Modeling Energy- and Momentum-dependent Scattering Relaxation Times in a Semi-Classical Model of Charge Transport using the Self-Scattering Technique

TL;DR

This paper analyzes and improves the self-scattering Monte Carlo technique for charge transport simulations, enabling accurate energy- and momentum-dependent relaxation times to be recovered and implemented efficiently.

Contribution

The authors demonstrate that the self-scattering technique can accurately recover energy- and momentum-dependent relaxation times, providing a clearer theoretical foundation for charge transport modeling.

Findings

Self-scattering Monte Carlo simulations match full relaxation rates.

The probability distribution of free-flight times aligns with analytical expressions.

Certain relaxation time forms may cause simulation failures.

Abstract

Improvement of numerical methods for calculating charge transport quantities of materials from the Boltzmann transport equation (BTE) is important for prediction of material properties. In particular, techniques which allow for more accurate models of scattering rates and band structures while remaining less computationally involved are valuable. The self-scattering technique is one such technique for implementing energy- and momentum-dependent scattering relaxation times in Monte Carlo simulations of charge transport or iterative techniques for solving the BTE. While the technique initially uses a constant relaxation time in the simulation algorithm, we found, upon analysis of the technique, that the energy and momentum total scattering relaxation time may be recovered. To show this, we preformed self-scattering Monte Carlo simulations of electron transport for both energy-dependent and independent relaxation times. The relaxation times and the fraction of scattering type selected in the simulation matched the full rates implemented in the simulation. In order to understand these results, we developed the theory behind the technique, demonstrating that the probability distribution function of free-flight times created using the self-scattering algorithm produces the analytical probability distribution function expression generated by full energy, momentum and time dependent relaxation times and probabilities. However, certain forms of relaxation times may cause the simulation to fail, depending on implementation. Clarity about such techniques is important for improvement of charge transport simulation models and implementation of ab initio scattering rates and band structures.