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.

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Due to different interface densities and arrangements, the compacted type nanocomposites may yield even lower thermal conductivity than embedded type nanocomposites. In this paper, the phonon transport and thermal conductivity in compacted type nanocomposites ͑nanowires and nanoparticles͒ are investigated using a deterministic phonon Boltzmann transport equation solver. The effects of interface density and characteristic size on the phonon energy transport in nanocomposites are studied. It is found that the silicon-germanium compacted nanoparticle composites can have lower value of thermal conductivity than that of compacted nanowire composites under the same characteristic size ͑21.6% lower when the characteristic size is 3 nm͒.

Articles you may be interested inLattice thermal conductivity of crystalline and amorphous silicon with and without isotopic effects from the ballistic to diffusive thermal transport regime A phonon Boltzmann equation solver using multiblock-structured grid system is developed and applied to study transverse thermal transport in silicon-germanium circular-wire nanocomposite ͑silicon nanowires embedded in germanium host matrix͒. Past studies usually assume geometric simplification for the circular-wire nanocomposite, so the heat transfer is actually modeled in a square-wire nanocomposite. To demonstrate geometry effect, phonon transport in both the circular-wire and square-wire nanocomposites are investigated with various wire spacings, volume fractions, and dimensions. In ballistic phonon transport, due to the smoothness of circular shape, the circular wire imposes less thermal resistance than the square wire. Nevertheless, in the geometric simplification, the wire spacing of the square-wire nanocomposite is larger than that of the circular-wire nanocomposite. The usual geometric simplification can overestimate the thermal conductivity of the circular-wire nanocomposite. The obtained results can provide essential information for the development of bulk-nanostructured thermoelectric devices.

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