Fourier-like conduction and finite one-dimensional thermal conductivity in long silicon nanowires by approach-to-equilibrium molecular dynamics

The thermal conductivity of cylindrical and smooth silicon nanowires is systematically studied as a function of diameter and length by fully atomistic simulations. A transient thermal regime is created and monitored by molecular dynamics. This approach-to-equilibrium methodology, already proven to be very efficient for bulk systems, is here applied to nanowires of length up to 1.2 micron, and diameter in the range 1 to 14 nm. It is shown that the temperature profile along the nanowire axis and its temporal evolution comply with the heat equation. A one-dimensional thermal conductivity is extracted from the characteristic decay time according to the time-dependent solution of the heat equation. Like for the bulk using the same method, the thermal conductivity exhibits a length dependence due to the slowly growing cumulative distribution of the phonon mean free paths. Unlike the bulk, the infinite-length saturation of the conductivity value can be observed in our simulations, thanks to a reduction of the phonon mean free path in the nanowires, estimated to be a few hundred nanometers. A finite thermal conductivity can be extracted for each diameter, and no divergence at long length is observed.