PHYSICAL REVIEW B 70, 195339 (2004)

Band edge alignment of pseudomorphic GaAs1−ySby on GaAs
J.-B. Wang,* S. R. Johnson, S. A. Chaparro,† D. Ding, Y. Cao, Yu. G. Sadofyev, and Y.-H. Zhang
Department of Electrical Engineering & Center for Solid State Electronics Research, Arizona State University,
Tempe, Arizona 85287, USA

J. A. Gupta
Institute for Microstructural Sciences, National Research Council Canada, Ottawa, K1A 0R6, Canada

C. Z. Guo
Department of Physics, Peking University, Beijing 100871, People’s Republic of China
(Received 25 August 2004; published 24 November 2004)
Measurements of the transition energies of GaAsSb quantum well samples with different barrier configurations reveal that the conduction band offset of the coherently strained GaAs1−ySby / GaAs heterojunction grown
on GaAs has a zero crossing at a Sb mole fraction of y = 0.43± 0.07. A type-I band alignment is formed for
lower Sb mole fractions and a type-II band alignment is formed for higher Sb mole fractions. This occurs as a
consequence of a considerable amount (58%) of the −1.58 eV bandgap bowing being distributed to the
conduction band. As a suitable active material for 1.3 µm emission, pseudomorphic GaAs0.643Sb0.357 grown on
GaAs is determined to have a weak, 23± 23 meV, type-I conduction band offset and a bandgap energy of
928± 4 meV.
DOI: 10.1103/PhysRevB.70.195339

PACS number(s): 68.65.Fg, 61.10.Nz, 78.55.Cr, 81.15.Hi

I. INTRODUCTION

The determination of band offsets of the GaAsSb/ GaAs
heterojunction is critical for theoretical modeling and device
design. For example, GaAsSb grown on GaAs is one of the
more promising active materials for GaAs substrate based,
1.3 µm vertical-cavity surface-emitting lasers,1,2 which are of
great importance for optical communication applications involving data links and optical interconnects. Both a weak
type-I and a weak type-II band alignment for the
GaAsSb/ GaAs heterojunction have been reported;2–13 from
these measurements it is clear that a majority of the band
offset occurs in the valance band resulting in a weak or almost flat conduction band alignment. Furthermore, typical
measurements of the GaAsSb/ GaAs band offset2–13 rely on
the determination of the electron-hole transition energy that
for the most part depends on the bandgap energy which is
much larger than the conduction band offset. Therefore, precise quantitative measurements of both the conduction band
offset and the bandgap energy must be carried out in order to
accurately determine the band alignment of GaAsSb/ GaAs.
In this paper, we measure two sets of carefully designed
quantum well (QW) samples with different barrier configurations to precisely determine the conduction band alignment
of GaAsSb/ GaAs with Sb mole fractions suitable for 1.3 µm
emission. In this approach the position and height of electron
barriers placed next to a GaAsSb active layer produce varying quantum confinement energy shifts that are sensitive to
the size and type of the GaAsSb/ GaAs conduction band offset. The resulting transition energy spectrum is fit to calculated results using the bandgap and the size and type of the
conduction band alignment as fitting parameters. The modeling calculations are done using arbitrary conduction band
offsets and bandgap values and consequently do not rely on
any previous experimental or theoretical bandgap values.
1098-0121/2004/70(19)/195339(8)/$22.50

This combined with multiple variable-barrier samples is the
key to our novel and robust approach which we call variable
barrier spectroscopy.
II. EXPERIMENT

In sample set A, a 7 nm thick GaAsSb layer is placed
between two fixed 75 nm thick Al0.50Ga0.50As barriers with 5
nm thick variable height AlxGa1−xAs barrier spacers between
the GaAsSb layer and the fixed barriers. Five samples were
grown with various aluminum mole fractions, x = 0.0, 0.1,
0.2, 0.3, and 0.4, resulting in conduction band barrier heights
of Ex = Ec共AlxGa1−xAs兲 − Ec共GaAs兲 = 0, 81, 162, 243, and 324
meV, respectively.14,15 In sample set B, a 7 nm thick GaAsSb
layer is placed between a set of fixed 75 nm thick
Al0.25Ga0.75As barriers with GaAs spacers of various thicknesses placed between the GaAsSb layer and the fixed barriers. Six samples were grown with GaAs spacer widths, d
= 0.0, 1.0, 2.0, 3.0, 6.0, and 9.0 nm.
The samples were grown by solid-source molecular beam
epitaxy using a VG V80H system outfitted with As and Sb
valved crackers to control the flux of the mixed group-V
active layers. In both cases the 5-layer QW systems were
grown on top of a 400 nm thick GaAs buffer on n+ (100)
GaAs substrates and were capped with a 30 nm thick GaAs
layer. The GaAs buffer and cap were grown at 590 °C and
the substrate temperature was ramped down (up) without
growth interruption during the first (second) 75 nm thick
AlGaAs barrier to facilitate the much lower 480 °C growth
temperature of the GaAsSb active region. The substrate
heater thermocouple was linearly ramped between two calibrated setpoints that had been determined before the growth
using pyrometry measurements of the bare GaAs substrate.
During the GaAsSb layer growth, the group-V fluxes were

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PHYSICAL REVIEW B 70, 195339 (2004)

WANG et al.
TABLE I. Run to run Sb mole fraction variation given by XRD
measurements.
Sample
Number
1
2
3
4
5
6

Sample set A
Al mole
Sb mole
fraction
fraction
0.10
0.40
0.00
0.30
0.20
-

0.351± 0.003
0.361± 0.003
0.363± 0.004
0.355± 0.003
0.353± 0.002
-

Sample set B
GaAs
Sb mole
spacer (nm)
fraction
6.0
1.0
3.0
0.0
9.0
2.0

0.361± 0.003
0.356± 0.002
0.358± 0.001
0.360± 0.001
0.352± 0.001
0.355± 0.003

Sb/ Ga= 0.45 and As/ Ga= 0.90, which for a growth temperature of 480 °C results in a Sb mole fraction around 0.35 and
a GaAsSb/ GaAs QW emission wavelength around 1.3 µm.
To achieve sharp mixed group-V interfaces during the
growth of the GaAsSb layer, the Sb valve was opened ⬃10 s
before the Sb shutter was opened, to allow the Sb flux to
stabilize before the GaAsSb layer was grown.
Knowledge of the Sb mole fraction in the GaAsSb layer is
critical in analyzing the transition energy spectrum; therefore
x-ray diffraction (XRD) measurements and theoretical fitting
were done for each sample. The high-resolution XRD measurements were performed with a Philips MRD system using
an asymmetric double-crystal, channel-cut monochromator
and the Cu K␣1 line. The measurements were acquired in
13-hour scans, with 18-arcsec steps and an acquisition time
of 60 s per point, scanning in a standard ␪ / 2␪ geometry
about the GaAs (004) symmetric substrate Bragg reflection.
The XRD measurements were fit with a genetic algorithm
which determines the global best fit to a model calculated
using dynamical XRD theory. Vegard’s law is assumed such
that the lattice constant of unstrained GaAs1−ySby is linear in
the mole fraction.
The GaAsSb mole fraction, the GaAs cap thickness, and
the mole fractions of the two fixed 75 nm thick AlGaAs
barriers were fitting parameters in the XRD modeling; all of
the other parameters of the 5-layer QW structure were fixed
at the nominal grown values, which are expected to be accurate within ±3% based on previous calibrations of the MBE
system. Minimizing the number of fitting parameters avoids
overfitting the XRD data as well as spurious parameter values caused by correlated parameters. Furthermore, only the
mole fraction (and not the thickness) of the GaAsSb layer is
extracted from the XRD analysis because (1) sensitivity
analysis of the XRD data indicates that the Sb mole fraction
and GaAsSb layer thickness are strongly correlated; and (2)
sensitivity analysis of the QW energy spectrum indicates that
the transition energies are an order of magnitude more sensitive to variations in the Sb mole fraction than to those in
the GaAsSb layer thickness.
The Sb mole fraction values obtained from the XRD
analysis are summarized in Table I. The 5 samples of set A
(variable barrier height) have an average value of 0.357 with
a high of 0.363± 0.004 and a low of 0.351± 0.003. The 6
samples of set B (variable spacer width) have an average

value of 0.357 with a high of 0.361± 0.003 and a low of
0.352± 0.001. These results indicate that the mixed group-V
composition was reliably controlled during the growth of
these samples, which is remarkable when one considers the
sources of instabilities in the growth of mixed group-V materials. The growth is done under an excess group-V flux
where the relative incorporation of Sb and As is very temperature dependent, for example, a 1 °C increase (decrease)
in substrate temperature during the growth of GaAsSb decreases (increases) the Sb mole fraction by 0.001. In addition
to the requirement that the substrate temperature be reproduced within a few degrees the As and Sb flux levels must be
reproduced to within 1% to achieve these results.
To determine the ground state energy transition of each
sample, photoluminescence (PL) measurements were carried
out at room temperature using an argon-ion laser emitting at
514 nm with an excitation power density of 35 W / cm2. The
luminescence was measured using a high-resolution spectrometer, liquid nitrogen cooled germanium detector, and a
computer controlled lock-in amplifier. Since the PL experiments were carried out at room temperature, exciton effects
are small and have been neglected. Furthermore, excitation
dependent measurements from 1 to 35 W / cm2 show that the
PL peak blue shifts by less than 0.5 meV for all samples,
demonstrating that any blue shift due to excitation density
differences caused by sample geometry is small and can be
neglected. The ground-state energy transition is therefore
reasonably assumed to coincide with the peak position of the
PL spectrum.
III. THEORETICAL MODELING

The measured transition energies for each sample set are
compared to a family of calculated transition energy curves
to determine the most likely pseudomorphic bandgap and
band offset values for each sample set. The band offset and
bandgap values used in the calculations are chosen (independent of previous bandgap or band offset measurements) over
a reasonable range of values that justify the observed transition energies. The calculated set of curves are reliable because the calculations only depend on the electron and
heavy-hole confinement energy shifts based on arbitrary
band alignment configurations of the quantum well system
and do not depend on less reliable calculations, such as bandgap and band offset values based on empirical expressions
and material strain calculations. In detail, the ground state
transition energies are calculated for the two sample sets (A
and B) using arbitrary GaAsSb/ GaAs conduction band offsets, ⌬Eqw
c = 60, 40, and 20 meV for a type-I alignment; 0
meV for flat bands; and −20, −40, and −60 meV for a type-II
alignment. The calculations are done using the transfer matrix method to solve a system of Schrödinger equations.15
Band mixing, intraband relaxation scattering, and band-gap
shrinkage are neglected, which is a valid approximation for
low injection PL measurements. The effective electron and
heavy-hole masses used in the calculations are given in Table
II.
The calculated results for sample set A are plotted as solid
circles in Fig. 1 for the case where the arbitrary preset band-

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BAND EDGE ALIGNMENT OF PSEUDOMORPHIC…

TABLE II. Material parameters, calculations, and experimental results.
Parameter

Symbol

lattice constant
elastic stiffness constant ratio
hydrostatic deformation potentials

a共Å兲
C12 / C11
ac共eV兲
a␯共eV兲
b共eV兲
me / m0
mhh / m0
mlh / m0
Ebulk
g 共eV兲
⌬Ebulk
c 共eV兲
⌬Ebulk
␯ 共eV兲
Eqw
g 共eV兲
⌬Eqw
c 共eV兲
⌬E␯qwhh共eV兲
⌬Eqw
vlh共eV兲

shear deformation potential
electron effective mass
heavy-hole effective mass
light-hole effective mass
bulk bandgap energy (300K)
bulk conduction band offset
bulk valence band offset
strained bandgap energy
strained electron band offset
strained heavy-hole band offset
strained light-hole band offset

GaAs

GaSb

GaAs0.643Sb0.357

5.65325a
0.4526a
−7.17a
1.16a
−1.7a
0.067a
0.5a
0.087a
1.424a
-

6.09593a
0.4553a
−6.85a
0.79a
−2.0a
0.0393a
0.4a
0.05a
0.726a
0.018a
−0.680a
1.053a
−0.524a
−0.895a
−0.340a

5.81129a
0.4534a
−7.06a
1.03a
−1.8a
0.0486a
0.471a
0.0738a
0.782c
0.232c
−0.410c
0.928± 0.004b
0.023± 0.023b
−0.473± 0.023b
−0.287c

(or calculated using values) from Refs. 15,17,18.
Measurements from this work.
c
Calculated using measurements from this work and the Bir-Pikus Hamiltonian (Ref. 17).
aValues
b

gap energy is 935 meV, which is selected as a reasonable
starting point by examination of the experimental data and
the calculations. It is important to note that any other reasonable choice for the preset bandgap value for calculation purposes, essentially shifts the curves up or down in energy
from those shown in Fig. 1, and does not affect the final
outcome of the analysis. A result of the fact that the deep
heavy-hole energy level is comparatively insensitive to small
changes in the hole barrier height when selecting a slightly
different preset bandgap value.
The solid curves shown in Fig. 1 are fits of the following
equation to the calculated results:

冉 冉

E PL = Eqw
g 共GaAsSb兲 + 2Ea exp
+ 92.3 meV.

冊 冊

Ex − Eb
− 0.94 − 1
Ex + Eb

共1兲

fixed at the experimental set of conduction band barrier
heights discussed above and Eqw
g 共GaAsSb兲 is fixed at the
preset bandgap energy used in the calculations; note that
Eqw
g 共GaAsSb兲 is converted into a fitting parameter when the
experimental data is analyzed. This procedure is used to parametrize the calculations in a functional form to facilitate
the extraction of the bandgap and band offset from the experimental data. In this parametrization, each individual conduction band offset has a unique set of distinguishing energies Ea and Eb which only weakly depend 共⬍1 / 250兲 on the
present bandgap value when selected within the 900 to 970
meV range. Equation (1) is related to the band alignment by
noting that Ea and Eb depend exponentially on the conducwith a characteristic energy, E0
tion band offset ⌬Eqw
c
= 118.6 meV, as given in the following two equations and
shown in the inset of Fig. 1:

冉

During the fit, Ea and Eb are fitting parameters, while Ex is

Ea = 11.5 + 26.1 · exp −

冊

⌬Eqw
c
meV,
E0

冉 冊

Eb = 44.0 + 22.0 · exp

FIG. 1. Theoretical calculations and model of the transition energy versus the AlGaAs barrier height for various GaAsSb/ GaAs
conduction band offsets.

⌬Eqw
c
meV.
E0

共2兲

共3兲

Physically, as illustrated in Fig. 1, the ground-state energy
transition increases by Ea, when the conduction band barrier
height, Ex, changes from 0 to 3Eb. The size of this shift is
strongly dependent on the band offset and is much larger
when a type-II band alignment is present. The change in the
transition-energy caused by the change in the barrier layer
originates mainly (99.7%) from the conduction band, because the deep heavy-hole energy level is virtually unaffected by changes in the barrier layer. Therefore, from a
practical point of view, the parameters depend on the quan-

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WANG et al.

FIG. 2. Theoretical model fit to results for the variable AlGaAs
barrier height experiment.

tum energy shifts in the conduction band, making this approach very sensitive to the size and the sign of the conduction band offset.
The experimental data for sample set A are plotted in Fig.
2 with the measured transition energies given by the open
circles. Since the Sb mole fraction of the samples varies
slightly (see Table I), the measured transition energies are
adjusted for the run-to-run variations in the Sb mole fraction
to improve the accuracy of the measurements. The solid
circles in Fig. 2 give the transition energies shifted to those
expected for a Sb mole fraction of exactly 0.357 (the average
value for the sample set) using the following self-consistent
fitting process. First, the bandgap and band offset is determined, assuming that the Sb mole fraction is the same average value for all samples. Using these values, the mole fraction dependence of the transition energy is determined, from
which the transition energy for each sample is adjusted to the
transition energy expected if a given sample had actually
possessed the average Sb mole fraction value. Next, the
bandgap and band offset are determined for the adjusted data
set. This self-consistent process is repeated until the bandgap
and band offset values converge. Since the Sb mole fraction
variation was small, this process converged in the first iteration.
If we had not adjusted the experimental PL data for the
sample to sample variation in the mole fraction, the inferred
bandgap and band offset values would still be within the
uncertainties reported. However, since the XRD measurements reveal a small variation in the sample to sample mole
fraction, our best estimate of the bandgap and band offset
must include this information. The error bars shown in Fig. 2
are determined from the uncertainty in the mole fraction
given by the XRD measurements. Each data point is numbered in the order that the samples were grown; a random
sequence was intentionally designed to minimize possible
systematic errors. Equations (1) through (3) are fit to the
qw
adjusted experimental results with Eqw
g 共GaAsSb兲 and ⌬Ec
as fitting parameters. The best-fit parameters give the bandgap energy as Eqw
g 共GaAsSb兲 = 929± 5 meV and the conduction band offset as a weak type-I band alignment with
⌬Eqw
g = 13± 26 meV for GaAs0.643Sb0.357 / GaAs. The uncertainties reported here are 2 times the standard error 共±2␴兲 in
the best-fit parameters given by the Levenberg-Marquart
algorithm.16

FIG. 3. Theoretical calculations and a model of the transition
energy versus GaAs spacer width for various GaAsSb/ GaAs conduction band offsets.

The calculations and investigation of sample set B follows
the same procedures described above for sample set A, with
the theoretical calculated results shown in Fig. 3 as the solid
circles. The solid curves are parametrizations of the calculations using the following equation:

冠 冉

E PL = Eqw
g 共GaAsSb兲 + 2Ea exp

冊 冡

db − d
− 1.14 − 1
db + d

共4兲

+ 74.9 meV.

During the fit, Ea and db are fitting parameters, while d is
fixed at the experimental set of GaAs spacer widths discussed above and Eqw
g 共GaAsSb兲 is fixed at the preset bandgap energy. Analogous to sample set A, each individual conduction band offset has a unique set of distinguishing
parameters Ea and db which only weakly depend 共⬍1 / 350兲
on the present bandgap value when selected within the 900
to 970 meV range. Ea and db are related by the constant
6.24 meV/ nm and increase exponentially, with characteristic
energy E0 = 68.8 meV, as the conduction band offset, ⌬Eqw
c ,
goes from type I to type II (see the inset of Fig. 3 and the
following equations):

冉

Ea = 7.8 + 29.5 · exp −

db =

冊

⌬Eqw
c
meV,
E0

Ea
nm.
6.24 meV

共5兲

共6兲

Physically, as illustrated in Fig. 3, the ground-state electron
energy level is shifted up by 1.1 Ea when the GaAs spacer
width d changes from db to 0. Again the magnitude of this
shift is strongly dependent on the band offset and is much
larger when a type-II band alignment is present.
The experimental data for sample set B (numbered in the
order that the samples were grown) are plotted in Fig. 4 with
the measured transition energies given by the open circles
and the measured transition energies adjusted for the run-torun variation in the Sb mole fraction given by the solid
circles. As was done for sample set A, the best estimate of
the bandgap and band offset includes adjustment of transition

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BAND EDGE ALIGNMENT OF PSEUDOMORPHIC…

FIG. 4. Theoretical model fit to results for a variable GaAs
spacer width experiment.

energies to those expected for a Sb mole fraction of exactly
0.357, the average value for sample set B. Equations (4)
through (6) are fit to the experimental data with
qw
Eqw
g 共GaAsSb兲 and ⌬Ec as fitting parameters. The best-fit
parameters give the bandgap as Eqw
g 共GaAsSb兲 = 927± 6 meV
and the conduction band offset as weak type I with ⌬Eqw
c
= 34± 24 meV for GaAs0.643Sb0.357 / GaAs.
To confirm that the choice of the preset bandgap value for
the calculations does not affect the outcome of the fit, the
same series of calculations and fits performed above are repeated using preset bandgap values (900 and 970 meV) that
are substantially away from the best-fit value. These new fits
are also shown in Figs. 2 and 4 and are indistinguishable
from the original fit for a preset bandgap value of 935 meV.
The results of this analysis are summarized in Table III with
the determined bandgap and band offset reported to a precision of 0.1 meV to resolve the differences. The choice of the
preset bandgap value at most changes the best-fit bandgap
and band offset values by ±0.1 meV well within the uncertainties reported here; demonstrating the robustness of this
approach.
The bandgap and conduction band offset values obtained
from sample sets A and B agree to within uncertainties. As a
best estimate, the average values from the two sample sets
qw
(Eqw
g = 928± 4 meV and ⌬Ec = 23± 23 meV) are reported in
Table II, where the uncertainty is given as 2 times the standard error. The resulting band edge diagrams for the 5-layer
QW structures are shown in Fig. 5. Where Fig. 5(a) gives the
variable barrier height structure showing the bandgap energy
TABLE III. Pseudomorphic bandgap and conduction band offset
for different present GaAsSb bandgap values.

Sample
set A
Sample
set B

Preset bandgap
(meV)

Determined
bandgap (meV)

Determined
band offset (meV)

900
935
970
900
935
970

929.3± 4.8
929.3± 4.8
929.4± 4.8
926.9± 5.6
927.0± 5.6
927.1± 5.6

12.8± 26.2
12.8± 26.2
12.9± 26.2
33.8± 23.8
33.8± 23.8
33.9± 23.8

FIG. 5. Band-edge diagram of 5-layer quantum-well structures
with variable AlGaAs barrier height shown in (a) and variable GaAs
spacer width shown in (b).

and the conduction band offset, an increase in the barrier
height (dotted line) and the resulting confinement energy
shift (dashed line), and the parameters Ea and Eb. Similarly,
Fig. 5(b) gives the variable spacer width structure showing a
decrease in the spacer width (dotted line) and the resulting
confinement energy shift (dashed line) and the model parameters Ea and db. Note that in both structures the confinement
energy shift essentially occurs in the conduction band because the deep heavy-hole level is insensitive to the variations in the band edge configuration.
Sensitivity analysis was performed to estimate the impact
that the uncertainty in the MBE system calibration may have
on the above measurements. In the worst case, the uncertainty in the transition energy is ±0.4 meV for a ±3% uncertainty in the barrier layer Al composition (sample set A) and
±0.2 meV for a ±2% uncertainty in spacer layer thickness
(sample set B). The uncertainties given are based on GaAs
and AlAs growth rate calibrations. Even if the growth rate
uncertainty is doubled, the uncertainty in the transition energy is still less than 1 meV and hence well within the uncertainties reported in this work. Furthermore, if these errors
are randomly applied (the worst case for the band offset measurement) the uncertainty in the measurement of the band
offset is at most ±0.5 meV; again well within the uncertainties reported here. The uncertainties in the x direction (due to
the growth calibration) are smaller than the size of the data
points and are not shown in Figs. 2 and 4.
The bulk bandgap and band offsets are estimated from the
pseudomorphic GaAs0.643Sb0.357 on GaAs measurements using the widely accepted Bir-Pikus Hamiltonian.17 The bulk
material values and the deformation potentials used in the
calculation are listed in Table II. The uncertainty in the calculated bulk material values is relatively large (approximately ±10%) because the deformation potentials are not
accurately known.9,14 The calculated strained light-hole band
offset is included in Table II for completeness.
IV. EMPIRICAL BAND EDGE MODEL

Assuming a simple parabolic bowing relation for the
GaAsSb band edges, the bandgap, conduction band edge,
and valence band edge for bulk and strained GaAs1−ySby as a
function of the Sb mole fraction are given in Eq. (7):
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TABLE IV. Calculated and experimentally determined parameters.
Parameter

Symbol

strained, qw

bulk

Bir-Pikus, ␧

Bandgap bowing
Conduction band bowing
Valence band bowing, heavy hole
Valence band bowing, light hole
Binary bandgap offset
Binary conduction band offset
Binary heavy-hole band offset
Binary light-hole band offset

bgj共eV兲
bcj共eV兲
bvj hh共eV兲
bvj lh共eV兲
⌬gj共eV兲
⌬cj共eV兲
⌬vj hh共eV兲
⌬vj lh共eV兲

−1.58c
−0.91c
0.67c
0.72c
0.371b
−0.524b
−0.895b
−0.340b

−1.71c
−0.98c
0.73c
0.73c
0.698a
0.018a
−0.680a
−0.680a

0.13b
0.07b
−0.06b
−0.01b
−0.327b
−0.542b
−0.215b
0.340b

aFrom

Refs. 15,17,18.
using the Bir-Pikus Hamiltonian (Ref. 17).
c
Calculated using the measurements from this work.
bCalculated

Eij共GaAs1−ySby兲 = Eij共GaAs兲 − ⌬Eij,
with i = g,c, vhh,lh and j = bulk,qw,␧,
where ⌬Eij = ⌬ij · y − bij · y · 共1 − y兲,
with ⌬ij ⬅ Eij共GaAs兲 − Eij共GaSb兲.

共7兲

The relations between the bandgap and the conduction and
valence band edges are
Egj = Ecj − E␯j ,

with ⌬gj = ⌬cj − ⌬␯j and bgj = bcj − b␯j . 共8兲

And the relations between the parameters of the strained QW
layer and bulk material are
bulk
bulk
bulk
Eqw
+ E␧i , ⌬qw
+ ⌬␧i and bqw
+ b␧i .
i = Ei
i = ⌬i
i = bi

共9兲
The constants bij and ⌬ij are the bowing parameters and the
end point offset of the curves, respectively. The subscript i
denotes the bandgap 共g兲, the conduction band 共c兲, or the
valence band 共␯兲 and the superscript j denotes bulk material
(bulk), a strained QW layer 共qw兲, or the energy shift due to
strain 共␧兲. The additional valence band subscripts refer to the
splitting of the heavy-hole 共hh兲 and the light-hole 共lh兲 bands
when strain is present. When used alone, v refers to the
lowest energy state for the holes, which is the heavy-hole
band in the present compressively strained material system.
The simple relation in Eq. (7) between strained and bulk
material arises because in addition to the strong bowing parameter in bulk GaAsSb the effects of strain through the
Bir-Pikus Hamiltonian can be accurately described to second
order in the Sb mole fraction. The values for the parameters
in Eq. (7) are listed in Tables II and IV. The values obtained
from, or calculated from values in the literature15,17,18 are
denoted a in Tables II and IV, the values measured in this
work are denoted b in Table II, the values calculated from the
literature using the Bir-Pikus Hamiltonian are denoted b in
Table IV, and the values calculated using the results from
this work are denoted c in Tables II and IV. Note that the
measured values report are an average of the values obtained
from the two sample sets.

The conduction and valence band (heavy-hole) edges for
strained GaAs1−ySby on GaAs are shown in Fig. 6. An examination of Fig. 6 and Eq. (7) shows that the band alignment of the GaAs1−ySby / GaAs heterojunction has a type-I to
qw
type-II crossover at a Sb mole fraction y = 共1 − ⌬qw
c / bc 兲
= 0.43± 0.07. The maximum in the conduction offset, ⌬Eqw
c
qw
qw qw
= 共⌬qw
c − bc 兲 · 共1 − ⌬c / bc 兲 / 4 = 41± 18 meV, occurs at y = 共1
qw
− ⌬qw
c / bc 兲 / 2 = 0.21± 0.03. The uncertainties reported here
are determined from the uncertainty in the band offset measurement, assuming a simple bowing model with fixed binary endpoints. It is important to note that the calculated
band offset at the GaSb endpoint has some uncertainty associated with it as well, coming mainly from the uncertainty in
the value of GaSb deformation potential. Using the scatter of
the deformation potential values in the literature, the uncertainty in the calculated GaSb endpoint is estimated to be
about ±40 meV, which if included would increase the uncertainties in the critical points of the conduction band by about
10%.
V. DISCUSSION

One of the important contributions of this work is the
quantification of the band bowing distribution which eliminates the need for an arbitrary assignment of the bandgap
bowing to the valence band7 or to the conduction band.19 The

FIG. 6. Composition dependence of the conduction and heavyhole band edges for pseudomorphic GaAs1−ySby on GaAs.

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BAND EDGE ALIGNMENT OF PSEUDOMORPHIC…

present study indicates that the bandgap bowing of strained
GaAsSb on GaAs is fairly evenly distributed between the
conduction band (58%) and valence band (42%). Furthermore, the band bowing parameters of the strained QW material are related to the bulk material band bowing and the
bowing introduced by the Bir-Pikus Hamiltonian [see Eq. (9)
and Table II] which also demonstrates a similar bowing distribution. The second order dependence of the Bir-Pikus
Hamiltonian on the mole fraction originates from the product
of parameters which are linearly interpolated in the mole
fraction and from the second order dependence of strain on
the mole fraction, using the conventional definition of
strain.15 For this material system, the band bowing of
strained GaAsSb on GaAs is reduced because the bowing
introduced by the strain opposes that of the bulk material. It
is interesting to note that these competing effects are also
observed in the bond lengths of strained alloy materials.20
The valence band offset ratio, Q␯, has been introduced in
the literature21 as a constant to describe the band alignments
of heterostructures, such as AlGaAs/ GaAs, where the band
edge energies vary linearly with composition. However, for
materials that exhibit band bowing, Q␯ is a function of composition, as shown in the equation following, where Q␯ is
given for a ternary material embedded in one of its constitute
binaries, such as InyGa1−yAs in GaAs or GaAs1−ySby in
GaAs:
Qqw
␯ ⬅

⌬Eqw
␯
⌬Eqw
g

=

qw
⌬qw
␯ − b␯ · 共1 − y兲
qw
⌬qw
g − bg · 共1 − y兲

.

共10兲

Here Q␯ is only constant when little or no bulk band bowing
or strain is present, namely b␯qw and bqw
g are very small, or
when the bowing distribution is by chance identical to the
qw
band offset distribution of the binary constitutes 共bqw
␯ / bg
qw
qw
qw
qw
qw
= ⌬␯ / ⌬g 兲. In either case Q␯ = ⌬␯ / ⌬g . Clearly for materials that exhibit substantial bowing, such as GaAsSb, it is
desirable to parametrize the conduction and valance band
edges in terms of constants rather than variable band offset
ratios.
In the previous studies, the strained bandgap energy of
GaAs1−ySby is often obtained from the bulk bandgap using
various bowing parameters and energy shifts due to strain
using various deformation potentials in the Bir-Pikus
Hamiltonian. The published bulk bandgap bowing
parameters14,22–27 of GaAs1−ySby are quite scattered; where
in early work22–24 the reported bulk bowing parameters range
from −1.0 eV to −1.2 eV for Sb mole fractions below 0.25,
more recently,25 −1.87 eV is given for mole fractions below
0.1, and very recently,14,27 bowing parameters around
−1.4 eV are given for a mole fraction around 0.5. The published deformation potentials for GaAs are quite
scattered,9,14 which results in substantial variations in the calculated band edge energy shifts. Therefore, the simultaneous
determination of the strained bandgap with strained band offset is critical for an accurate determination of the band alignment of GaAsSb/ GaAs. This is undoubtedly difficult to
achieve from measurements of a single sample, however, is
straight forward using the suitably designed sample sets presented here.

The accuracy of the conduction band edge shown in Fig.
6 is of paramount importance in determining the
GaAsSb/ GaAs band alignment. The accuracy of this curve
away from the measured value (around 36% Sb) depends on
the appropriateness of the simple bowing model and the accuracy of the bowing parameters which are subject to uncertainty introduced in calculating the band edges of coherently
strained GaSb. Nevertheless, the bowing parameters presented in Table IV are in reasonable agreement with those
reported in the literature. This work asserts both band alignment types for GaAsSb/ GaAs, depending on the Sb mole
fraction present. It is important to note that this is typical
when the constituent binaries form a negative offset in the
conduction band, ⌬qw
c ⬍ 0, and a significant amount of negaqw
tive bowing is present, bqw
c ⬍ ⌬c , in which case the conduction band edge will exhibit the observed positive-curvature
zero-crossing. On the other hand, for a material system
where the constituent binaries form a positive offset,
⌬qw
c ⬎ 0, and where a significant amount of positive bowing
qw
is present in the conduction band, bqw
c ⬎ ⌬c , the conduction
band edge will again form a zero crossing, but with the opposite curvature. A similar type of behavior could occur in
the valence band of some material systems.
Various band alignments for the GaAsSb/ GaAs material
system have been presented in the literature. A weak type-I
band alignment with the conduction band offset ⌬Eqw
c
⬃ 35 meV is reported2,3 for Sb mole fractions of 0.12 and
0.30, respectively. A magneto-optical study4 of
GaAsSb/ GaAs QWs concludes a weak type-I band alignment as well. On the other hand, there are several reports5–11
of a type-II band alignment with Q␯ ranging from 1.05 to 2.1.
Large excitation-dependent blue shifts in PL measurements
from GaAsSb/ GaAs12 and GaAsSb/ InGaAs13 QWs have
also been attributed to a type-II band alignment. In our experience, the PL blue shifts observed in highly strained QW
materials are predominantly a result of spatial band filling
caused by inhomogeneous composition, and are consequently inconclusive as regards the band alignment present.
In the samples presented here, the GaAsSb QWs were intentionally grown 20 °C below the optimal growth temperature
for device applications, in order to reduce strain driven Sb
segregation and hence minimize the impact of inhomogeneous composition on the measurements. The samples presented here exhibit very small excitation-dependent blue
shifts 共⬍0.5 meV兲 for excitation densities from 1 to
35 W / cm2.
Much of the previous work revolves around fitting Q␯ (or
Qc = 1 − Q␯) as a constant or in some cases as a compositiondependent function, where the strained bandgap of GaAsSb
is deduced from an empirical expression for bulk bandgap
and subsequently corrected for the strain induced energy
shift using the Bir-Pikus Hamiltonian, while in many cases
neglecting the significant uncertainty introduced by the uncertainty in the deformation potentials. In the present study
we improve on previous work by using variable barrier spectroscopy measurements of multiple samples to simultaneously measure both the pseudomorphic bandgap of
GaAsSb and the pseudomorphic conduction band offset of
GaAsSb/ GaAs. Notwithstanding the reliability of the binary
bulk
+ ⌬␧i , obtained from the literature and
band offsets, ⌬qw
i = ⌬i

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PHYSICAL REVIEW B 70, 195339 (2004)

WANG et al.

the Bir-Pikus Hamiltonian, our results give a thorough and
accurate description of the GaAs1−ySby / GaAs band alignments and bowing parameters of GaAsSb. Furthermore, the
second-order empirical band-edge model given in Eqs. (7)
through (9) is a consistent and thorough model developed to
offer a simple and clear description of the compositional dependence of band edges.
The GaAs0.643Sb0.357 / GaAs bandgap and band offset results presented here agree with our previous work,28 of
933± 6 meV and 19± 19 meV, respectively. In our previous
work, the Sb mole fraction was not measured independently
for each sample and therefore corrections for the run-to-run
variations in the mole fraction were not included. Furthermore, in our previous work we underestimated the Sb mole
fraction at about 30% for 1.3 µm emission using electron
diffraction measurements, which resulted in an overestimation of the bowing parameters. Therefore the very accurate
mole fraction measurements in this work provides a more

*Corresponding author. Electronic address: jbwang@asu.edu
†Presently

at Lytek Corporation, 4717 East Hilton Avenue, Phoenix,
Arizona 85034, USA.
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accurate and reliable measurement of the GaAsSb bowing
parameters.
In conclusion, experimental data fitting and theoretical
modeling confirm that the conduction-band offset of the
GaAs1−ySby / GaAs heterojunction forms a relatively weak,
23± 23 meV, type-I alignment, for a Sb composition in the
neighborhood of 36% where 1.3 µm emission is observed.
Using a simple bowing model, the GaAs1−ySby / GaAs conduction band offset is found to exhibit a zero crossing at the
Sb mole fraction y = 0.43± 0.07, forming a type-I band alignment at the lower Sb mole fractions and a type-II band alignment at the higher Sb mole fractions, which is a result of a
substantial amount of negative band bowing 共−0.91 eV兲 in
the conduction band.
This work is partially supported by the National Science
Foundation under Grant No. 0070125.

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