Phonon transport modeling using Boltzmann transport equation with anisotropic relaxation times
Phonon transport modeling using Boltzmann transport equation with anisotropic relaxation times
复制标题
使用具有各向异性弛豫时间的玻尔兹曼输运方程进行声子输运建模
DOI：
10.1115/1.4006169
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发表时间：
2012
影响因子：
--
通讯作者：
J. Murthy
中科院分区：
文献类型：
--
作者：
C. Ni;J. Murthy
基于声子玻尔兹曼输运方程（BTE），利用各向异性弛豫时间建立了亚微米热输运模型。一个先前发表的模型，全散射模型，由王开发，直接计算三声子散射相互作用，通过强制执行能量和动量守恒。然而，它是计算上非常昂贵的，因为它需要在迭代数值求解过程中的散射相互作用的数百万的评价。各向异性弛豫时间模型采用单模弛豫时间，但弛豫时间是从满足守恒规则的三声子相互作用的详细考虑中推导出来的，并且是波矢的函数。由此产生的模型是显着较便宜的全散射模型，但纳入方向和色散行为。模型发展中的一个关键问题是三声子正常（N）散射过程的作用。Callaway之后，修改了整体弛豫速率，以包括由于N过程引起的声子分布函数的偏移。这样得到的弛豫时间与亨利和陈从平衡分子动力学模拟中提取的数据进行了比较。通过将体硅和硅薄膜的热导率预测值与实验测量值进行比较，验证了各向异性弛豫时间声子BTE模型的正确性。然后，该模型用于模拟硅金属氧化物半导体场效应晶体管（MOSFET）中的热输运，并导致接近全散射模型的结果，但使用更少的计算时间。
A sub-micron thermal transport model based on the phonon Boltzmann transport equation (BTE) is developed using anisotropic relaxation times. A previously-published model, the full-scattering model, developed by Wang, directly computes three-phonon scattering interactions by enforcing energy and momentum conservation. However, it is computationally very expensive because it requires the evaluation of millions of scattering interactions during the iterative numerical solution procedure. The anisotropic relaxation time model employs a single-mode relaxation time, but the relaxation time is derived from detailed consideration of three-phonon interactions satisfying conservation rules, and is a function of wave vector. The resulting model is significantly less expensive than the full-scattering model, but incorporates directional and dispersion behavior. A critical issue in the model development is the role of three-phonon normal (N) scattering processes. Following Callaway, the overall relaxation rate is modified to include the shift in the phonon distribution function due to N processes. The relaxation times so obtained are compared with the data extracted from equilibrium molecular dynamics simulations by Henry and Chen. The anisotropic relaxation time phonon BTE model is validated by comparing the predicted thermal conductivities of bulk silicon and silicon thin films with experimental measurements. The model is then used for simulating thermal transport in a silicon metal-oxide-semiconductor field effect transistor (MOSFET) and leads to results close to the full-scattering model, but uses much less computation time.