Thermal conductivity modeling of periodic porous silicon with aligned cylindrical pores

We present a frequency-dependent phonon Boltzmann transport equation (BTE) solver to study phonon transport in arbitrary geometries. For composite and porous structures, most simulations adopted either gray-medium approximation or geometric simplification in phonon BTE model. To show the importance of considering the frequency-dependent phonon transport, transverse thermal transport in periodic porous silicon (PS) with aligned square-cylindrical pores is investigated by the present frequency-dependent phonon BTE solver and gray-medium phonon BTE solver. It is found that phonon size effect is underestimated by adopting the gray-medium approximation in sub-micron scale. To demonstrate geometry effect, the frequency-dependent phonon BTE solver is applied to study transverse thermal transport in the PS with square-cylindrical and circular-cylindrical pores for various characteristic sizes and porosities. The pore shape is found to make great difference to the thermal conductivity of the PS when the characteristic size is decreased or the porosity is increased. Our results indicate the importance of considering the frequency dependence of phonon transport as well as the exact geometry of material structure in the analysis of micro-and nanostructured materials. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4730962]