Semi-implicit Lax-Wendroff kinetic scheme for electron-phonon coupling

TL;DR

This paper introduces a semi-implicit Lax-Wendroff scheme for modeling electron-phonon interactions in metals, enabling larger time steps and efficient simulation across ballistic to diffusive regimes.

Contribution

The paper presents a novel semi-implicit kinetic scheme that integrates physical evolution into numerical modeling, overcoming limitations of traditional methods.

Findings

Efficiently captures electron-phonon coupling from ballistic to diffusive regimes.

Allows larger time steps independent of relaxation time and mean free path.

Provides a new computational tool for thermal management in microelectronics.

Abstract

A semi-implicit Lax-Wendroff scheme is developed for electron-phonon coupling process in metals based on the two-temperature kinetic equations. The core of this method is to integrate the evolution information of physical equations into the numerical modeling process, which leads to that the time step or cell size is not limited by the relaxation time and mean free path. Specifically, the finite difference method is used to solve the kinetic model again when reconstructing the interfacial distribution function, through which the particle migration, scattering and electron-phonon coupling processes are coupled together within a single time step. Numerical tests demonstrate that this method could efficiently capture electron-phonon coupling or heat conduction processes from the ballistic to diffusive regimes. It provides a new tool for describing electron-phonon coupling or thermal management in microelectronic devices.