Thermal transport of nanocrystalline Si is of great importance for the application of thermoelectrics. A better understanding of the modal thermal conductivity of nanocrystalline Si will be expected to benefit the efficiency of thermoelectrics. In this work, the variance reduced Monte Carlo simulation with full band of phonon dispersion is applied to study the modal thermal conductivity of nanocrystalline Si. Importantly, the phonon modal transmissions across the grain boundaries which are modeled by the amorphous Si interface are calculated by the mode-resolved atomistic Greens function method. The predicted ratios of thermal conductivity of nanocrystalline Si to that of bulk Si agree well with that of the experimental measurements in a wide range of grain size. The thermal conductivity of nanocrystalline Si is decreased from 54 percent to 3 percent and the contribution of phonons with mean free path larger than the grain size increases from 30 percent to 96 percnet as the grain size decreases from 550 nm to 10 nm. This work demonstrates that the full band Monte Carlo simulation using phonon modal transmission by the mode-resolved atomistic Greens function method can capture the phonon transport picture in complex nanostructures, and therefore can provide guidance for designing high performance Si based thermoelectrics.
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