Electronic band structure of isotopically pure germanium: Modulated transmission and reflectivity study

The piezomodulated and photomodulated reflectivity spectra of monoisotopic Ge ${(}^{70}$Ge, ${}_{}{}^{73}{}_{}{}^{}\mathrm{Ge}$, ${}_{}{}^{74}{}_{}{}^{}\mathrm{Ge}$, ${}_{}{}^{76}{}_{}{}^{}\mathrm{Ge}$) and natural Ge measured at T=6 K show clear signatures of the ${\mathit{E}}_0$ and the ${\mathit{E}}_0$+${\mathrm{\Delta }}_0$ transitions; their energies increase with increasing isotopic mass. From a comparison of the phonon-assisted indirect transition energies obtained from electromodulated and wavelength-modulated transmission and photoluminescence, the isotopic mass dependence of both the indirect gap and the relevant zone-boundary phonons are deduced. The isotopic-mass dependence of the energy gaps is interpreted in the context of the electron-phonon interaction and the volume expansion of the crystal lattice.