Raman Spectrum of Cubic ZnS

Abstract

We present a detailed study of the first- and second-order Raman effect in cubic ZnS using both 4880 and 5145 \AA{} excitation. Our primary interest is to determine to what extent information on lattice dynamics can be extracted from Raman studies in a case where the crystal structure is relatively simple. Aside from interpreting the observed spectra and determining the energies of the phonon branches at the Brillouin-zone center and boundary, the study emphasizes two things. First, we examine experimentally the relation between first-order Raman intensities and the linear electro-optic effect. We find that the linear electro-optic constant derived from the absolute Raman intensities of the longitudinal- (LO) and transverse- (TO) optic modes agrees quite well with the constant obtained from direct measurement. This close agreement is particularly significant in the zinc-blende structure, since only one electro-optic constant and two optical modes are involved in the comparison. Also, it provides experimental evidence that the macroscopic, and not the local, electric field caused by the polar phonons should be used in calculations involving semiconducting crystals. Second, emphasis was also placed on comparing the observed selection rules or polarization properties of the second-order Raman effect with that predicted at the two most important or highest-symmetry critical points ($X$ and $L$) on the Brillouin-zone boundary. The agreement between observed and calculated selection rules is quite good, although in some cases, certain polarization characteristics which are allowed by symmetry are not detected. Also, some evidence of two-phonon scattering from other points in the Brillouin zone is found. The polarization properties of single-crystal Raman spectra are more conveniently discussed in terms of the irreducible representations of the polarizability, rather than depolarized spectra or depolarization ratios which apply more directly to liquid or polycrystalline samples. The observed and calculated selection rules for second-order Raman scattering are compared in detail, using these polarizability representations. The LO and TO phonon energies are 271 and 352 ${\mathrm{cm}}^{\ensuremath{-}1}$ at the zone center and 306 and 333 ${\mathrm{cm}}^{\ensuremath{-}1}$ at the zone boundary, and the TA and LA energies are 88 and 110 ${\mathrm{cm}}^{\ensuremath{-}1}$ at the boundary.