Thermal energy transport model for macro-to-nanograin polycrystalline semiconductors

Understanding thermal energy transport in polycrystalline semiconductors is important for the efficiency of electronic devices and thermoelectric materials. In this paper, we study the reduction of the transport of thermal energy in polycrystalline semiconductors generated by the shortening of the phonon mean free paths due to grain boundary scattering. We calculate the reduction of the thermal conductivity in polycrystals, from macro-to-nanograin sizes and different temperatures, by using a theoretical approach based on the kinetic theory of transport processes. The approach involves an exact expression for the reduction of the phonon mean free paths that includes their directional, frequency, and polarization dependence. By comparing the results of our model for the reduced thermal conductivity of the grain against the thermal boundary Kapitza resistance calculated by others, we find that the thermal conductivity of polycrystalline Si and SiC materials is dominated by the reduced thermal conductivity of the grain. We also show that in order to accurately calculate the thermal conductivity, the proportion of heat transported by transverse and longitudinal phonons must be correctly taken into account. By using the model, we study grain boundary scattering effects on the reduction of the thermal conductivity of polycrystalline silicon and silicon carbide. The calculated results are compared with experiments at different temperatures and grain sizes without using free adjustable variables (e.g., defects concentration) or phenomenological formulas to account for the reduced thermal conductivity of the grain. (C) 2011 American Institute of Physics. [doi:10.1063/1.3665211]