Reconstruction of the phonon relaxation times using solutions of the Boltzmann transport equation

Abstract

We present a method for reconstructing the phonon relaxation time distribution ${\ensuremath{\tau}}_{\ensuremath{\omega}}=\ensuremath{\tau}(\ensuremath{\omega})$ (including polarization) in a material from thermal spectroscopy data. The distinguishing feature of this approach is that it does not make use of the effective thermal conductivity concept and associated approximations. The reconstruction is posed as an optimization problem in which the relaxation times ${\ensuremath{\tau}}_{\ensuremath{\omega}}=\ensuremath{\tau}(\ensuremath{\omega})$ are determined by minimizing the discrepancy between the experimental relaxation traces and solutions of the Boltzmann transport equation for the same problem. The latter may be analytical, in which case the procedure is very efficient, or numerical. The proposed method is illustrated using Monte Carlo solutions of thermal grating relaxation as synthetic experimental data. The reconstruction is shown to agree very well with the relaxation times used to generate the synthetic Monte Carlo data and remains robust in the presence of uncertainty (noise).