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

Abstract

Using rotating-analyzer ellipsometry we have measured the three complex components ${\mathit{P}}_{11}$(\ensuremath{\omega}), ${\mathit{P}}_{12}$(\ensuremath{\omega}), and ${\mathit{P}}_{44}$(\ensuremath{\omega}) of the linear piezo-optical tensor ${\mathit{P}}_{\mathit{i}\mathit{j}\mathit{k}\mathit{l}}$(\ensuremath{\omega}) 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 \ensuremath{\epsilon}(\ensuremath{\omega}) 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 ${\mathit{P}}_{11}$(\ensuremath{\omega}), ${\mathit{P}}_{12}$(\ensuremath{\omega}), and ${\mathit{P}}_{44}$(\ensuremath{\omega}) 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 (${\mathrm{\ensuremath{\delta}}}_{\mathit{J}1}$,${\mathrm{\ensuremath{\delta}}}_{\mathit{J}2}$) were determined for the ${\mathit{E}}_{1}$-${\mathit{E}}_{1}$+${\mathrm{\ensuremath{\Delta}}}_{1}$ transitions; they show good agreement with prior work.