Chapter 4 - Computational method of thermal transport property

Abstract

Thermal transport is external phenomenon of lattice vibration, specifically, characterized by the phonon transport behaviors. Macroscopically, thermal transport means the magnitude of heat flux when a conductor is placed in a temperature gradient. It obeys the Fourier's law, which has been widely used in many applications for bulk materials. According to the Fourier's law, the thermal conductivity is only related to the material properties independent of the sample size. But the validity of Fourier's law has been questioned for low-dimensional materials. The divergent thermal conductivity scales with sample length L, k∼Lβ was obtained for one-dimensional and quasi–one-dimensional nanostructures.1 For the single-wall carbon nanotube at room temperature, β is 0.3–0.4.2 For two-dimensional nanostructure, the thermal conductivity scales logarithmically with system size. The logarithmic relation was observed for graphene when the length is up to 1mm.3 Those results indicated that the Fourier's law is unfit to analyze the thermal transport of one-dimensional and two-dimensional nanostructures. And then, different methods had been developed to calculate the thermal transport properties of low-dimensional materials, including phonon Boltzmann transport equation, molecular dynamics (MD) simulations, and nonequilibrium Green's function (NEGF), etc. Different methods were used to study specific thermal transport problems of different range of scales. In this chapter, we present MD and the NEGF method for the evaluation of thermal conduction properties carried by phonons.