Isotopic dependence of the E-0 \u27 and E-1 direct gaps in the electronic band structure of Si

The E-0(\u27) direct transition of Si between its valence band maximum (Gamma(8)(+)) and conduction band minimum (Gamma(6)(-)) and the E-1 direct transition along \u3c 111 \u3e are studied in isotopically enriched Si-28, Si-29, and Si-30 employing photomodulated reflectivity. Their energies (E-G) at low temperature are found to increase with increasing isotopic mass (M) according to E-G(M)=E-G(infinity)-CM-1/2, as predicted in the theory for band gap renormalization by zero-point vibrations through electron-phonon interaction and volume changes associated with anharmonicity. Here E-G(infinity) is the energy gap of the infinitely massive isotope, free of renormalization effects