New calculations of the quantum yield of silicon in the near ultraviolet

Abstract

The rigorous expression for the quantum yield for electron-hole pair production was simplified using assumptions inspired by Kane's random-$k$ approximation and by recent results of Alig, Bloom, and Struck. The resulting approximation was intuitively satisfying. It required integration with respect to kinetic energy of the product of the joint distribution of the photogenerated electrons and holes and the average number of electron-hole pairs created by the cascade of impact ionizations initiated by a carrier with a given kinetic energy. The first quantity in the integrand was calculated from a self-consistent, first-principles band structure for silicon; the second was obtained from results of Alig, Bloom, and Struck. The results agreed reasonably well with recent experimental measurements of the quantum yield of silicon in the ultraviolet.