Molecular-dynamics simulation of thermal conductivity of silicon crystals

We investigate the thermal conductivity of bulk silicon crystals based on molecular-dynamics (MD) simulations. If it is taken that the system size must be larger than the phonon mean free path, several hundreds of millions of atoms must be computed for crystals with large thermal conductivity values such as Si. We demonstrate in this work that the thermal conductivity of Si crystals can be simulated by MD techniques using several thousands of atoms with periodic boundary conditions. We identify that the key issues generating size artifacts in small molecular-dynamics systems are the frequency cutoff imposed by the simulation domain length and the correlation artifacts caused by the periodic boundary conditions. Our method relies on the spectral Green-Kubo formulation combined with a model-based extrapolation. The obtained thermal conductivity results are in good agreement with the reference data. Both the Green-Kubo formulation and the Boltzmann transport equation lead to the prediction that the thermal conductivities of bulk crystals depend on the frequency of the thermal disturbance. This result has important implications for high-frequency electronic devices.