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 (GWA) for semiconductors. The IIR is calculated from the quasiparticle (QP) width in the GWA, 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 GWA 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.

Figure 1

Energy bands calculated by the $\text{QSGW}\alpha$ method [Eq. (9)], with $\alpha$ chosen to reproduce the experimental band gap $E_G$. In wurtzite GaN, $E_G=3.44\text{eV}$ (Ref. 21) and $\alpha =0.79$. Data for other compounds can be found in Table .

Figure 2

(Color online) Impact ionization rates ${\tau }_{\mathbf{k}n}^{-1}$ as a function of the initial electron energy ${\epsilon }_{\text{in}}$ (measured from the bottom of conduction band). The present GWA calculation is shown by large (red) plus signs. It is superposed on previous calculations: Si and InAs from Sano and Yoshii (Ref. 6), GaAs from Jung et al. (Ref. 7), ZnS and GaN from Kuligk et al. (Ref. 13). Open boxes in the ZnS and GaN data are screened exchange results from Picozzi et al. (Ref. 10); solid circles are exact exchange results (Ref. 13). We used $500\mathbf{k}$ points in the 1st Brillouin zone for GaN, and 1728 points for the cubic compounds [regular mesh including the $\Gamma$ point (Ref. 16)].