Towards more accurate molecular dynamics calculation of thermal conductivity: Case study of GaN bulk crystals
Towards more accurate molecular dynamics calculation of thermal conductivity: Case study of GaN bulk crystals
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DOI：
10.1103/physrevb.79.115201
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发表时间：
2009-03
影响因子：
3.7
通讯作者：
Xiaowang Zhou;Sylvie Aubry;Reese E. Jones;Abraham Greenstein;P. Schelling
中科院分区：
文献类型：
--
作者：
Xiaowang Zhou;Sylvie Aubry;Reese E. Jones;Abraham Greenstein;P. Schelling
用分子动力学模拟方法计算不同体系的热导率，文献之间存在显著差异。在某些情况下，发现了非物理结果，例如负导热系数。以氮化镓为例，采用直接非平衡法，对结果进行了广泛的分子动力学模拟和蒙特卡罗分析，以量化分子动力学方法的不确定性水平，并确定能够产生足够精确的导热系数计算的条件。我们发现计算误差主要是由统计热波动引起的。将结果外推到无限大系统的极限往往会放大误差，偶尔会导致非物理结果。通过在样本长度范围内使用适当选择的系统执行较长时间的平均，可以减少批量估计中的误差。如果与每个样品长度相关的电导率估计误差保持在一定阈值以下，则获得非物理体积值的可能性变得微不足道。利用这里开发的蒙特卡罗方法，我们确定了用直接法获得的体热导率的概率分布。我们还观察到一种非线性效应，它可能成为重大误差的来源。对于这里给出的非常准确的结果，我们预测[0001]GaN的导热系数在300 K时为$185\text{}\text{W}/\text{K}\text{m}$，在500 K时为$102\text{}\text{W}/\text{K}\text{m}$，在800 K时为$74\text{}\text{W}/\text{K}\text{}\text{m}$。利用工作中获得的见解，我们在300 K， 500 K和800 K下，分别实现了体积（无限样本长度）GaN导热系数小于$10\text{}\text{W}/\text{K}\text{m}$, $5\text{}\text{W}/\text{K}\text{m}$和$15\text{}\text{W}/\text{K}\text{m}$的相应误差水平（标准差）。
Significant differences exist among literature for thermal conductivity of various systems computed using molecular dynamics simulation. In some cases, unphysical results, for example, negative thermal conductivity, have been found. Using GaN as an example case and the direct nonequilibrium method, extensive molecular dynamics simulations and Monte Carlo analysis of the results have been carried out to quantify the uncertainty level of the molecular dynamics methods and to identify the conditions that can yield sufficiently accurate calculations of thermal conductivity. We found that the errors of the calculations are mainly due to the statistical thermal fluctuations. Extrapolating results to the limit of an infinite-size system tend to magnify the errors and occasionally lead to unphysical results. The error in bulk estimates can be reduced by performing longer time averages using properly selected systems over a range of sample lengths. If the errors in the conductivity estimates associated with each of the sample lengths are kept below a certain threshold, the likelihood of obtaining unphysical bulk values becomes insignificant. Using a Monte Carlo approach developed here, we have determined the probability distributions for the bulk thermal conductivities obtained using the direct method. We also have observed a nonlinear effect that can become a source of significant errors. For the extremely accurate results presented here, we predict a [0001] GaN thermal conductivity of $185\text{ }\text{W}/\text{K}\text{ }\text{m}$ at 300 K, $102\text{ }\text{W}/\text{K}\text{ }\text{m}$ at 500 K, and $74\text{ }\text{W}/\text{K}\text{ }\text{m}$ at 800 K. Using the insights obtained in the work, we have achieved a corresponding error level (standard deviation) for the bulk (infinite sample length) GaN thermal conductivity of less than $10\text{ }\text{W}/\text{K}\text{ }\text{m}$, $5\text{ }\text{W}/\text{K}\text{ }\text{m}$, and $15\text{ }\text{W}/\text{K}\text{ }\text{m}$ at 300 K, 500 K, and 800 K, respectively.