Equivalence of the equilibrium and the nonequilibrium molecular dynamics methods for thermal conductivity calculations: From bulk to nanowire silicon

TL;DR

This paper demonstrates that equilibrium and nonequilibrium molecular dynamics methods produce equivalent results for calculating thermal conductivity across bulk, 2D, and 1D silicon structures, resolving previous inconsistencies.

Contribution

It provides a systematic comparison and establishes the quantitative equivalence of EMD and NEMD methods for diverse silicon allotropes, including bulk, silicene, and nanowires.

Findings

EMD and NEMD methods agree quantitatively for all studied systems.

The effective length in EMD correlates with the system size in NEMD.

The methods are interchangeable for thermal conductivity calculations in silicon.

Abstract

Molecular dynamics simulations play an important role in studying heat transport in complex materials. The lattice thermal conductivity can be computed either using the Green-Kubo formula in equilibrium MD (EMD) simulations or using Fourier's law in nonequilibrium MD (NEMD) simulations. These two methods have not been systematically compared for materials with different dimensions and inconsistencies between them have been occasionally reported in the literature. Here we give an in-depth comparison of them in terms of heat transport in three allotropes of Si: three dimensional bulk silicon, two-dimensional silicene, and quasi-one-dimensional silicon nanowire. By multiplying the correlation time in the Green-Kubo formula with an appropriate effective group velocity, we can express the running thermal conductivity in the EMD method as a function of an effective length and directly compare it with the length-dependent thermal conductivity in the NEMD method. We find that the two methods quantitatively agree with each other for all the systems studied, firmly establishing their equivalence in computing thermal conductivity.