Prediction of the thermal conductivity anisotropy of Si nanofilms. Results of several numerical methods

The purpose of this work is to predict the in-plane and cross-plane thermal properties of crystalline silicon films. Several thicknesses from 20 nm to 6 μm and mean temperatures between 20 and 500 K have been investigated. Heat transport properties in silicon films have been studied through three different techniques: a semi-analytical method based upon the Kinetic Theory, a deterministic solution of the Boltzmann Transfer Equation (BTE) through the Discrete Ordinate Method and a statistical handling of the BTE by means of Monte Carlo Method. Each technique requires a model for the bulk material dispersion curves and the collision times of the different scattering processes. The three techniques have been validated through their correct prediction of silicon bulk thermal conductivity. Comparisons with in-plane thermal conductivity calculations and measurements have been also discussed. Thus, the cross-plane thermal conduction properties have been predicted. The expected temperature and thickness variations of the thermal conduction properties have been observed: the cross-plane thermal conduction appears to be less efficient than the in-plane thermal conduction, which proves that a significant anisotropy exists.