Physical Review B 72,15 (2005) 153203;
The E-0(') direct transition of Si between its valence band maximum (Gamma(8)(+)) and conduction band minimum (Gamma(6)(-)) and the E-1 direct transition along < 111 > 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.
temperature-dependence;; interband transitions;; silicon;; semiconductors;; electroreflectance;; ge;; modulation;; spectra
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