Microscopic theory of second-order Raman scattering in silicon under uniaxial stress

A microscopic calculation of the second-order Raman-scattering efficiency of silicon, with special emphasis on the effects of uniaxial stress, is presented. Employing diagrammatic perturbation theory, the scattering efficiency is obtained for incident- and scattered-photon energies either on or off resonance. A numerical evaluation employs realistic models for the electronic band structure and phonon spectra, and sums over all two-, three-, and four-band scattering channels. The scattering efficiency is normalized by the integrated first-order efficiency, and the results of the calculation are quantitatively compared with experimental data for second-order Raman scattering in crystalline silicon under [001] stress, taken with an incident laser energy of 2.34 eV.