Stress-Induced Shifts of First-Order Raman Frequencies of Diamond- and Zinc-Blende-Type Semiconductors

Abstract

In this paper we report measurements of the effects of large static uniaxial stress along [001], [111], and [110] on the frequency of the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ensuremath{\approx}0$ optical phonons in Ge, GaAs, GaSb, InAs, and ZnSe using first-order Raman scattering. In the absence of stress, the first-order Stokes-Raman spectrum of diamond-type materials exhibits a single peak which corresponds to the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ensuremath{\approx}0$ triply degenerate optical phonons (${F}_{2g}$ or ${\ensuremath{\Gamma}}_{{25}^{\ensuremath{'}}}$) while the zinc-blende materials exhibit two peaks, corresponding to the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ensuremath{\approx}0$ LO and TO phonons. The application of the uniaxial stress causes polarization-dependent splittings and/or shifts which are linear in the stress. From these observed splittings and shifts we have obtained experimental values for the phenomenological coefficients ($p, q, \mathcal{r}$) which describe the changes in the "spring constant" of these optical phonons with strain. Comparison of the experimental values is made with several theoretical considerations based on bond-stretching and bond-bending interactions between atoms. The shift due to the hydrostatic component of the strain yields a value for the mode-Gr\"uneisen parameter, which is compared with the results of hydrostatic-pressure measurements. For the zinc-blende-type materials, the doubly degenerate TO-phonon line exhibits both a splitting and shift with stress, while only a shift is observed for the singlet LO-phonon line. In the case of the III-V compounds, one of the split TO lines has a stress dependence equal to that of the LO-phonon line, while this is not the case for the group II-VI material (ZnSe) we have investigated. This latter result is interpreted in terms of the stress dependence of the effective charge.