Thermal conductivity modeling of micro- and nanoporous silicon

This study aims at developing an approximate model to predict the effective thermal conductivity of porous silicon at both micro- and nano- scales. The model accounts for different transport mechanisms and reduces to the Fourier's law and phonon radiative transport expression in the diffusive and ballistic limits respectively. The effects of the pore size, the pore shape (square, rectangular, and triangular cylinders), and the porosity on the thermal conductivity are all taken into consideration. In particular, the geometrical effect is addressed by introducing the geometry-dependent view factor and porosity function. The accuracy of the proposed model is confirmed by comparing its predictions with the Monte Carlo simulations for two pore sizes, 100 nm and 500 nm, and a porosity ranging between 0.06 and 0.31. In addition, the geometric effect on the heat transport is also confirmed, which is found more conspicuous in the ballistic limit.