Abstract
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.
Highlights
Метод расчетаВ работе проводится вычисление эффективного коэффициента теплопроводности бинарной гетероструктуры — сверхрешетки
Calculation of the effective thermal conductivity of a superlattice based on the Boltzmann transport equation using first−principle calculations
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
Summary
В работе проводится вычисление эффективного коэффициента теплопроводности бинарной гетероструктуры — сверхрешетки. Из первопринципных расчетов требуется получить: кристаллическую структуру рассматриваемых материалов, гармонические и ангармонические силовые константы, диэлектрический тензор и тензор эффективных зарядов Борна; после чего, используя формулы (3)—(12) можно вычислить время релаксации τ0. В качестве примера приложения описанной техники рассмотрим расчет теплопроводности бинарной гетероструктуры GaAs/AlAs для различных периодов сверхрешетки. Более прямолинейный и точный подход заключается в экспериментальном установлении профиля распределения, что продемонстрировано в работе [19] для гетероструктуры InAs/GaAs. Рис. 1. Сравнение рассчитанного (BTE — Boltzmann Transport Equation) и экспериментально полученного в работе [23] эффективного коэффициента теплопроводности для различных периодов сверхрешетки GaAs/AlAs. Рис. 2. Расчет эффективного коэффициента теплопроводности для сверхрешетки GaAs/AlAs с периодом 10 × 10: а—в — выбранные профили концентрации AlAs в периоде сверхрешетки; г — уточненный результат для различных профилей распределения AlAs
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More From: Izvestiya Vysshikh Uchebnykh Zavedenii. Materialy Elektronnoi Tekhniki = Materials of Electronics Engineering
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