Solving Nongray Boltzmann Transport Equation in Gallium Nitride
Solving Nongray Boltzmann Transport Equation in Gallium Nitride
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DOI：
10.1115/1.4036616
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发表时间：
2017-10
影响因子：
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通讯作者：
A. Vallabhaneni;Liang Chen;M. Gupta;Satish Kumar
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文献类型：
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作者：
A. Vallabhaneni;Liang Chen;M. Gupta;Satish Kumar
一些研究已经证实，扩散傅立叶模型是不足以模拟在亚微米长度尺度的热传输。因此，玻尔兹曼输运方程（BTE）被用来改善电子器件中的热预测，其中弹道效应占主导地位。在这项工作中，我们研究了稳态热输运在氮化镓（GaN）薄膜使用的BTE。采用第一性原理-密度泛函理论（DFT）计算了GaN的声子性质。尽管并行化，解决BTE是相当昂贵的，需要大量的计算资源。在这里，我们提出了两种方法来加快解决BTE的过程中没有显着损失的温度预测的准确性。第一种方法是在远离热点的地方使用傅立叶模型，在那里弹道效应可以忽略不计，然后将其与热点附近区域的BTE模型耦合。第二种方法是通过使用自适应模型来加速BTE模型本身，该自适应模型更快地求解，因为具有低Knudsen数的声子模式的BTE被类似傅立叶方程取代。这两种方法都涉及到基于声子平均自由程（mfp）来选择截止参数。对于在本工作中考虑的GaN基器件，第一种方法减少了约70%的计算时间，而自适应方法减少了60%的情况下，在整个域中解决全BTE相比。使用这两种方法一起减少了超过85%的总计算时间。这里提出的方法是通用的，可以用于任何材料。这些方法是相当有价值的多尺度热建模，在解决器件级问题，以更快的速度，而没有显着的准确性损失。[DOI 10.1115/1.4036616]
Several studies have validated that diffusive Fourier model is inadequate to model thermal transport at submicron length scales. Hence, Boltzmann transport equation (BTE) is being utilized to improve thermal predictions in electronic devices, where ballistic effects dominate. In this work, we investigated the steady-state thermal transport in a gallium nitride (GaN) film using the BTE. The phonon properties of GaN for BTE simulations are calculated from first principles—density functional theory (DFT). Despite parallelization, solving the BTE is quite expensive and requires significant computational resources. Here, we propose two methods to accelerate the process of solving the BTE without significant loss of accuracy in temperature prediction. The first one is to use the Fourier model away from the hot-spot in the device where ballistic effects can be neglected and then couple it with a BTE model for the region close to hot-spot. The second method is to accelerate the BTE model itself by using an adaptive model which is faster to solve as BTE for phonon modes with low Knudsen number is replaced with a Fourier like equation. Both these methods involve choosing a cutoff parameter based on the phonon mean free path (mfp). For a GaN-based device considered in the present work, the first method decreases the computational time by about 70%, whereas the adaptive method reduces it by 60% compared to the case where full BTE is solved across the entire domain. Using both the methods together reduces the overall computational time by more than 85%. The methods proposed here are general and can be used for any material. These approaches are quite valuable for multiscale thermal modeling in solving device level problems at a faster pace without a significant loss of accuracy. [DOI: 10.1115/1.4036616]