Theory of phonon-assisted Auger recombination in semiconductors

A theory is developed of phonon-assisted Auger recombination in semiconductors on the basis of the Green's-function formalism. As a result, the divergence difficulty, which is inherent in the earlier theory based on the second-order perturbation approach, can be avoided. It is shown that results of the present theory are different from those of the earlier theory in the following respects. For $p-\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ and $p-\mathrm{G}\mathrm{a}\mathrm{S}\mathrm{b}$ the pure collision Auger recombination is almost negligible in comparison with the phonon-assisted Auger recombination over the whole temperature range of interest. The result that the pure collision Auger process is negligible even at 300 K for $p-\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ is remarkably contrasted from that of the earlier theory. The theory is applicable to $p-\mathrm{G}\mathrm{a}\mathrm{S}\mathrm{b}$, to which the earlier theory is not applicable. When one takes into account the free-carrier screening of the electron-phonon interaction for the first time, it is indicated that the effect is considerably important in $p-\mathrm{G}\mathrm{a}\mathrm{S}\mathrm{b}$ but not in $p-\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$.