Unified theory of the impurity and phonon scattering effects on Auger recombination in semiconductors

Abstract

I have developed a theory of impurity- and phonon-assisted Auger recombination in semiconductors. The theory is based on the Green's function, which is derived by taking into account both the impurity scattering and the phonon scattering. The function is shown as a test to explain well the conductivity data of heavily doped $n$-type Ge. The theory is applied to $p$-type materials of GaAs, InP, GaSb, and InAs for acceptor concentrations between ${10}^{17}$ and ${10}^{20}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ and for temperatures between 77 and 500 K. Those materials are typical in that the band-gap energy ${E}_{G}$ is much larger than the spin splitoff energy ${\ensuremath{\Delta}}_{0}$ for the former two materials and these are comparable for the latter two. It is shown that the impurity- and phonon-assisted Auger recombination is predominant in materials with ${E}_{G}>>{\ensuremath{\Delta}}_{0}$ for the acceptor concentrations between ${10}^{17}$ and ${10}^{19}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ and/or for the temperatures below 300 K. Except for these cases the Auger recombination is roughly or well described by the pure collision Auger process. On the other hand, at light-doping levels the Auger recombination assisted by the phonon scattering alone is predominant for all materials. It is stressed that an analysis based on the pure collision Auger process leads to erroneous numerical results for most cases of practical interest.