Intervalley scattering potentials of Ge from direct exciton absorption under pressure

We have measured the dependence on pressure of the low-temperature (10 K) direct exciton optical absorption of Ge up to 12.3 GPa. The sharp exciton peak at the direct energy gap (${\mathit{E}}_0$) of Ge is found to broaden significantly with increasing pressure. This effect, which is attributed to intervalley scattering via electron-phonon interaction, is most pronounced for pressures above ∼0.6 GPa, where the X valley becomes the lowest conduction-band minimum. From the pressure-induced exciton broadening we determine the Γ to X point intervalley deformation-potential constant ${\mathit{D}}_{\mathrm{\Gamma }\mathit{X}}$=2.2(3) eV/Å and an upper bound of ${\mathit{D}}_{\mathrm{\Gamma }\mathit{L}}$=4.5 eV/Å for scattering from Γ to the L valleys. The deformation potential ${\mathit{D}}_{\mathrm{\Gamma }\mathit{X}}$ of Ge is about 50% smaller compared to isoelectronic GaAs. This difference is attributed to the fact that interatomic matrix elements between s and d states of the Γ and X conduction-band minima as well as the d character of the X minimum are larger in GaAs.