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

Abstract

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 ${\mathit{E}}_{0}$+${\mathrm{\ensuremath{\Delta}}}_{0}$ 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.