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 (E₀) 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 D_ΓX=2.2(3) eV/{} and an upper bound of D_ΓL=4.5 eV/{} for scattering from {Γ} to the L valleys. The deformation potential D_ΓX 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.