An anisotropic full Brillouin zone model for the three dimensional phonon Boltzmann transport equation
An anisotropic full Brillouin zone model for the three dimensional phonon Boltzmann transport equation
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DOI：
10.1016/j.cma.2017.01.010
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发表时间：
2017-04
影响因子：
7.2
通讯作者：
Francis G. VanGessel;P. Chung
中科院分区：
文献类型：
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作者：
Francis G. VanGessel;P. Chung
本文提出了一种通过求解三维声子玻尔兹曼输运方程（BTE）来模拟微尺度热输运的模型和数值方法。在小区域中，完整的布里渊区具有有限数量的振动模式，如由Born von-Karman边界条件确定的。由于这种离散性，本方法允许一般的晶体各向异性和有限维效应，自然允许各向异性的热传输和能量流。该方法示出和验证使用各向同性流的解析解。在此基础上，对立方晶体材料的鳍式场效应晶体管的温度和能量进行了数值计算。计算了各向异性导热系数及其对温度场的影响。各向同性的解决方案和各向异性模型之间的差异被证明是显着的温度差异约10%。在较大的尺度下，散射效应占主导地位，解决方案的差异变得更小，宏观各向同性是由于材料的立方对称性恢复。
A model and associated numerical method are presented for simulation of heat transport at the microscale via the solution of the three dimensional phonon Boltzmann Transport Equation (BTE). In small domains, the full Brillouin Zone has a finite number of vibrational modes, as determined by Born von-Karman boundary conditions. As a result of this discreteness, the present method allows for general crystal anisotropy and finite dimensional effects that naturally permit anisotropic thermal transport and energy flow. The method is shown and verified using analytical solutions for isotropic flows. Then numerical experiments are performed to calculate temperature and energy in a fin field effect transistor made of a cubic crystalline material. The anisotropic thermal conductivity and the consequences on thermal fields are calculated. The differences between an isotropic solution and the anisotropic model are shown to be significant with differences in the temperatures approximately 10%. At larger scales, where scattering effects dominate, differences in the solutions become smaller and macroscopic isotropy is recovered due to the cubic symmetry of the material.