Calculation of Heat Transfer in Nanosized Heterostructures

Abstract

We calculate the temperature regime in nanosized AlAs/GaAs binary heterostructures. When modeling the heat transfer in nanocomposites, it is important to take into account that heat dissipation in multilayer structures with the size of layers of the order of the mean free path of the energy carriers (phonons and electrons) occurs not in the lattice but at the boundaries (interfaces) of the layers. In this regard, the use of classical numerical models based on the Fourier law is limited, causing significant errors. To obtain more accurate results, we use a model in which the heat distribution is assumed to be constant inside the layer, and the temperature changes stepwise at the boundaries of the layers. A hybrid approach is used for these calculations: the finite-difference method with an implicit time approximation scheme and a mesh-free model based on a set of radial-basis functions for the spatial approximation. The parameters of the bases are calculated by solving the systems of linear algebraic equations. In this case, only the weights of neuroelements with fixed centers and widths are chosen. As approximators, the set of frequently used basis functions is considered. To increase the speed of the calculations, the algorithm is parallelized. The computation time is evaluated to assess the performance gain with the use of the parallel implementation of the method.