Electron-phonon renormalization of electronic band gaps of semiconductors: Isotopically enriched silicon

Abstract

Photoluminescence and wavelength-modulated transmission spectra displaying phonon-assisted indirect excitonic transitions in isotopically enriched $^{28}\mathrm{Si}$, $^{29}\mathrm{Si}$, $^{30}\mathrm{Si}$, as well as in natural $\mathrm{Si}$, have yielded the isotopic mass $(M)$ dependence of the indirect excitonic gap $({E}_{gx})$ and the relevant phonon frequencies. Interpreting these measurements on the basis of a phenomenological theory for $(\ensuremath{\partial}{E}_{gx}∕\ensuremath{\partial}M)$, we deduce ${E}_{gx}(M=\ensuremath{\infty})=(1213.8\ifmmode\pm\else\textpm\fi{}1.2)$ meV, the purely electronic value in the absence of electron-phonon interaction and volume changes associated with anharmonicity.