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Impact ionization rates for Si, GaAs, InAs, ZnS, and GaN in the $GW$ approximation

We present first-principles calculations of the impact ionization rate (IIR) in the $GW$ approximation ($GW$A) for semiconductors. The IIR is calculated from the quasiparticle (QP) width in the $GW$A, since it can be identified as the decay rate of a QP into lower energy QP plus an independent electron-hole pair. The quasiparticle self-consistent $GW$ method was used to generate the noninteracting hamiltonian the $GW$A requires as input. Small empirical corrections were added so as to reproduce experimental band gaps. Our results are in reasonable agreement with previous work, though we observe some discrepancy. In particular we find high IIR at low energy in the narrow gap semiconductor InAs.