Impact ionization rate calculation based on $GW$ approximation

Impact ionization (IMI) means the electron-hole pair production due to high energy electron (or hole). It can control the performance of devices related to the high-field transport process. For solar cell, it was proposed to use IMI for efficient energy conversion. The IMI rate can be identified as the lifetime of an electron (imaginary part of the self-energy). Since the electron-hole pair spectrum is included in the screened Coulomb interaction $W$, it should be important to use full $W$ for the calculation of the lifetime. However, to our knowledge, no such calculation has been presented for semiconductors until now. For example, Ref.[1] uses a model $W$. In addition, the conventional formalism of Ref.[1] contains some double-counting problem. We will show our calculation for the IMI rate based on our recently-developed quasi-particle self-consistent $GW$ method for semiconductors. Our calculation predicts a rather smaller IMI rate. [1] A. Kuligk, N. Fitzer, and R. Redmer, PRB71, 085201(2005) [2] T.Kotani, M. van Schilfgaarde, and S.V. Faleev, PRB76, 165106 (2007)