Dynamical lattice thermal conductivity, Shastry sum rule and second sound in bulk semiconductor crystals

TL;DR

This paper models the frequency-dependent lattice thermal conductivity in bulk semiconductors, exploring second sound phenomena and the Shastry sum rule using a phonon transport framework with modified Debye-Callaway model.

Contribution

It introduces a compact, causality-compliant expression for dynamical thermal conductivity and analyzes second sound and sum rule applicability within Boltzmann phonon transport.

Findings

Derived a convolution-type relation for heat flux and temperature gradient.

Identified conditions for second sound propagation in semiconductors.

Assessed the impact of nanoparticles on phonon scattering and thermal response.

Abstract

The paper discusses the fundamental behavior of the dynamical lattice thermal conductivity k(W) of bulk cubic semiconductor crystals. The calculation approach is based on solving Boltzmann-Peierls Phonon Transport Equation in the frequency domain after excitation by a dynamical temperature gradient, within the framework of the single relaxation time approximation and using modified Debye-Callaway model. Our model allows us to obtain a compact expression for k(W) that captures the leading behavior of the dynamical thermal conduction by phonons. This expression fulfills the causality requirement and leads to a convolution type relationship between the heat flux density current and the temperature gradient in the real space-time domain in agreement with Gurtin-Pipkin theory. The dynamical behavior of k(W) is studied by changing ambient temperature as well as different intrinsic and extrinsic parameters including the effect of embedding semiconductor nanoparticles as extrinsic phonon scattering centers. The paper investigates also the applicability of Shastry Sum Rule and the possibility of existence and propagation of second sound in the frame work of Boltzmann theory.