Influence of Uniaxial Stress on the Indirect Absorption Edge in Silicon and Germanium

TLDR

The indirect optical absorption edge in silicon and germanium has been studied under shear strain. The study used a vibrating‑slit spectrometer to resolve fine structure and determined deformation‑potential constants by neglecting strain dependence of phonon energies. The transmission spectrum splitting varies with stress direction, magnitude, and light polarization, reflecting strain‑induced band‑structure changes and exciton energy shifts, with quantified deformation‑potential constants for Si and Ge.

Abstract

The indirect optical absorption edge in silicon and germanium has been studied in the presence of shear strain. The splitting observed in the transmission spectrum is dependent on the direction and magnitude of the applied stress and on the polarization of the light with respect to the stress axis. The results have been interpreted in terms of changes in the valence- and conduction-band structure with strain. Neglecting strain dependence of phonon energies, various deformation potential constants have been determined from the experiments. The values are: Si, 80\ifmmode^\circ\else\textdegree\fi{}K: ${\ensuremath{\Xi}}_{u}=8.6\ifmmode\pm\else\textpm\fi{}0.2$ eV, $|b|=2.4\ifmmode\pm\else\textpm\fi{}0.2$ eV, $|d|=5.3\ifmmode\pm\else\textpm\fi{}0.4$ eV, ${\ensuremath{\Xi}}_{d}+\frac{1}{3}{\ensuremath{\Xi}}_{u}\ensuremath{-}a=3.8\ifmmode\pm\else\textpm\fi{}0.5$ eV. Si, 295\ifmmode^\circ\else\textdegree\fi{}K: ${\ensuremath{\Xi}}_{u}=9.2\ifmmode\pm\else\textpm\fi{}0.3$ eV, $|b|=2.2\ifmmode\pm\else\textpm\fi{}0.3$ eV, ${\ensuremath{\Xi}}_{d}+\frac{1}{3}{\ensuremath{\Xi}}_{u}\ensuremath{-}a=3.1\ifmmode\pm\else\textpm\fi{}0.5$ eV. Ge, 80\ifmmode^\circ\else\textdegree\fi{}K: ${\ensuremath{\Xi}}_{u}=16.2\ifmmode\pm\else\textpm\fi{}0.4$ eV, $b=\ensuremath{-}1.8\ifmmode\pm\else\textpm\fi{}0.3$ eV, $d=\ensuremath{-}3.7\ifmmode\pm\else\textpm\fi{}0.4$ eV, ${\ensuremath{\Xi}}_{d}+\frac{1}{3}{\ensuremath{\Xi}}_{u}\ensuremath{-}a=\ensuremath{-}2.0\ifmmode\pm\else\textpm\fi{}0.5$ eV. An observed nonlinear dependence of the splitting on stress has been interpreted as shifts of the exciton energies with uniaxial stress. A special experimental technique using a vibrating slit in the spectrometer was used in order to obtain an accurate determination of the fine structure in the absorption spectrum.