Theory of Thermal Relaxation of Electrons in Semiconductors

TL;DR

This paper investigates the complex thermal relaxation dynamics of hot electrons in semiconductors, revealing non-exponential decay patterns caused by slow phonon thermalization, and introduces a generalized model to accurately describe these processes.

Contribution

It develops a first-principles Boltzmann framework to analyze phonon-electron interactions and proposes a generalized 2-temperature model that accounts for phonon thermalization effects.

Findings

Decay of electronic temperature often deviates from single-exponential behavior.

Non-thermal vibrational modes emerge during thermal relaxation.

Spectral electron-phonon and phonon-phonon couplings can be inferred from multi-exponential decay patterns.

Abstract

We compute the transient dynamics of phonons in contact with high energy "hot" charge carriers in 12 polar and non-polar semiconductors, using a first-principles Boltzmann transport framework. For most materials, we find that the decay in electronic temperature departs significantly from a single-exponential model at times ranging from 1 ps to 15 ps after electronic excitation, a phenomenon concomitant with the appearance of non-thermal vibrational modes. We demonstrate that these effects result from the slow thermalization within the phonon subsystem, caused by the large heterogeneity in the timescales of electron-phonon and phonon-phonon interactions in these materials. We propose a generalized 2-temperature model accounting for the phonon thermalization as a limiting step of electron-phonon thermalization, which captures the full thermal relaxation of hot electrons and holes in semiconductors. A direct consequence of our findings is that, for semiconductors, information about the spectral distribution of electron-phonon and phonon-phonon coupling can be extracted from the multi-exponential behavior of the electronic temperature.