Isotope and temperature shifts of direct and indirect band gaps in diamond-type semiconductors

We calculate the isotope and temperature shifts of the indirect and direct band gaps in natural silicon (M{}=28.09 u), in natural diamond ¹²C and its isotope ¹³C, in natural germanium (M{}=72.59 u), and the isotope ⁷⁰Ge, and in the isotope mixture 75.7Ge, due to the deformation-potential-type electron-phonon interaction (within the pseudopotential-bond-charge-model framework). We compare these results to existing experimental information and to data obtained by us with spectroscopic ellipsometry. We find that there are small, but noticeable shifts of the band gaps between different isotopes (about 13 meV for diamond, 1 meV for germanium). The isotopic influence on the broadenings of the E₁ transition in Ge is also observed.