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

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 $\left(M\right)$ dependence of the indirect excitonic gap $\left(E_{gx}\right)$ and the relevant phonon frequencies. Interpreting these measurements on the basis of a phenomenological theory for $\left(\partial E_{gx}∕\partial M\right)$, we deduce $E_{gx}\left(M=\infty \right)=\left(1213.8\pm 1.2\right)$ meV, the purely electronic value in the absence of electron-phonon interaction and volume changes associated with anharmonicity.