  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.
