Ab initio Calculation of the Effective Thermal Conductivity Coefficient of a Superlattice Using the Boltzmann Transport Equation

Abstract

The effective thermal conductivity coefficient of a binary semiconductor heterostructure is calculated by an example of the GaAs/AlAs superlattice at different layer periods and different ambient temperatures. The applicability of the Fourier-law models is strongly limited on the investigated scale, since they do not take into account the quantum-mechanical properties of materials, which leads to a large deviation from the experimental data. However, the use of molecular dynamics methods allows us to obtain accurate solutions; however, these methods are much more demanding of computing resources and require a nontrivial potential selection problem to be solved. In the investigations of the nanostructures, good results are obtained using the methods based on solving the Boltzmann transport equation for phonons; they make it possible to obtain a fairly accurate solution at a lower computational complexity compared with the molecular dynamics methods. To calculate the thermal conductivity coefficient, a modal suppression model is used, which approximates the solution of the Boltzmann transport equation for phonons. The dispersion and phonon scattering parameters are obtained using ab initio calculations. The two-phonon processes related to the isotopic disorder and the barrier three-phonon scattering processes are taken into account. To increase the accuracy of the calculations, the inhomogeneity of the distribution of materials over the superlattice layers is taken into account. A comparison of the results obtained with the experimental data shows their close agreement.