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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.

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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.