On the effect of phonon decay on electronic transitions in ionic crystal semiconductors

Generally electronic processes in semiconductors are accompanied by phonon excitations. These excitations themselves influence electronic transitions. On the other hand excited phonons decay by interaction with other impurities in the crystal, which act as a heat-bath. The resulting competition between phonon exciting electronic processes and phonon decay is described by Pauli's master equation. By expansion of its solutions into phonon decay solutions the problem can be separated into different decay equations for phonons and electrons as proposed by Stumpf. Assuming linear phonon-heat-bath coupling the phonon decay equation can be solved exactly by a generating function technique. The appropriate phonon decay frequencies are calculated for a simple heat-bath model.