Infrared lattice vibration spectra of CuInSe2 and CuGaTe2

Solid State Communications, Vol. 28, pp. 449—454. © Pergamon Press Ltd. 1978. Printed in Great Britain

0038—1098/78/1108—0449 $02.00/0

INFRARED LATFICE VIBRATION SPECTRA OF CuInSe2 AND CuGaTe2 V. Riede, H. Sobotta, H. Neumann and Hoang Xuan Nguyen Sektion Physik, Karl-Marx-Universität, 701 Leipzig, DDR and W. Moller and G. Kuhn Sektion Chemie (Fachbereich Kristallographie), Karl-Marx-Universität, 703 Leipzig, DDR (Received 24 July 1978 by A.R. Miedema) The lattice vibration spectra of CuInSe2 and CuGaTe2 were investigated by infrared reflectivity measurements in the wavenumber range from 55 to 5000cm’. The mode energies were determined by a Kramers—Kronig analysis of the spectra. The results are compared with existing measurements and some general trends in the phonon energies of the I—Ill—V!2 compounds are discussed.

THE LATTICE VIBRATION SPECTRA of the I—Ill—S2 compounds have been studied extensively by infrared reflectivity and Raman scattering measurements [1—7] and different theoretical models have been used in order to explain the experimental phonon spectra [1 5, 8, 9] Less information is available concerning the lattice vibrations of the selenides and tellurides of the I—Ill—V!2 compound family, especially for the Cucontaining compounds the data is scarce [10—12] except the case of CuInSe2 [13] However, the optical mode frequencies of [131 seem to be doubtful for two reasons. Firstly, it is a well-known experimental fact that the frequencies of the highest B2 and E modes are practically unaffected by a replacement of Cu for Ag [3]. Comparing the corresponding mode frequencies for CuInSe2 from [13] with recently published measurements for AgInSe2 [14] it can be seen that the difference in the phonon energies is almost one order of magnitude larger than in all other compound pairs investigated so far [2,3,5] Furthermore, the highest mode frequencies of [13] differ markedly from the measurements reported in [11] Secondly, Gan etal. [13] observed a sudden dip of the strongest Reststrahl band in the mixed crystal system (CuInSe2)1 —x 2(ZnSe)~going from x = 0 to x = 0.08 and ascribed this effect to the influence of substitutional disorder on the selection rules. To the knowledge of the authors, no similar effects have been found in other semiconductor alloys [15] although substitutional disorder should be present in many other mixed crystal systems, too, Besides, it is interesting to note that (i) this anomaly in the composition dependence of the strongest Reststrahl band disappears if the frequencies of the highest B2 and E modes of CuInSe2 are assumed to be nearly equal to ,

.

.

.

.

—

449

those of AgInSe2 and (ii) no such effects were observed on the ZnSe-rich side of the alloy [131although the influence of substitutional disorder should be present in this case, too. To elucidate these problems we have reinvestigated the infrared reflectivity spectrum of CuInSe2 and the obtained results are discussed in view of some general trends found in the lattice vibrations of the I—Ill—V!2 compounds. Furthermore, some measurements of the infrared optical properties of CuGaTe2 are reported for the first time. The samples used in the experiments were grown by reaction of stoichiometric mixtures of the pure elements (Cu: 99.999%; Ga, In, Te: 99.9999%; Se: p.A.) in a sealed quartz ampoule evacuated to a pressure of about 10~torr. To minimize the risk of explosion due to the exothermal reaction of the group III and group VI elements and to guarantee complete reaction of the elements to the ternary compound the synthesis was performed in a two-zone furnace in which the I—Ill melt was at a higher temperature than the group VI element. The polycrystalline ingots obtained in this manner were then submitted to a directed freezing solidification in a modified zone-melting apparatus to increase the size of the single crystalline regions in the samples. In the case of CuInSe2 single crystaffine specimens with typical diametersof about 15 mm and thicknesses of about 1 mm with the [221] direction perpendicular to the large plane of the sample could be selectively cut from the ingots. For CuGaTe2 the single crystalline regions had typical diameters of about 3 mm and, therefore, only polycrystalline samples could be prepared for the far-infrared optical measurements. X-ray analysis was used to confirm the structure and the lattice constants of the compounds. The latter were ,

450

INFRARED LATTICE VIBRATION SPECTRA OF CuInSe2 AND CuGaTe2 0.9

R 0.8

I

I

Vol. 28, No.6

I

-

to.7

: : 0.1

~flL111)J\

UInSe2

~

‘1

—

0 50

100

I 200

150

I 250

—1

-

.300

P[cm ]

1 [111] and E I c.

Fig. 1. Reflectivity spectra of CuInSe2 for the two polarizations E 8

found to be in good accordance with published values [16] .Conductivity type and carrier concentrations of the samples were determined by Hall effect measurements. The CuInSe2 samples were always n-type conducting with electron concentrations of 1015 _1016 3, the CuGaTe cm 2 samples showed p-type conductivity with rather high3.hole concentrations of about 1—3 Reflectivity x 1018 cm spectra at nearly normal incidence of light were measured at room temperature in the wavenumber range P = 55—5000cm’ using a single-beam spectrometer. The orientation of the CuInSe 2 samples enabled us to measure reflectivity spectra with the polarizations El c and Eli [ill]. The [111] direction makes an angle of about 350 with the c axis and, there-

the B2 modes the Elies modes. However, cdiscriminate fore, axis.only Under about these 65% conditions of thefrom intensity it would beparallel difficult totothe because we used an angle of incidence of about 15°the angle between the electric vector E and the c axis could be reduced to about 20°.In this case the intensity parallel to the c axis increases to more than 80% and we can hope that the corresponding spectra are dominated by the B2 modes. The measurements on the CuGaTe2 samples were made with unpolarized light. The experimental spectra were analysed by the Kramers—Kronig method using the standard normalincidence formulae. The deviations due to the non-zero angle of incidence were estimated to be within the experimental error. The reflectivity spectra of CuInSe2 are represented in Fig. 1 the calculated optical constants n(P), k(P) and ,

n

I

1c

CuInSe2

I

_____________________________________ I I I

0

kt 6 4

2 0

cli 60 40

(b)

—

—

(‘i

-

______

-

-

20 0 50

100

150

2~X1

250

3X]

~ tcm’] Fig. 2. Calculated optical constants n(P) (a), k(P) (b) and e(P)l (c) for CuInSe2.

Vol. 28, No.6

INFRARED LATTICE VIBRATION SPECTRAOF CuInSe2 AND CuGaTe2

451

Table 1. Vibrational mode frequencies and dielectric constants of CuInSe2 This work ~TO

(cm~)

(cm~)

~LO

Ref. [13] 1) ~T0 (cm (infrared)

~L0

(cm1)

P (cm’)

(Raman)

El [111] (B 2 modes) 212 169 63

231 195 66 = =

035 0.24

=

~

=

15.2 8.5

248 188

274 196

—

—

Ic

1 79

=

0

~

252; 275 194 96 (p\~2 =

1.73

j=1\VTO)j

‘

Elc(Emodes) 215 .206 167

229 212 184

—

—

64

67

—

R0 R,.

—

= =

036 0.26

~0

=

600 =

16.0 9.5

248

274

252; 275

—

—

—

188 153 78

191 153 78

—

—

—

60/600

2 are given in Fig. 2. According to [17], Ie(P)l ~ + k mode frequencies were determined from the TO= and LO the maxima and minima of le(P)I, respectively; a determination of the LO mode frequencies from the maxima of Im (— 11) yielded the same values within the accuracy of the method. The results are compiled in Table 1; for comparison the corresponding vibrational mode frequencies of [13] are also given, For the polarization E II [ill] which is very near to E c under our experimental conditions we observed three infrared active modes as expected from group theory [1] In the polarization direction E I c only four modes are found instead of the six possible ones [1] which seems to be usual for many chalcopyrite materials [181.ThefrequenciesofthehighestB2 andEmodes are in good agreement with the value of ~TO = 216 cm~ reported in [11]and are very near to the corresponding frequencies of AgInSe2 [14] The other mode frequencies are somewhat higher than the corresponding ones in AgInSe2 [14] which is due to the increased influence of the group I element on these modes [1,5,9, 18] .However, as can be seen from Table 1, all our mode frequencies are below those of [13] and it remains an open question how this discrepancy can be explained. At Pindependent <55 cm’ and P> 1000Rcm~we found wavenumber reflectivities 0 and R00, respectively, and k ~ n (see also Fig. 2). Thus, we were able to determine the low and high frequency dielectric .

.

,

1.68

=

191

(~\

78 61 1.60

f=i\PT0)i

constants Eo and 600, respectively, using the relation R = [(..J~1)/(..~/~ + 1)] 2, The reflectivity of the total radiation for frequencies smaller than SOcm’ could be measured by using the échelette grating in zero order. The resulting reflectivities and dielectric constants are given in Table 1. The ratio of 60/600 can be also calculated in terms of the TO and LO mode frequencies using the Lyddane— Sachs—Teller relation. For crystals such as the I—!II—V1 2 semiconductors, which are uniaxial, the Lyddane—Sachs—Teller relation may be written for each polarization perpendicular or parallel to the c axis [1], —

2

(1)

=

~

/ = i\Vro).

with n = 4 for theE modes and n = 3 for the B2 modes. The resulting 60/600 ratios are in good accordance with the 60 /600 values determined from the reflectivity (see Table 1). A typical reflectivity spectrum of a polycrystalilne CuGaTe2 sample is shown in Fig. 3(a). Probably, the increase of R at low wavenumbers is due to the high 3 present free carrier concentrations of about 1018 cm in the samples. The calculated Ie(P)I curve is given in Fig. 3(b), and the TO mode frequencies determined from the maxima of ie(P)l are 209, 200 and 166 cm’.

452

INFRARED LATTICE VIBRATION SPECTRA OF CuInSe2 AND CuGaTe2 0.8

I

I

R

CuGaTe2

j.!5cm~

20

-

15

-

I

I

Vol. 28, No.6 I

I

CuAtS2,ø /

300K

0.2

—

I

I

I

—

IEl~::

50

//

AgGaS2/

—

I

0

CuGaS2

10

o’~

•

AgInS2 CuInS2/ ~

-

//

//

CuA!Se2

~

I

100

I

150

I

///7

200

250

300

~I1

/~7

AgGaTe2 AgInTe2

_______________

Fig. 3. Reflectivity spectrum (a) and calculated I e(i3)I curve (b) for CuGaTe2. It maybe that the very weakly pronounced structure near about 72 cm~(see Fig. 3) is also caused by an infrared active mode masked by the free carrier effects. In view of the large discrepancy between our measurements and those of [13]for CuInSe2 it was of interest look for arguments in favour the one or the othertoresult considering some generaloftrends in the phonon spectra of the I—III—VI2 compounds. We have already mentioned the fact that the frequencies of the highest B2 and E modes are only slightly affected by an exchange of the group I element. A compilation of all available data (Table 2) shows that the differences

0

I

0

I

5

[orb.units]

Fig. 4. Plot of t40(B2) aginst the effective reduced mass according to (2). between the corresponding wavenumbers are usually 1—6 cm’ whereas the results of [13] from it 1. deviate Furthermore, those for AgInSe2 by at least 33 cm is interesting to note that the i’~ 0(B2)and iiTo(E) values for CuInSe2 from [13] are nearly equal to those for CuGaSe2 and AgGaSe2 which cannot be understood within existing models for the lattice vibrations of the I—III—V12 compounds [1, 5, 9]. Our results for the highest modes of CuGaTe2 are very near to the

Table 2. Comparison of the frequencies of the highest B2 and E modes of Cu—III—V12 —Ag—III—V12 compound pafrs. The values in parenthesis are from measurements with unpolarized light Compound

i’To(B2) (cm~)

PT0(E) (cm’)

CuGaS2 AgGaS2

368 367

363 368

CuInS2 AgInS2 CuGaSe2 AgGaSe2 CuInSe2

323

AgInSe2 CuGaTe2 AgGaTe2

321 (329)

254 248 212 248 208

250 250 215 248 215 (200; 209)

198

I

10

204

Ref. [5] [5] [5] [3] [12] [19] This work [13] [14] This work [191

Vol. 28, No.6

INFRARED LATTICE VIBRATION SPECTRA OF CuInSe2 AND CuGaTe2

453 [see (2)] valuesa against theaccordance effective reduced / for the with = 1/2 in with themass results I—Ill—S 2 compounds [5, 9]. We see that the sulphides, selenides and, probably, also the tellurides follow sep. arate curves which can be fairly approximated by straight lines. This result is independent of the choice of the force constant ratio a = k1v1/k111_y1. The force constants decrease in the sequence from S to Se and Te which is in agreement with an estimation given in [18]. The value of i3~0(B2)for CuInSe2 from [13] is also given in Fig. 4, and the marked deviation from the selenide curve is obvious. Thus, regardless of the tentative and simplified character of our considerations it seems to be justified to suppose that our results for CuInSe2 are in better 2eff

frequencies the thus, highest B2 andthe E modes in AgGaTe2 (see Table 2)ofand, confirm above mentioned general tendency. Another interesting fact which follows from theoretical model calculations for the I—Ill—S2 compounds [5,9] is that the lattice vibration spectra are dominated by the bond stretching force constants k1_~1and k111_v1 of the 1—VI and III—VI bonds and that these force constants have nearly the same values for all sulphides with k1v1 (~—~)ki11_v1. In view of this result it seems to be not unreasonable to look for some general trends in the lattice vibration spectra of the I—III—VI2 compounds using a linear chain model. According to [1] the frequency of the highest optical mode in a tetra-atomic linear chain is given by =

kIII_VI/jleff

=

k111_v1

1 + 1 m111 2mvi

tice vibration agreement withspectra the general of the trends I—III—VI2 observed compounds in the latinvestigated so far. With regard to the dominant role of

/\ ~Ii 2mvij1 + ai[1 + —1+ lal— + 2mvi 1m1 .—L— + i \2 + a 1/2 m 111 2mvi) m~~1

the VI element influence in determining forcebond constants . predominant and group the of thethe Ill—VI on the highest mode frequencies [5, 9] it is interesting to ‘2~ note that a similar situation seems to be present also in

—

—

‘-

‘

where m1,VI m111 and mvirespectively, are the masses group I, III and elements, and of a =the ki_vi/ k111_v1. Reasonably, this frequency must be identified with the highest B2 orE modes [1]. In Fig. 4 we have plotted the corresponding i40(B2)

the Tl—III—V12 compounds. Recently published values for the highest transverse optical mode frequencies 3To for = T1GaS2 [20] (~To = 367 and for T1GaSe2 250.3 cm~) are very nearcm~) to those AgGaS[21] (i 2 (or CuGaS2) and AgGaSe2 (or CuGaSe2), respectively (see Table 2)

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INFRARED LATTICE VIBRATION SPECTRAOF CuInSe2 AND CuGaTe2

Vol. 28, No.6

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