Raman scattering by phonon polaritons in ZnS

Solid State Communications, Vol. 35, pp. 73—74. Pergamon Press Ltd. 1980. Printed in Great Britain. RAMAN SCA11’ERING BY PHONON POLARITONS IN ZnS G. Livescu* and 0. Brafman Department of Physics and Solid State Institute, Technion-Israel Institute of Technology, Haifa, Israel (Received 3 March 1980 by M. Cardona) The experimental difficulties in recording the phonon..polariton spectra of ZnS crystals are discussed. The measured polariton dispersion in cubic ZnS is presented and is found to be in good agreement with the calculated one. THE POLARJTON SPECTRA of a number of binary compounds were reported since the first polariton study of GaP [1] One would expect ZnS to be a natural candidate for such measurements: it is a well known and readily available classic compound, which is transparent throughout the visible region and was intensively studied in Rainan and infrared, and its dielectric constant and its index of refraction were reported [2,3] Nevertheless the polariton dispersion of ZnS was calculated [4], but not measured. It is hard to believe that no attempt was made to study the ZnS polariton spectrum and therefore we looked into the possible difficulties that might have been faced by doing so. Due to its TO antiresonance at around 1.8 eV the TO to LO intensity ratio (ITo/lw) is relatively small but increases with the frequency of the incident light [5] This means that favorable conditions for studying the ZnS polariton dispersion should be found in the short wavelength part of the visible region. In our earlier attempts no polariton lines were detected although the crystals were excited by the 4579 A laser line, The polariton intensity calculation we have made using the ‘TO/ILO at this wavelength clearly showed that there is not any theoretical reason which might explain the non-appearance of a polariton spectrum in ZnS. One therefore is left with the possibility of a technical difficulty. In the case of ZnS one should suspect the crystals at the first place. It is well known that the structural quality of ZnS crystals grown by any known technique is problematic. In addition to the two famous ZnS modifications zincblende and wurtzite, a great number of polytypes were found in ZnS crystals [6] These polytypes are stacked in parallel strips and all of them are perpendicular to a common axis [1111 in cubic notation or [00.1] in hexagonal coordinates). The polytypes have

slightly different energy gaps and different birefringence, which to first approximation depend linearly upon the percentage of the hexagonality of the polytype [6]. This in itself would not explain the difficulty in observing the polariton spectrum, though questions may arise when interpreting the data as to changes in symmetry, in the index of refraction and in the number of phonon lines due to the larger number of atoms per primitive unit cell of the polytypes. The principle difficulty in detecting polaritons was assumed to emerge from the polytype stacking. The width of the strips of uniform polytypesmay vary from a fraction of a micron to tens of microns. The borders between adjacent polytypes are non-transparent in the sense that they scatter or reflect the light. For this reason the ZnS platelet simulates an uneven grating diffracting the light, such that the angle of the scattered light and therefore also the wavevector of the polaritons are not well defmed. We believed this to be the reason for not obtaining polaritons from synthetic ZnS crystals. The only really cubic ZnS crystal we came across was a sphalerite mineral, which was most kindly provided to us by Prof. M. Cardona (it originated in the Pirenees and was obtained from the Minerals Supplier Juan Montal, Vilafranca del Penadés, Spain.) This sample 8 x 6 x 2 mm3 of pale yellow color was almost entirely black between crossed polarizers. Moreover, hardly any striations were found and none in the region used in the experiment. The forward scattering polariton spectra were taken using a 100 mW 4579 A line of an Ar’ laser and a triple spectrometer set for a resolution of 3—4 cm’. The incident laser beam was parallel to the [110] axis and was focused onto the sample by a 130 cm focal length lens, in order to minimize the angular spread of the incident radiation. An annulus restricted the angle of the scattered light such that ~1i/i,1’= 1/4 for 2°~ ~# 6°,i~j’being the external angle. For ~fr< 2°the intensity was too low to be measured. Because of the use of an annulus, selection rules were such that both the

.

.

.

.

___________

~ Work in partial fulfillment of the requirements for the M.Sc. degree. 73

74

RAMAN SCAUERING BY PHONON POLARITONS IN ZnS I

I I

Vol. 35, No.1 I

280-

270 ~s~3.8°

-

I I

I

—

4,_50 I

II

—

I

E 0

I

—2603

q~

3.20

250

I

-

1000

I

2.60

I

250

w

I

300 (cm-1)

350

Fig. 1. Forward Raman scatteringof cubic ZnS at 100 K at various external scattering angles The ~‘.

vertical dashed line is at WTO indicate the polariton peaks.

2000

2500

3000

cq (cm-1 Fig. 2. The polariton dispersion of ZnS: The circles represent the experimental results, the full line is the calculated polariton dispersion and the dashed line indicates the external angles.

I

200

1500

279 cm~the arrows

polariton and the LO phonon were allowed. The spectra were taken at 100 K for three reasons: to obtain narrower lines, to improve the ITO/ILO ratio and most important to reduce the intensity of the 216 cm’ line which is a difference band (TO(L) TA(L)) [7] such that its tail will not interfere with the polariton line, Near forward scattering spectra at various angles ~1~’ are shown in Fig. 1. A straight line is drawn at 279 cm~, which is the TO frequency at large angle and is seen also in the polariton configuration, where it is not allowed. —

It appears due to back reflection which is always present and especially at low temperatures, when windows are unavoidable and index matching liquids cannot be used. The polariton wavevector is calculated from8k/~~ the 2 = (ak/aw)2 w~(q)+ ~ where relation q =n A dn/dA is determined from the refraction index data of [3] and wp(q) is the measured polariton wavevector dependent frequency. The polariton dispersion is calculated from cq = When damping is excluded, which can

and the calculated polariton dispersion is shown in Fig. 2. The fit is as good as one can expect. It is obtained with e~,= 5.2 and S = 3.0 ±0.1 (‘~.‘~o = 279 cm~, WLO = 351 cm’) and therefore e 0 = e,~+ S = 8.2 compared with the values of 8.1 ±0.2 (80 K) and 8.3 ±0.2 (300 K) measured by Berlincourt [2]. In conclusion, the polanton dispersion in cubic ZnS was reported and the special difficulties in recording the polariton spectra in this material were discussed. Acknowledgements We are indebted to Prof. M. Cardona for providing us with the sphalerite crystals on which this report is based. We thank H. Katz for his expert technical assistance. —

REFERENCES 1. 2. 3. ~,

—

5.

6. certainly be the case here, e(w) = e~,+ S/(1 w2/w4~o) where S and WTO are the strength and frequency of the 7. single polar mode. The fit between the experimental —

C.H. Henry & J.J. Hopfield,Phys. Rev. Lett. 15, 965 (1965). D. Berlincourt, H. Jaffe & L.R. Shiozawa, Phys. Rev. 129, 1009 (1963). W.L. Bond, J. Phys. 1674&(1965). S. Ushioda, A.Appi. Pinczuk, W.36, Taylor E. CornBurstein, Proc. mt. Conf. II— VI Semiconducting pounds (Edited by D.G. Thomas). Benjamin New York (1967). J.L. Lewis, R.L. Wadsack & R.K. Chang, Proc. mt. Conf on Light Scattering in Solids (Edited by M. Balkanski). Flammarion, Paris (1971). 0. Brafman & I.T. Steinberger, Phys. Rev. 143, 501 (1966). 0. Brafman & SS. Mitra, Proc. mt. Conf. on Light Scattering in Solids (Edited by M. Balkanski). Flammarion,Paris (1971).