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 $E_0$, $E_0+{\Delta }_0$, $E_1$, and $E_1+{\Delta }_1$ electroreflectance peaks of Ge and GaAs, and the ${E_0}^{\prime }$ electroreflectance peaks of Si. From the stress-induced splittings and shifts of the $E_0$, $E_0+{\Delta }_0$ 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 ${\Lambda }_1$-conduction and ${\Lambda }_3$-valence bands of Ge and GaAs have been determined from the stress dependence of the $E_1$ and $E_1+{\Delta }_1$ peaks of these materials. We have attributed the observed stress-induced changes in intensity of these peaks to the intraband splitting of the ${\Lambda }_3$-orbital valence bands. The experimental results are compared with our theoretical calculations. The stress dependence of the ${E_0}^{\prime }$ 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.