Cross-plane heat conduction in nanoporous silicon thin films by phonon Boltzmann transport equation and Monte Carlo simulations

Abstract

The study on the heat conduction in nanoporous silicon structures has drawn much attention due to their significance for developing highly-efficient thermoelectric materials. In the nanostructures whose characteristic lengths are comparable to the phonon mean free path (MFP), ballistic transport and boundary scattering will lead to the size-dependence of effective thermal conductivity. In the present work, the cross-plane thermal transport along the pore axial direction in nanoporous silicon thin films (i.e. silicon thin films crossed by nanoscale cylindrical channels) is investigated by using the phonon Boltzmann transport equation (BTE) and the Monte Carlo (MC) simulations. It is found that the effective thermal conductivity varies not only with the porosity but also with the film thickness and pore radius. The smaller the film thickness or the pore radius, the smaller is the effective thermal conductivity for a given porosity. An analytical model for the cross-plane effective thermal conductivity of nanoporous silicon thin films is obtained on the basis of the phonon BTE. The model can capture the size effects due to the film thickness and the pore radius simultaneously, and be reduced to the Fourier’s law based model for macroporous materials. Good agreements have been achieved between the present model and the MC simulations. Our model can be useful for predicting and controlling phonon transport for thermoelectric devices.