off can be observed. With increasing the InAs and/or GaSb
layer widths, the red-shift of the cut-off absorption can be
observed. The rather wide absorption spectrum seen here is
induced mainly by the presence of the dispersed minibands in a
SL. We find that a more efficient THz absorption can be observed
for samples with larger InAs well widths. For example, a strong
absorption (about a factor of 2) at 1THz can be seen for a sample
with the well widths 8.5/3.0nm than that with the well widths
6.3/7.9nm. More pronounced cut-off of the THz absorption can be
achieved for samples with smaller band-gaps. Furthermore, we
find that the intensity of THz absorption in InAs/GaSb SLs
increases with temperature T. With increasing T a red-shift of
the cut-off absorption can be observed.
nðKÞ ¼ ð?1Þj_2k2=2m?
nðkzÞ is the energy spectrum
hole(j ¼ 1),or and
In an InAs/GaSb type-II SL, the energy spacing among the
In this study, we have found that the THz band-gap energy can
be realized in InAs/GaSb based type-II SLs with the layer widths
about 8.5/2.8 or 6.1/7.9nm. The THz band-gap decreases with
increasing InAs/GaSb layer widths. In such SLs, THz optical
absorption can be achieved via type-II transition and the cut-off
of the absorption spectrum can be observed at THz frequencies.
The cut-off frequency is red-shifted with increasing the InAs/GaSb
ARTICLE IN PRESS
Fig. 1. Band-gap energy between the bottom of the lowest electron miniband in
the InAs layer and the top of the highest heavy-hole miniband in the GaSb layer as
a function of GaSb (InAs) layer width LB(LA) at a fixed InAs (GaSb) layer width, in
the upper (lower) panel. The results are shown for kz¼ 0.
Fig. 2. Optical absorption spectrum at a fixed InAs (GaSb) layer width LA(LB) for
different GaSb (InAs) layer widths, in the upper (lower) panel. The results are
shown at T ¼ 77K.
L.L. Li et al. / Microelectronics Journal 40 (2009) 812–814
layer widths and/or temperature. We have also found that the
intensity of THz absorption in such SLs increases with tempera-
ture. These features favor the application of InAs/GaSb type-II SLs
as practical THz photodetectors working at relatively high
temperatures. We hope these theoretical predictions and findings
can be verified experimentally.
This work was supported by the Chinese Academy of Sciences,
National Natural Science Foundation of China, and by the
Department of Science and Technology of Yunnan Province, China.
 B. Ferguson, X.C. Zhang, Nat. Mater. 1 (2002) 26.
 For a review, P.H. Siegel, IEEE Trans. Microwave Theory Tech. 50 (2002) 910.
 See, e.g., G. Bastard, Wave Mechanics Applied to Semiconductor Heterostructures,
Monographies de Physique, Paris, 1992.
 See, e.g., G. Grosso, G.P. Parravicini, Solid State Phys. (2000).
 P.A. Folkes, G. Gumbs, W. Xu, M.T. Lara, Appl. Phys. Lett. 89 (2006) 202113.
 W. Xu, Appl. Phys. Lett. 89 (2006) 171107.
ARTICLE IN PRESS
L.L. Li et al. / Microelectronics Journal 40 (2009) 812–814