Comparison of molecular dynamics methods and interatomic potentials for calculating the thermal conductivity of silicon.

We compare the molecular dynamics Green-Kubo and direct methods for calculating thermal conductivity κ, using as a test case crystalline silicon at temperatures T in the range 500-1000 K (classical regime). We pay careful attention to the convergence with respect to simulation size and duration and to the procedures used to fit the simulation data. We show that in the Green-Kubo method the heat current autocorrelation function is characterized by three decay processes, of which the slowest lasts several tens of picoseconds so that convergence requires several tens of nanoseconds of data. Using the Stillinger-Weber potential we find excellent agreement between the two methods. We also use the direct method to calculate κ(T) for the Tersoff potential and find that the magnitude and the temperature-dependence are different for the two potentials and that neither potential agrees with experimental data. We argue that this implies that using the Stillinger-Weber or Tersoff potentials to predict trends in kappa as some system parameter is varied may yield results which are specific to the potential but not intrinsic to Si.