Eur. Phys. J. B 67, 15-25 (2009)
https://doi.org/10.1140/epjb/e2008-00464-6

Phonon transport in silicon, influence of the dispersion properties choice on the description of the anharmonic resistive mechanisms

Laboratoire d'Énergétique et de Mécanique Théorique et Appliquée, Nancy Université – CNRS, BP 70239, 54506 Vandœuvre-Les-Nancy Cedex, France

Corresponding author: ^a David.Lacroix@lemta.uhp-nancy.fr

Received: 5 August 2008
Published online: 24 December 2008

Abstract

Thermal conductivity in semiconductors is investigated through the phonon transport description. From the former studies based on the gas kinetic theory to the recent ones using the Monte Carlo methods or the radiative multifux models, each technique involves the dispersion properties of the crystal lattice. Besides, most of these studies have been done in the frame of the relaxation time approximation of collision processes. In this study, the importance of the choice of the dispersion curves and time relaxation parameters are pointed out. A complete description of the transverse umklapp interaction is provided without any adjustment parameters. New insights of the energy conservation surface calculation, involved in phonon-phonon time relaxation expression, are provided. Using simple and more complex models, we have determined the heat transport properties, in the temperature range from 50 K to 1000 K in bulk silicon. We especially focused our attention on the thermal conductivity as a function of the phonon anharmonic resistive mechanisms for two models of dispersion: “linear” and “quadratic”. We demonstrate that very different thermal conductivity properties can be calculated according to the chosen description of lattice vibrations.