Intrinsic Piezobirefringence of Ge, Si, and GaAs

The stress-induced birefringence of Ge, Si, and GaAs and its dispersion in the region immediately below the fundamental absorption edge are reported. The measurements were performed at room temperature and for stresses along the [001] and [111] directions up to 5 × ${10}^9$ dyn/${\mathrm{cm}}^2$. The carrier concentration of the samples ($n$ type) was low enough (≤ ${10}^{16}$ ${\mathrm{cm}}^{-3\mathrm{}}$) to make free-carrier piezobirefringence negligible in the spectral region of our measurement ($\lambda \le 2.5$ μ). The data for Ge and GaAs are analyzed using an interband one-electron model for the optical constants, which includes the effects of the dispersion of the $E_0$, $E_0+{\Delta }_0$, $E_1$, $E_1+{\Delta }_1$, and $E_2$ gaps. The silicon data are fitted with a model which includes dispersion centers at 4.4 eV ($E_2$) and at 3.2 eV ($E_0^{}{}_{}{}^{\prime }$ and $E_1$). These models provide a good description of the experimental data and have some bearing upon the question of the accuracy of deformation potentials determined from piezobirefringence data.