Effect of hydrostatic pressure on the direct absorption edge of germanium

Abstract

The dependence of the direct gap of germanium (${\ensuremath{\Gamma}}_{{25}^{\ensuremath{'}}}\ensuremath{\rightarrow}{\ensuremath{\Gamma}}_{{2}^{\ensuremath{'}}}$) on hydrostatic pressures up to 104 kbar has been measured. This dependence is found to be sublinear and to reflect mostly the nonlinearity in the compressibility. The linear pressure coefficient found for the gap is (1.53 \ifmmode\pm\else\textpm\fi{} 0.05) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}2}$ eV/kbar while the quadratic one amounts to -(4.5 \ifmmode\pm\else\textpm\fi{} 1) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}5}$ eV/${\mathrm{kbar}}^{2}$. When the gap is plotted as a function of lattice constant a small sublinearity remains. This sublinearity is well reproduced by a calculation based on empirical pseudopotential coefficients. At pressures above 8 kbars a strong tail develops below the direct edge. It is attributed to ${\ensuremath{\Gamma}}_{{25}^{\ensuremath{'}}}\ensuremath{\rightarrow}{L}_{1}$ and ${\ensuremath{\Gamma}}_{{25}^{\ensuremath{'}}}\ensuremath{\rightarrow}{\ensuremath{\Delta}}_{1}$ indirect transitions. The strength of the direct exciton edge is found to evolve with pressure in a way proportional to the ${\ensuremath{\Gamma}}_{{25}^{\ensuremath{'}}}\ensuremath{\rightarrow}{\ensuremath{\Gamma}}_{{2}^{\ensuremath{'}}}$ gap energy. At 105 kbar the material is found to become opaque as a result of a phase transition.