Isotope effects on the electronic critical points of germanium: Ellipsometric investigation of the E

Within the past years the optical excitations of electrons have been measured for semiconductor samples of different isotope compositions. The isotope shift observed have been compared with calculations of the effects of electron-phonon interaction on the electronic band structure. While qualitative agreement has been obtained, some discrepancies remain especially concerning the E1 and $E_{1}+\Delta_{1}$ transitions. We have remeasured the effect of isotope mass on the E1 and $E_{1}+\Delta_{1}$ transitions of germanium with several isotopic compositions. The results, obtained by means of spectroscopic ellipsometry, confirm that the real part of the gap self-energies induced by electron-phonon interaction is larger than found from band structure calculations, while the imaginary part agrees with those calculations, which are based on a pseudopotential band structure and a bond charge model for the lattice dynamics. Our results agree with predictions based on the measured temperature dependence of the gaps. We compare our data for E1 and $E_{1}+\Delta_{1}$ with results for the lowest direct (E0) and indirect (Eg) gaps. The measured values of $\Delta_{0}$ and $\Delta_{1}$ increase noticeably with increasing isotope mass. Similar effects have been observed in the temperature dependence of $\Delta_{1}$ in $\alpha{-}{\rm Sn}$ and $\rm GaSb$. A microscopic explanation for this effect is not available