Effective-mass theory of resonant Raman scattering by semiconductor donors.

Abstract

We derive the Raman scattering cross section for transitions between states of a shallow semiconductor donor within a one-electron effective-mass theory that uses the \ensuremath{\Pi}\ensuremath{\cdot}A interaction to second order. For interband enhanced scattering, we show that the cross section is given by the product of the (free-) conduction-band-electron cross section and a form factor which depends upon the donor wave functions. We show that within one-electron theory the cross section has a truncated resonance at the band gap, even in the absence of lifetime broadening, but that the absolute cross section is quite huge, particularly for light-mass (narrow-gap) semiconductors. The results of this theory, together with the availability of tunable lasers resonant with semiconductor band gaps, point to the possibility for novel tunable far-infrared sources, and the use of light scattering as a sensitive analytical tool for characterizing impurities in semiconductors.