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

TLDR

In unstressed diamond‑type semiconductors the Raman spectrum shows a single triply degenerate peak, whereas zinc‑blende materials display separate LO and TO peaks; applying uniaxial stress induces polarization‑dependent splittings or shifts that vary linearly with stress. The study measures how large static uniaxial stresses along [001], [111], and [110] directions shift the k≈0 optical phonon frequencies in Ge, GaAs, GaSb, InAs, and ZnSe via first‑order Raman scattering. Experimental phonon shifts were compared to theoretical models that account for bond‑stretching and bond‑bending interactions to extract phenomenological coefficients (p, q, r). The measured splittings and shifts yielded phenomenological coefficients and a mode‑Grüneisen parameter comparable to hydrostatic‑pressure data; in zinc‑blende materials the TO phonon splits and shifts while the LO phonon only shifts, whereas in III‑V compounds one split TO line follows the LO stress dependence, a behavior absent in ZnSe and attributed to stress‑dependent effective charge.

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.