Phonon relaxation times extracted from first principles thermal conductivity calculations

The lattice thermal conductivity of semiconductors, $\kappa _L $, is a key component in assessing a material's utility for thermoelectric applications. Calculations of $\kappa _L $ commonly employ phonon relaxation times, $\tau _{ph} $. Over the past few decades, a variety of mathematical forms have been used for these$\tau _{ph} $s to represent the phonon-phonon scattering [1], which dominates the behavior of $\kappa _L $ around and above room temperature. However, these forms have typically been obtained in a low frequency/low temperature approximation where umklapp scattering is weak and outside the thermal regime of interest for thermoelectrics. Recently we have developed a first principles approach that accurately calculates $\kappa _L $ using no adjustable parameters [2]. In this presentation, we use our \textit{ab initio} results for Si, Ge and diamond to examine the accuracy of the different models for $\tau _{ph} $, and we identify alternative models. [1] See for example, M. Asen-Palmer et al., Phys. Rev. B 56, 9431 (1997), and references therein. [2] D. A. Broido, M. Malorny, G. Birner, N. Mingo and D. A. Stewart, Appl. Phys. Lett. 91, 231922 (2007).