Two-phonon scattering in non-polar semiconductors: a first-principles study of warm electron transport in Si

Abstract

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 non-polar 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, β.Although the 1ph theory overestimates the low-field mobility by only around 20%, it overestimates β by over a factor of two over a range of temperatures and crystallographic axes. We show that the discrepancy in β is reconciled by inclusion of on-shell iterated 2-phonon (2ph) scattering processes, indicating that scattering from higher-order electron-phonon interactions is non-negligible even in non-polar semiconductors. Further, a ∼ 20% underestimate of the low-field mobility with 2ph scattering suggests that non-trivial cancellations may occur in the perturbative expansion of the electron-phonon interaction.

Transport and noise of hot electrons in GaAs using a semi-analytical model of two-phonon polar optical phonon scattering

“…Recent works have extended these calculations to beyond low-field transport and noise properties. [21][22][23][24] In GaAs, it was found that although the qualitative shape of the drift velocity versus electric field curve was predicted correctly compared to experiment, the magnitude of the drift velocity was overpredicted by about 50%. [23] The inclusion of the next-leading-order term of scattering involving two phonons (2ph) yielded a low-field mobility and drift velocity with substantially improved agreement.…”