In this work, we calculate the effective thermal conductivity coefficient for a binary semiconductor heterostructure using the GaAs/AlAs superlattice as an example. Different periods of layers and different ambient temperatures are considered. At the scale under consideration, the use of models based on the Fourier law is very limited, since they do not take into account the quantum-mechanical properties of materials, which gives a strong discrepancy with experimental data. On the other hand, the use of molecular dynamics methods allows us to obtain accurate solutions, but they are significantly more demanding on computing resources and also require solving a non-trivial problem of potential selection. When considering nanostructures, good results were shown by methods based on the solution of the Boltzmann transport equation for phonons; they allow one to obtain a fairly accurate solution, while having less computational complexity than molecular dynamics methods. To calculate the thermal conductivity coefficient, a modal suppression model is used that approximates the solution of the Boltzmann transport equation for phonons. The dispersion parameters and phonon scattering parameters are obtained from first-principle calculations. The work takes into account 2-phonon (associated with isotopic disorder and barriers) and 3-phonon scattering processes. To increase the accuracy of calculations, the non-digital profile of the distribution of materials among the layers of the superlattice is taken into account. The obtained results are compared with experimental data showing good agreement.
When considering the thermal processes of multilayer nanostructures, a significant part of the energy is dissipated at the boundaries of the layers; to take this factor into account, the Kapitza resistance is used in the simulation. In this study, we calculate the thermal resistance at the Si/SiO2 interface (alpha-quartz) structures for the temperature range up to 567 K. The calculations are carried out based on the acoustic and diffuse mismatch models. The results obtained, in particular, can be used in constructing models of heat transfer in microelectronics.
Abstract. The article discusses the calculation of the temperature regime in nanoscale AlAs/GaAs binary heterostructures. When modeling heat transfer in nanocomposites, it is important to take into account that heat dissipation in multilayer structures with layer sizes of the order of the mean free path of energy carriers (phonons and electrons) occurs not at the lattice, but at the layer boundaries (interfaces). In this regard, the use of classical numerical models based on the Fourier law is limited, because it gives significant errors. To obtain more accurate results, we used a model in which the heat distribution was assumed to be constant inside the layer, while the temperature was stepwise changed at the interfaces of the layers. A hybrid approach was used for the calculation: a finite−difference method with an implicit scheme for time approximation and a mesh−free model based on a set of radial basis functions for spatial approximation. The calculation of the parameters of the bases was carried out through the solution of the systems of linear algebraic equations. In this case, only weights of neuroelements were selected, and the centers and «widths» were fixed. As an approximator, a set of frequently used basic functions was considered. To increase the speed of calculations, the algorithm was parallelized. Calculation times were measured to estimate the performance gains using the parallel implementation of the method.
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