Piezo-optical response of Ge in the visible–uv range

Using rotating-analyzer ellipsometry we have measured the three complex components ${\mathit{P}}_{11}$(ω), ${\mathit{P}}_{12}$(ω), and ${\mathit{P}}_{44}$(ω) of the linear piezo-optical tensor ${\mathit{P}}_{\mathit{i}\mathit{j}\mathit{k}\mathit{l}}$(ω) of Ge in the 1.6–5.6 eV photon energy range. This was accomplished by applying static uniaxial stress to Ge crystals along the [111] and [001] crystallographic directions, and monitoring the stress-induced changes in the dielectric function ε(ω) at room temperature. The real and imaginary parts of each component were directly obtained. They show, in general, good Kramers-Kronig consistency. A comparison with pseudopotential calculations of ${\mathit{P}}_{11}$(ω), ${\mathit{P}}_{12}$(ω), and ${\mathit{P}}_{44}$(ω) for strained Ge is also given. In addition, deformation-potential constants (${\mathit{D}}_1^1$,${\mathit{D}}_1^5$,${\mathit{D}}_3^3$,${\mathit{D}}_3^5$) and spin-exchange parameters (${\mathrm{\delta }}_{\mathit{J}1}$,${\mathrm{\delta }}_{\mathit{J}2}$) were determined for the ${\mathit{E}}_1$-${\mathit{E}}_1$+${\mathrm{\Delta }}_1$ transitions; they show good agreement with prior work.