On the Determination of Thermal Conductivity From Frequency Domain Thermoreflectance Experiments
On the Determination of Thermal Conductivity From Frequency Domain Thermoreflectance Experiments
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DOI：
10.1115/1.4052655
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发表时间：
2022-01-01
影响因子：
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通讯作者：
Mazumder, Sandip
中科院分区：
文献类型：
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作者：
Saurav, Siddharth;Mazumder, Sandip
对傅里叶和双曲热传导方程进行数值求解，以模拟频域热反射 (FDTR) 实验。数值解决方案可以隔离泵浦和探测激光光斑尺寸效应并使用真实的边界条件。在时域中求解方程，并针对 200 kHz-200 MHz 的调制频率范围计算换能器温度（在探测激光点上平均）和调制泵浦激光信号之间的相位滞后。数值计算表明，提取的热导率值对泵浦和探测激光光斑尺寸都很敏感，而解析解（基于汉克尔变换）无法隔离这两种效应。然而，对于相同的有效（组合）光斑尺寸，这两种解决方案非常一致。如果基底（计算域）足够大，则发现远场边界条件对计算的相位滞后没有影响。发现换能器和基底之间的界面电导对提取的热导率有一定影响。对于所研究的特定情况，双曲热传导方程产生的结果与傅里叶热传导方程几乎相同。本研究中考虑的硅基板的数值提取热导率值（最佳拟合）约为 82-108 W/m/K，具体取决于所使用的泵浦和探测激光光斑尺寸。
The Fourier and the hyperbolic heat conduction equations were solved numerically to simulate a frequency-domain thermoreflectance (FDTR) experiment. Numerical solutions enable isolation of pump and probe laser spot size effects and use of realistic boundary conditions. The equations were solved in time domain and the phase lag between the temperature of the transducer (averaged over the probe laser spot) and the modulated pump laser signal was computed for a modulation frequency range of 200 kHz-200 MHz. Numerical calculations showed that extracted values of the thermal conductivity are sensitive to both the pump and probe laser spot sizes, while analytical solutions (based on Hankel transform) cannot isolate the two effects. However, for the same effective (combined) spot size, the two solutions are found to be in excellent agreement. If the substrate (computational domain) is sufficiently large, the far-field boundary conditions were found to have no effect on the computed phase lag. The interface conductance between the transducer and the substrate was found to have some effect on the extracted thermal conductivity. The hyperbolic heat conduction equation yielded almost the same results as the Fourier heat conduction equation for the particular case studied. The numerically extracted thermal conductivity value (best fit) for the silicon substrate considered in this study was found to be about 82-108 W/m/K, depending on the pump and probe laser spot sizes used.