OPTICAL PHONONS IN I-III-VI2 COMPOUNDS

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OPTICAL PHONONS IN I-III-VI2 COMPOUNDS

W. Koschel, F. Sorger, J. Baars

To cite this version:

W. Koschel, F. Sorger, J. Baars. OPTICAL PHONONS IN I-III-VI2 COMPOUNDS. Journal de Physique Colloques, 1975, 36 (C3), pp.C3-177-C3-181. �10.1051/jphyscol:1975332�. �jpa-00216302�

JOURNAL DE PHYSIQUE Colloque C3, supplkment au no 9 , Tome 36, Septembre 1975, page C3-177

OPTICAL PHONONS IN I-HI-VIZ COMPOUNDS

W. H. KOSCHEL, F. S O R G E R and J. BAARS

Institut fiir Angewandte Festkorperphysik der Fraunhofer-Gesellschaft 7800 Freiburg, Eckerstrasse 4, Germany

Rhumb. - Les phonons optiques (k

-

⁰⁾ de CuInS2, AgInS2 et CuFeS, ont ete analyses par des mesures d'absorption et de reflexion dans la region de 1 000 jusqu'a 50 cm-1. La determination des frequences des phonons optiques transversaux et longitudinaux a et6 effectuk B I'aide dqCquations Kramers-Kronig ainsi que de modtles classiques d'oscillateurs. Les rksultats sont cornparks aux spectres connus de CuAIS,, CuGaS2 et AgGaS2. Une comparaison systematique des frequences des modes montre quc les constantcs de force des differents coniposes 1-111-S2 sont presque egales.

Les differences des frequences des modes correspondants paraissent dependre principalement des differentes masses des cations.

Abstract. - The optical phonons at k = 0 of CuInS,, AgInS2 and CuFeS?. were analysed by infrared reflection and absorption measurements in the region from 1 000 to 50 cm- 1. To determine the transverse and longitudinal optical phonon frequencies Kranlers-Kronig integrations as well as classical oscillator models were used. The results are compared with the known phonon spectra of CuAIS2, CuGaS, and AgGaSz. It is shown by a systematic comparison of the mode frequencies that the force constants of the different I-111-S2 compounds are almost equal. The frequency diffe- rence between corresponding modes appear to be mainly due to the different cation masses.

l . Introduction. - During the past few years the phonon spectra of I-111-VIZ and 11-IV-V, compounds of the chalcopyrite structure have been studied exten- sively by infrared reflectivity and first order Raman scattering measurements. For the zone center phonons of various compounds of the IT-TV-V, family a nearly complete set of results has been published [l-81. Also the phonon spectra of certain I-111-VI, compounds are well known, namely the phonon spectra of CuAIS, [9], AgGaS, [10-121 and CuGaS, [12-141. F o r a detailed interpretation of the latter phonon spectra additional information on other I-111-S, compounds is needed however.

I n this paper we present the phonon modes of CuInS,, AgInS, and CuFeS, a s obtained from the analysis of infrared reflectivity and transmissivity data.

The primary objective of this study was to investigate the effect of the cation masses on the phonon energies of the I-111-S, compounds. Further, the limits for a comparison with the dispersion curves of the binary zincblende analogues were investigated. Finally, by a comparison of the known phonon spectra of I-111-S, compounds a firm assignment of previously debatable AgGaS, and CuGaS, modes was accomplished.

than the corresponding ZB Brillouin zone and the symmetry points X and W of ZB transform into f (k ⁼ 0) of CH.

Therefore, the zone center vibrational modes of the C H lattice ( l ) may be derived in a first approximation from modes at

r,

X and W of the ZB lattice. In this way combinations of symmetry coordinates can be obtained for the zone center modes of CH, taking the cor- responding ZB vibration as a starting point [10, 1 l].

This ZB approximation has been used to interpret the phonon frequencies and IR-oscillator strengths of several C H compounds [2, 4, 1 l]. I t has been shown, however, by a calculatiorl of the phonon spectra for 11-IV-P, compounds [S] based on a Keating model, that modes of the same symmetry type may be strongly mixed by the influence of the different cation masses and by the different force constants (U,,, U,, in an ABC, compound). This mode mixing may lead to a strong frequency splitting of those modes which derive from the same ZB mode and t o a considerable transfer of IR-oscillator strength. These deviations from the ZB-approximation will be considered in the interpreta- tion of the results for the I-111-S, compounds.

3. Experimental. - The CuInS, crystals used for 2, Vibrational modes of the chalcopyrite lattice. - this study were grown by Halogen transport reaction.

The chalcopyrite (CH) lattice can be interpreted as a They had well formed ( 1 12)-faces. The reflectivity has superstructure of the zincblende (ZB) lattice. The ideal

tetragonal unit cell of the C H lattice has twice the _{(,) The} total number of optical CH modes is 2r2, volume of the corresponding cubic unit cell. The ₃

r,,

³

r ,

and 6

r5.

Except the

rz

modes all modes are Raman Brillouin zone of the C H lattice is four times smaller active, the ^r4 and ^I-5 modes are infrared active as well.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1975332

C3-178 W. H. KOSCHEL, F. SORGER A N D J. BAARS been recorded with the electric vector being parallel to ₁₀₀

< 110

>

^{( E I} c, T , modes) and parallel to < 1 1 1

>,

₈₀

which is closest to E

//

c (T4 modes). The T,-T, mode

coupling has been considered in evaluating the reflecti- ⁶ o vity of the (1 12)-faces and the E

//

c-spectrum was 2 o extrapolated by a comparison with AgGaS, and 20

CuGaS, [10]. The spectra were recorded with a Fourier spectrometer (50-500 cm-') and with a grating spectro- meter (100-1 000 cm-').

CuFeS, was available as a natural crystal which was CuGaS;! E l C

large enough for cutting a ( 1 10) face of suitable size for

c

²⁰

the optical measurements. At this (1 10) face the confi- 1 guration E

//

c is easily obtained.

The reflectivity spectra of CuInS, and CuFeS, were _AgGaS2

E l C

analysed in the usual way by Kramers-Kronig analysis and least squares fits with systems of damped harmonic ^a oscillators. A detailed analysis for CuFeS, will be ²⁰ published elsewhere r151. Therefore. iust the mode fre-

-

^{, <}

quencies of CuFeS, are included in table 1 without

further discussion. Only very small AgInS, crystals of poor quality were q ; u l n S 2 E l C

1

available. Therefore, the analysis was restricted to the ²⁰ evaluation of absorption spectra. The samples consisted

01 bo 200 ^l 300 ^{1 "} LOO L 50 0 600

of 3 mg AgInS, and 700 mg KJ, which were powdered, W A V E N U M B E R (cm-') mixed, and formed to a tablet by pressure. A tablet of

pure KJ was used as a reference. The absorption spec- trum was recorded from 200 to 500 cm-'. Absorption spectra of CuAlS,, CuGaS,, AgGaS, and CuTnS, have been obtained by the same procedure.

4. Results and discussion. - In figure 1 the recorded reflectivity spectrum of CuInS, for E

I

c (T, modes) is presented, where it can be compared with the cor- responding spectra of CuAlS,, CuGaS, and AgGaS,.

A few general statements can be made by direct inspection. First, at most 4 of the 6 possible bands are in evidence. An additional weak band has been observed for CuGaS, (97-99 cm-') and AgGaS, 90-93 cm-' according to ref. [12]). The m issing bands

@TO

(cm- l)

E l c 321 295 244

FIG. 1. - Reflectivity of CuInS2 compared with CuAlS2 [9], CuGaS2 and AgGaSz [l01 for E l c (TJ modes).

seem to have LO-TO splittings which are too small to be detected by IR-reflectivity.

Second, the bands of highest frequency seem to be sensitive to the replacement of the group 111 atoms only. Their frequencies are almost unaffected by the replacement of the group I atoms. In contrary to this, the weaker band between 200 and 280 cm-

'

seems to be more sensitive to the replacement of the group I atoms.

This striking behaviour will be discussed in more detail in a later section.

Mode parameters for T, and f 4 modes of CuInS, and CuGaS,

CuInS, CuGaS,

( c 2 5 ) S, (cm- ^Yj l ) (C,o'-p) ^WLO

Yj

(cm- l ) Sj (cm - l)

OF'TICAL PHONONS IN I-111-V12 COMPOUNDS C3-179

AgGoS2 E IIC

c

_{Cu Ins2 E llC}

, 1

20

0 100 200 300 LOO 500 600

WAVENUMBER (cm-l)

FIG. 2. - Reflectivity of CuInSz compared with CuAlSz [g], CuGaSz and AgGaS2 [l01 for E / c (r4 modes).

A similar behaviour is observed for the reflectivity with E

//

c

(r,

modes, Fig. 2). For this configuration the reflectivity spectra exhibit 2 of the 3 possible bands onIy. However, the same statements as before can be made. When AI is replaced by Ga or In the band at highest frequency is shifted considerably to lower fre- quencies. When Cu, however, is substituted by Ag in CuGaS, the second band shifts to lower frequencies only.

In this connection the knowledge of the AgInS, Reststrahlbands is of interest for a further clarification of the effect of the different cations. As mentioned before, no large AgInS, crystals were available to perform reflectivity measurements. Therefore, we studied the powder absorption spectrum of this compound (Fig. 3). For comparison the absorption spectra of CuAIS,, CuGaS,, AgGaS, and CuInS, are also shown in figure 3. The assignment of the cor- responding modes is easily obtained. Again the position of the high frequency band seems to be unaffected by the replacement of Cu by Ag in CuInS,.

In the following section we will proceed to a more quantitative analysis of the phonon spectra of the I-111-S, compounds.

The results of the reflectivity analysis for CuTnS, are listed in table I, where the longitudinal (W,,) and transverse (W,) optical phonon frequencies are given together with the parameter values of a least squares fit by a system of damped oscillators. For the oscillator

I I I I I

J

2 0 0 300 LOO 5 0 0

WAVENUMBER (crfill)

FIG. 3. - Absorption spectra of AgInS2, CuInSz, AgGaSz, CuGaSz and CuAlS2.

parameters the notation of reference [l31 is used. The corresponding values for CuGaS, 1101 are listed for comparison ('). They were obtained from a recent reflectivity analysis at a (110) face. For CuGaS, two weak modes are present in addition to the three strong polar high frequency modes in the E l c spectrum.

These weak modes could not be observed for CuInS,.

The reflectivity spectra which were obtained for CuFeS, a t a (I 10) face were analysed in the same way.

A compilation of the phonon energies for the I-111-S, compounds is given in table 11. The binary analogues of these compounds are ZnS and Gap. The corresponding zone center and zone boundary phonon energies for the ZB compounds are listed for comparison.

For studying the effect of the different force constants of ternary and binary compounds, it is useful to compare CuGaS, with ZnS, since the masses of Cu and Ga are comparable to Zn. The nearest neighbor bond

(2) The CuGaS2 phonon frequencies given here are in good agreement with the Raman results rcported by Bettini and Hol- zapfel [14]. They differ somewhat from the values given in reference [l21 and reference [13].

W. H. KOSCHEL, F. SORGER A N D J. BAARS

Infrared and Raman active phonons of ternary su@des

Symmetry Frequency (cm-. l) Symmetry

CH

cu~1s2

^(a) cuGaS2 (b) CuFeS2 ^(C) AgGaS2 ^{( d )} CuInSz AgInS2 ZnS ( e ) Gap ( J ) ZB

- - - - - - -

r 4 ( L / T ) 4981446 4011368

~ S ( L I T ) 4971444 3841363

~ S C L I T ) 432 3521332

r3

^{- 358}

rl

^{315 312}

r 4 ( L / T ) 2841271 2811262 r d L / T ) 2661263 2761262

r3 268 203

rs(L1T) 2171216 1601156

r 4 ( ~

+

^{T) 112 -}

r3

98 97

r 5 ( L

+

^{T) - (97)}

r 5 ( L i T) 76 74

( O ) Ref.191.

( b ) Ref. [IO, 141, sce also ref. [l 21.

p) Ref. [IS].

( d ) Ref. 110, 121, see also ref. [l l ] .

(.) Ref. [l 61.

(f) Ref. [17].

stretching force constants for CuGaS, are expected to accompanied by bands of weak oscillator strength differ from that of ZnS in the following way : deriving from optic X and W modes of ZB.

Next we will consider the effect of the different

a ~ u - ~ < a ~ n - ~ < a ~ a - ~ . cations on the phonon energies of the I-111-S, The strong polar modes of highest frequency in

CuGaS, may be related to the T,, polar mode of ZnS.

The considerable shift of the T,, band to higher energies in CuGaS, may be attributed to the stronger force constant a,,-, which seems to be comparable with that of Gap. The high frequency modes of CuGaS, therefore are connected mainly with motions of Ga and S atoms in antiphase.

When the cubic symmetry is transformed into the tetragonal symmetry then T15 splits into f 4 and T,.

The f,-f, splitting of the high frequency modes in CuGaS, is relatively small (5 cm-'), the oscillator strengths, however, differ remarkably. This is an indi- cation for a transfer of oscillator strength by a mixing with other infrared active modes.

The strong polar T, bands of CuGaS, between 352 cm-' and 262 cm-' are related to X, and W, of ZB. If we assume that the dispersion from X, to W, is small in ZnS, then the CH structure must be responsible for the large splitting of these modes (Aw,, = 70 cm- l ) . This may be attributed to a mixing and repulsing of the T5(X,) and T5(W4) modes.

A large splitting is also observed for the T4 and T3 modes of CuGaS, which derive from W, of ZB. The f,(W,) mode seems to be shifted to lower energies due to the contribution of the weaker bound Cu atom.

compounds.

The frequency of the totally symmetric T,(W ,)-mode hardly varies from CuAlS, (315 cm-') to CuGaS, (312 cm-') and to AgGaS, (295 cm-'), since this mode represents motions of the sulfur atoms only.

The T3(X3) and f ,(W,) modes of CH represent pure cation motions in the simple ZB approximation, and therefore they are expected to be very sensitive to the replacement of the cations. The well-known f3(X3) mode of CuAIS, (268 cm-') was used to assign the corresponding modes for CuGaS, (203 cm-' accord- ing to ref. [12]) and for AgGaS, (180 cm-').

As mentioned before, the T4 and T, modes of highest frequency are mainly vibrations of the group I11 atoms and the S atoms in antiphase, without considerable contribution of the group I atoms. The replacement of the group I atoms (CuGaS, ^t,AgGaS,, CuInS, ^o AgInS,) does not change the position of the high frequency modes. Furthermore the change of the f4(T) frequency from CuAlS, (446 cm-') to CuGaS,/AgGaS, (3681367 cm-') and to CuInS,/

AgTnS, (3231329 cm-') corresponds in good approxi- mation to the change which would be expected from the reduced masses for the antiphase vibrations of AI-S, Ga-S and In-S. This indicates, that the force constants of these compounds are comparable :

The splitting of the C H modes in a high frequency a A 1 - ~ ^% ciGa-S z and a mid frequency group, which are well separated in

CuGaS,, is a consequence of the deviation from the ZB The force constant a,,-, of CuFeS, seems to be approximation. In a simple ZB model one would slightly lower than a,,-,.

expect one degenerate strong polar mode of CH which On the other hand the TO frequencies of the second has its position near the

r , ,

band of ZB and which is group of polar modes seem to be more sensitive to the

OPTICAL PHONONS IN I-111-V12 COMPOUNDS C3-181

group 1 atoms. The T4(W2) frequencies show a syste- matic dependence on the different cations : CuAlS, (271 cm- ^l), CuGaS, (262 cm-'), CuInS, ( 2 3 4 G - l ) , AgGaS, (222cm- l ) and AglnS, (2% cm- ^l).

- -

The

r,, r,

and I'5 modes between 112 cm-' and 65 cm-' are related to acoustic modes of ZB at X and W. Going from CuAlS,, to CuGaS, and AgGaS, a shift to lower frequencies is observed. A comparison of the different compounds may help to assign the missing modes, which have not been observed in Raman and infrared spectra.

In conclusion, we have investigated the phonon spectra of I-111-S, compounds and their relation to the phonon dispersion curves of ZB compounds. A

consistent assignment of the corresponding modes for the different compounds of the I-111-S, family has been obtained. The effects of the cation masses and the different force constants have been discussed. Further information, however, must be obtained by detailed model calculations which may be fitted to the experi- mental data.

Acknowledgments. - We would like to thank Dr. A. Rauber for supplying the CuInS, and AgInS, crystals. Stimulating discussions with Dr. M. Bettini, MP1 fiir Festkorperforschung Stuttgart, are gratefully acknowledged. We are indebted to H. 0. Mossle for technical assistance.

References

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B 2 (1970) 960.

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[3] MILLER, A., HOLAH, G. D., CLAKK, W. C., J. Phys. Chem.

Solids 35 (1974) 685.

[4] KOSCHEL, W. H., SOKGER, F., BAARS, J., Solid State Com- m m . 15 (1974) 719.

[5] B r n ~ h ~ , M., BAUHOFER, W., CARDONA, M., NITSCHE, R., Phys. Stat. Sol. (b) 63 (1974) 641.

[6] BETTIM, M., MILLER, A., Phys. Stat. Sol. (b) 66 (1974) 579.

[7] ATTOKESI, M., PINCZUK, A., GAVINI, A., 12th Int. Conf.

Phys. Semicond., Teubner, Stuttgart (1974) p. 321.

[8] BETTIM, M., Phys. Stat. Sol. ( b ) 69 (1975) 201.

[g] KOSCHEL, W. H., HOHLEK, V., R ~ U B E K , A., BAAKS, J., Solid State Commun. 13 (1973) 101 1.

[l01 KOSCHEI*, W. H., Thesis, Universitlt Freiburg (1974).

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[l21 VAN DER ZIEL, J. P., MEIXNEK, A. E., KASPER, H. M., DITZENRERGER, J. A., Phys. Rev. B 9 (1974) 4286.

[l31 BAAKS, J., KOSCHEL, W. H., Solid Stare Commun. 11 (1972) 1513.

[l41 B E ~ N I , M., HOLZAPFEL, W. B., Solid State Commun. 16 (1975) 27.

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