Rearrangement collision theory of phonon-driven exciton dissociation

TL;DR

This paper develops a rigorous theoretical framework based on Dyson's S-matrix formalism to accurately compute phonon-mediated exciton dissociation rates in semiconductors, crucial for photovoltaic technology.

Contribution

It extends scattering theory to multi-channel processes involving composite quasiparticles, providing new formulas for exciton dissociation rates applicable to ab initio calculations.

Findings

Derived expressions enforce energy conservation in exciton dissociation.

Compared temperature-dependent exciton rates across different channels.

Validated the formalism with a three-dimensional model system.

Abstract

Understanding the processes governing the dissociation of excitons to free charge carriers in semiconductors and insulators is of central importance for photovoltaic applications. Dyson's $\mathcal{S}$-matrix formalism provides a framework for computing scattering rates between quasiparticle states derived from the same underlying Hamiltonian, often reducing to familiar Fermi's golden rule like expressions at first order. By presenting a rigorous formalism for multi-channel scattering, we extend this approach to describe scattering between composite quasiparticles and in particular, the process of exciton dissociation mediated by the electron-phonon interaction. Subsequently, we derive rigorous expressions for the exciton dissociation rate, a key quantity of interest in optoelectronic materials, which enforce correct energy conservation and may be readily used in ab initio calculations. We apply our formalism to a three-dimensional model system to compare temperature-dependent exciton rates obtained for different scattering channels.