Comparison on two ways of phonon spectral property reconstruction from thermal spectroscopy experiment

Abstract

We examine the reliability of the cumulative thermal conductivity as a function of the free path, F (Λ), in the context of reconstruction of phonon transport properties from thermal spectroscopy experiments. We specifically show that a given F (Λ) does not correspond to a unique relaxation-times function, in the sense that more than one distribution of relaxation-times can result in the same F (Λ). Since different relaxation-time distributions will, in general, lead to different thermal responses, F (Λ) does not uniquely predict the material thermal response in all transport regimes. This implies that in the context of thermal transport at the nanoscale within the Boltzmann relaxation-time approximation framework, the "fundamental" property that should be reconstructed from the thermal spectroscopy experiments is the frequency-dependent relaxation-times function (provided group velocities are known), since it explicitly appears in the governing equation as the input material property. Extensive global optimization studies show that a previously proposed formulation for reconstruction based on the frequency-dependent relaxation-times function [Physical Review B 94, 155439 (2016)] provides numerically unique solutions.