Two-phonon scattering in nonpolar semiconductors: A first-principles study of warm electron transport in Si

The ab initio theory of charge transport in semiconductors typically employs the lowest-order perturbation theory in which electrons interact with one phonon (1ph). This theory is accepted to be adequate to explain the low-field mobility of nonpolar semiconductors but has not been tested extensively beyond the low-field regime. Here, we report first-principles calculations of the electric field dependence of the electron mobility of Si as described by the warm electron coefficient 0. Although the 1ph theory overestimates the low-field mobility by only around 20%, it overestimates 0 by over a factor of two over a range of temperatures and crystallographic axes. We show that the discrepancy in 0 is reconciled by the inclusion of on-shell iterated two-phonon (2ph) scattering processes, indicating that scattering from higher-order electron-phonon interactions is non-negligible even in nonpolar semiconductors. Further, a similar to 20% underestimate of the low-field mobility with 2ph scattering suggests that nontrivial cancellations may occur in the perturbative expansion of the electron-phonon interaction.