Numerical Study of Thermal Conductivity Reduction in Nanolayered Si-Ge Structures by Solving the Equation of Phonon Radiative Transfer

Abstract

Materials with low thermal conductivity, high electrical conductivity, and high Seebeck coefficient are required for high efficiency solid-state energy conversion. Although semiconductors are the best thermoelectric materials, they rarely have the desired properties. Nanostructures such as superlattices, quantum wires, and quantum dots provide novel methods to improve the solid-state energy conversion efficiency through electron and phonon transport engineering. In this paper a semiconducting superlattice consisting of periodic nano layers of silicon and germanium has been studied. Due to nano scale effects, conductive heat transfer does not satisfy the Fourier's law of thermal conduction, and the equation of phonon radiative transfer has been solved instead. A computational method similar to Discrete Ordinate Method in thermal radiation was implemented, and the equations were solved numerically. The results show that the thermal conductivity of the nano structure is much lower than the macro structures with the same aspect ratio. It was also noticed that with a constant ratio of layers' thicknesses, more reduction in layers' thicknesses causes more temperature jump at the interfaces and consequently more reduction in the effective thermal conductivity, that finally improves the thermoelectric properties. It was also shown that the effective thermal conductivity depends on the density of interfaces per unit length of the superlattice, when the heat flow direction is perpendicular to the layers.

Heat transfer modelling in the Si–Ge nanoparticle composites by numerical solution of the equation of phonon radiative transfer

“…The method implemented for the numerical solution of the EPRT [25] is based on the finite difference method and is similar to the discrete ordinate method in thermal radiation. A detailed computer programming is applied to extract the results in 25 different cases.…”