Mesoscopic Hydro-Thermodynamics of Phonons

TL;DR

This paper develops a mesoscopic hydrodynamics framework for phonons in semiconductors, deriving coupled hyperbolic equations for quasi-particle and energy densities, and applies it to analyze thermal effects in silicon mirrors under high-intensity X-ray pulses.

Contribution

It introduces a generalized hydrodynamics approach for phonons based on a non-equilibrium statistical formalism, deriving new coupled equations and analyzing thermo-elastic effects.

Findings

Coupled Maxwell-Cattaneo-like hyperbolic equations for phonon densities.

Derivation of a generalized Guyer-Krumhansl equation for heat flux.

Application to thermal distortion in silicon mirrors under FEL pulses.

Abstract

A generalized Hydrodynamics, referred to as Mesoscopic Hydro-Thermodynamics, of phonons in semiconductors is presented. It involves the descriptions of the motion of the quasi-particle density and of the energy density. The hydrodynamic equations, which couple both types of movement via thermo-elastic processes, are derived starting with a generalized Peierls-Boltzmann kinetic equation obtained in the framework of a Non-Equilibrium Statistical Ensemble Formalism, providing such a Mesoscopic Hydro-Thermodynamics. The case of a contraction in first order relevant variables is worked out in detail. The associated Maxwell times are derived and discussed. The densities of quasi-particles and of energy are found to satisfy coupled Maxwell-Cattaneo-like hyperbolic equations. The analysis of thermo-elastic effects is done and applied to investigate thermal distortion in silicon mirrors under incidence of high intensity X-ray pulses in free electron laser (FEL) facilities. The derivation of a generalized Guyer-Krumhansl equation governing the flux of heat and the associated conductivity coefficient is also presented.