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

TL;DR

This study uses first-principles calculations to analyze electron mobility in silicon, revealing that two-phonon scattering processes significantly influence charge transport beyond the traditional one-phonon approximation.

Contribution

It demonstrates the importance of including two-phonon scattering in first-principles models to accurately predict electron mobility in non-polar semiconductors.

Findings

One-phonon theory overestimates the warm electron coefficient by over a factor of two.

Including two-phonon scattering aligns theoretical predictions with observed mobility.

Higher-order electron-phonon interactions are non-negligible in non-polar semiconductors.

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, $\beta$. Although the 1ph theory overestimates the low-field mobility by only around 20%, it overestimates $\beta$ by over a factor of two over a range of temperatures and crystallographic axes. We show that the discrepancy in $\beta$ 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.