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Temperature dependence of the energy gap of zinc‐blende CdSe and Cd1-xZnxSe epitaxial layers

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The temperature dependence of the energy gap of zinc‐blende CdSe and Cd 1-x Zn x Se has been determined over the entire range of composition from optical transmission and reflection measurements at temperatures between 5 and 300 K. The experimental results can be expressed by the following modified empirical Varshni formula, whose parameters are functions of the composition x: E g (x,T)=E g (x,0)-β(x)T<sup>2</sup>/[T+γ(x)]. E g (x,0) exhibits a nonlinear dependence on composition, according to E g =E g (0,0)(1-x)+E g (1,0)x-ax(1-x). The parameters β(x) and γ(x) can be expressed by β(x)=β(0)(1-x)+β(1)x+bx(1-x) and γ(x)=γ(0)(1-x)+γ(1)x. © 1996 American Institute of Physics.
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Temperature dependence of the energy gap of zincblende CdSe and
Cd1−xZnxSe epitaxial layers
U. Lunz, J. Kuhn, F. Goschenhofer, U. Schüssler, S. Einfeldt et al.
Citation: J. Appl. Phys. 80, 6861 (1996); doi: 10.1063/1.363753
View online: http://dx.doi.org/10.1063/1.363753
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Temperature dependence of the energy gap of zinc-blende CdSe
and Cd
1
2
x
Zn
x
Se epitaxial layers
U. Lunz,a) J. Kuhn, and F. Goschenhofer
Physikalisches Institut der Universita
¨tWu
¨
rzburg, Am Hubland, 97074 Wu
¨rzburg, Germany
U. Schu
¨ssler
Mineralogisches Institut der Universita
¨tWu
¨
rzburg, Am Hubland, 97074 Wu
¨rzburg, Germany
S. Einfeldt
Institut fu
¨r Festko
¨rperphysik, Universita
¨t Bremen, Kufsteiner Street, 28359 Bremen, Germany
C. R. Becker and G. Landwehr
Physikalisches Institut der Universita
¨tWu
¨
rzburg, Am Hubland, 97074 Wu
¨rzburg, Germany
~Received 24 June 1996; accepted for publication 17 September 1996!
The temperature dependence of the energy gap of zinc-blende CdSe and Cd12xZnxSe has been
determined over the entire range of composition from optical transmission and reflection
measurements at temperatures between 5 and 300 K. The experimental results can be expressed by
the following modified empirical Varshni formula, whose parameters are functions of the
composition x:Eg(x,T)5Eg(x,0) 2
b
(x)T2/@T1
g
(x)#.Eg(x,0) exhibits a nonlinear dependence
oncomposition,accordingtoEg5Eg(0,0)(12x)1Eg(1,0)x2ax(12x).Theparameters
b
(x) and
g
(x) can be expressed by
b
(x)5
b
(0)(12x)1
b
(1)x1bx(12x) and
g
~x!5
g
~0!~12x!1
g
~1!x.
©1996 American Institute of Physics. @S0021-8979~96!09524-2#
I. INTRODUCTION
Cd12xZnxSe is commonly used as quantum well mate-
rial in ZnSe-based laser diodes.1Bulk Cd12xZnxSe crystal-
lizes either in the cubic zinc-blende structure ~x.0.7!,inthe
hexagonal wurtzite structure ~x,0.5!or in mixture of these
two for 0.5<x<0.7.2However, growth of Cd12xZnxSe on
GaAs~100!substrates with molecular beam epitaxy ~MBE!
results in films of the zinc-blende structure over the entire
range of composition. Literature values for the energy gap of
zinc-blende CdSe at 300 K vary from 1.66 to 1.74 eV. Spec-
troscopic ellipsometric measurements result in a value of
1.74 eV3,4 as well as a value of 1.66 eV.5Reflection
spectroscopy6and photomodulation spectroscopy7also yield
a value of 1.66 eV at 300 K. The energy gap of Cd12xZnxSe
alloys has been determined at 300 K by reflection
spectroscopy8and spectroscopic ellipsometry.5In these in-
vestigations we have grown Cd12xZnxSe films on GaAs with
0<x<1 and measured their energy gap Egusing optical
transmission and reflection in the temperature range from 5
to 300 K.
II. EXPERIMENT
Growth of ternary Cd12xZnxSe films with a typical
thickness of 1
m
mon~100!GaAs was carried out in a Riber
2300 molecular beam epitaxy ~MBE!system. Cd~6N!,
Zn~6N!, and Se~6N!, were used as source materials. The
growth of zinc-blende alloys was monitored by means of
reflection high-energy electron diffraction ~RHEED!. The
composition of the alloys were determined by electron probe
microanalysis ~EPMA!with an experimental uncertainty of
<1.0%. Optical transmission and reflection measurements
were carried out with a Fourier transform spectrometer,
Bruker IFS 88, in the 1.2–3.2 eV energy range in order to
obtain the energy gap Eg. For the transmission measure-
ments, the absorbing GaAs substrates had to be removed as
described elsewhere.9
III. RESULTS AND DISCUSSION
The energy gap Egof these alloys was determined from
optical transmission. From the transmission data, the absorp-
tion coefficient was calculated in the region of strong absorp-
tion using the formula according to Swanepoel:10
a
51
dln A
Twith A516n2s
~n11!3~n1s2!,~1!
where Tis the transmission. The refractive index of glass s
and the refractive index of the layer nwere assumed to be
constant in the region of strong absorption. The refractive
index nand the thickness dof the layer were estimated from
the reflection spectra. Assuming parabolic band structure, the
absorption coefficient
a
is proportional to ~E2Eg!0.5 and an
extrapolation to
a
250 yields a good approximation of the
energy gap Eg. Figure 1 shows the transmission and reflec-
tion spectra and the squared absorption coefficient of a
Cd0.47Zn0.53Se layer at 300 K. The energy gap is indicated by
an arrow. The variation of the band-gap energy with compo-
sition at temperature Tis conventionally described by the
quadratic equation:
Eg~x,T!5Eg~0,T!~12x!1Eg~1,T!x2ax~12x!,~2!
where Eg(0,T) and Eg(1,T) are the energy gaps of CdSe and
ZnSe at temperature Tand the deviation from linearity is
given by a. In Fig. 2 the energy gaps of the alloys over the
entire range of composition at 5 and 300 K are shown. In our
measurements we obtained a value of Eg~CdSe!51.66 eV at
room temperature and a value of Eg~ZnSe!52.68 eV. The
a!Electronic mail: lunz@physik.uni-wuerzburg.de
6861J. Appl. Phys. 80 (12), 15 December 1996 0021-8979/96/80(12)/6861/3/$10.00 © 1996 American Institute of Physics
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observed nonlinearity can be described by a50.48 and 0.42
at 5 and 300 K, respectively. Kim et al.5carried out ellipso-
metric measurements at room temperature on zinc-blende
CdSe and Cd12xZnxSe films. This resulted in the following
equation for the energy gap Egas a function of the compo-
sition x:Eg(x)51.6610.73x10.30x2, which corresponds to
a value of a50.30 at 300 K. Their values for the binaries
agree well with our data, but the energy gap of the ternaries
are slightly larger than our values, i.e., DEg<35 meV. The
deviation of the results of Kim et al. from our measurements
are probably due to the different methods used in determin-
ing the composition x. Kim et al. determined the composi-
tion from the lattice constant, assuming a linear dependence
~Vegard’s law!, however, they made no statement concern-
ing their experimental error. We have found, that the large
lattice mismatch of Cd12xZnxSe to the GaAs substrate leads
to a broadening of the rocking curves and thus an error in the
composition, which is larger than the error in measurements
by EPMA, a method independent of lattice mismatch and
sample quality. The full width at half maximum ~FWHM!of
the ~004!rocking curves of the Cd12xZnxSe layers on GaAs
is between 250 and 900 arcsec. The maximum deviation in
the composition xbetween XRD and EPMA is, in our case,
about 5% absolute, which could easily account for the dis-
crepancy between their results and ours.
In contrast to the value of 1.66 eV for the energy gap of
CdSe at 300 K in this investigation and by other groups,
Janowitz et al.4and Ninomiya et al.3obtained a value of
1.74 eV. However, according to Janowitz et al. experimental
difficulties occur in the analysis of the second derivative
spectra due to the presence of interference fringes, which
results from the finite thickness of the samples and the low
absorption of CdSe in this energy range.
The temperature dependence of Cd12xZnxSe can be ex-
pressed by the empirical Varshni11 formula, where the pa-
rameters
b
and
g
are functions of the composition x:
Eg~x,T!5Eg~x,0!2
b
~x!T2
T1
g
~x!~3!
and Eg(x,0) can be described by Eq. ~2!. The parameters
b
(x) and
g
(x) can be expressed by the following relations:
b
~x!5
b
~0!~12x!1
b
~1!x1bx~12x!,~4!
g
~x!5
g
~0!~12x!1
g
~1!x.~5!
For the binaries, the results from a least square fit to the
Varshni formula are
ZnSe: Eg~1,0!52.82 eV,
b
~1!55.7331024eV/K,
g
~1!565 K.
CdSe: Eg~0,0!51.74 eV,
b
~0!54.7731024eV/K,
g
~0!5295 K.
The values of the nonlinearity parameters aand bare
a50.47 eV,
b521.1431024eV/K,
where aand bresult from a fit over all experimental data.
Figure 3 shows the temperature dependence of the energy
gap Egof several alloys with different compositions. The
curves represent the temperature dependence of the energy
gap for the compositions according to Eqs. ~3!~5!. The de-
viation of the experimental values from this empirical rela-
tionship corresponds to the experimental uncertainty in the
composition. We have estimated, that the experimental un-
certainty in Egis <620 meV. Our value of 1.66 eV for the
energy gap of CdSe at room temperature agrees well with the
data of Kim et al.,5Shan et al.,7and Samarth et al.6At low
temperatures, we obtained a value of 1.74 eV for Eg~CdSe!,
which is smaller by '25 meV than that of Shan et al. as
determined by photomodulation spectroscopy. A possible ex-
FIG. 1. Transmission ~solid line!and reflection ~dotted line!spectra at 300
KofaCd
12x
ZnxSe layer with x553% ~left axis!and the squared absorption
coefficient
a
2~dashed line, right axis!. An extrapolation to
a
250 leads to an
estimation of the energy gap Eg, which is indicated by the arrow.
FIG. 2. Dependence of the energy gap of Cd12xZnxSe for different tempera-
tures. The curves are least-squares fits according to Eq. ~2!. The experimen-
tal error in the energy gap is 0.02 eV.
6862 J. Appl. Phys., Vol. 80, No. 12, 15 December 1996 Lunz
et al.
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planation of this slight discrepancy is the following: Shan
et al. employed a ZnTe buffer layer before the growth of the
CdSe layer, which reduces the effect of strain due to the
lattice mismatch between CdSe and ZnTe. They also argue,
that the different thermal expansion coefficients can be ne-
glected, provided the CdSe is thick enough. If this is the
case, their optical measurements yield the properties of un-
perturbed bulk CdSe. In our case, the transmission spectra of
CdSe at low temperatures exhibit no excitonic absorption
due to the relatively poor structural quality as a consequence
of the large lattice mismatch between CdSe and GaAs or a
consequence of the different thermal expansion coefficients
of CdSe and the glass holder or the glue. Our somewhat
smaller value for Eg~CdSe!at low temperatures may be
caused by strain, which results for either of the above rea-
sons.
IV. SUMMARY
In conclusion zinc-blende CdSe and Cd12xZnxSe alloys
have been grown and their energy gap has been determined
as a function of temperature. An empirical formula Eg(x,T),
which describes the energy gap as a function of composition
and temperature has been derived. A small deviation from
a previously published empirical formula can probably be
ascribed to a different method of determining the composi-
tion x.
ACKNOWLEDGMENTS
The authors would like to thank P. Wolf-Mu
¨ller and T.
Schuhmann for sample preparation. The support of the
Bundesministerium fu
¨r Bildung und Forschung ~BMBF!is
gratefully acknowledged.
1M. A. Haase, J. Qiu, J. M. DePuydt, and H. Cheng, Appl. Phys. Lett. 59,
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FIG. 3. Temperature dependence of the energy gap of several alloys. The
lines represent fits of the experimental data using the Varshni formula.
6863J. Appl. Phys., Vol. 80, No. 12, 15 December 1996 Lunz
et al.
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