Piezo-Electroreflectance in Ge, GaAs, and Si

We have investigated the effect of static uniaxial compression along the [001], [110], and [111] directions on the ${E}_{0}$, ${E}_{0}+{\ensuremath{\Delta}}_{0}$, ${E}_{1}$, and ${E}_{1}+{\ensuremath{\Delta}}_{1}$ electroreflectance peaks of Ge and GaAs, and the ${{E}_{0}}^{\ensuremath{'}}$ electroreflectance peaks of Si. From the stress-induced splittings and shifts of the ${E}_{0}$, ${E}_{0}+{\ensuremath{\Delta}}_{0}$ peaks of Ge and GaAs, the hydrostatic and shear deformation potentials of the k=0 valence-band maximum have been determined. We have also observed a nonlinear stress dependence of the energies of these peaks, which is caused by the stress-induced coupling between the upper stress-split valence band and the spin-orbit split band. A theory for the stress-induced variations in intensity caused by this interaction will be presented and compared with the experimental results. The hydrostatic and shear deformation potentials of the ${\ensuremath{\Lambda}}_{1}$-conduction and ${\ensuremath{\Lambda}}_{3}$-valence bands of Ge and GaAs have been determined from the stress dependence of the ${E}_{1}$ and ${E}_{1}+{\ensuremath{\Delta}}_{1}$ peaks of these materials. We have attributed the observed stress-induced changes in intensity of these peaks to the intraband splitting of the ${\ensuremath{\Lambda}}_{3}$-orbital valence bands. The experimental results are compared with our theoretical calculations. The stress dependence of the ${{E}_{0}}^{\ensuremath{'}}$ electroreflectance peaks of Si for [001] stress seems to indicate that [100] critical points are responsible for this structure. However, we have also observed large polarization-dependent intensity changes for [111] stress, which we have not been able to explain on the basis of the above assignment.