Resonant indirect optical absorption in germanium

Abstract

The optical absorption coefficient of pure Ge has been determined from high-accuracy, high-precision optical measurements at photon energies covering the spectral range between the indirect and direct gaps. The results are compared with a theoretical model that fully accounts for the resonant nature of the energy denominators that appear in perturbation-theory expansions of the absorption coefficient. The model generalizes the classic Elliott approach to indirect excitons, and leads to a predicted optical absorption that is in excellent agreement with the experimental values using just a single adjustable parameter: the average deformation potential ${D}_{\mathrm{\ensuremath{\Gamma}}L}$ coupling electrons at the bottom of the direct and indirect valleys in the conduction band. Remarkably, the fitted value, ${D}_{\mathrm{\ensuremath{\Gamma}}L}=4.3\ifmmode\times\else\texttimes\fi{}{10}^{8}\phantom{\rule{0.16em}{0ex}}\mathrm{eV}/\mathrm{cm}$, is in nearly perfect agreement with independent measurements and ab initio predictions of this parameter, confirming the validity of the proposed theory, which has general applicability.