具有任意几何形状的纳米级材料系统的频域热反射测量的数值拟合程序

R. Warzoha, Adam A. Wilson, Brian F. Donovan, A. Smith, N. Vu, Trent Perry, Longnan Li, N. Miljkovic, E. Getto
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引用次数: 2

摘要

在这项工作中,我们开发了一个数值拟合程序,用于提取具有非标准,非半无限几何形状的材料的多个热参数,使用频域热反射(FDTR)。数值拟合程序基于二维或三维有限元分析,允许包含非半无限边界条件,而非半无限边界条件在频域热扩散方程的解析解中不能考虑。我们通过将其与广泛文献中用于FDTR和半无限基材(SiO2, Al2O3和Si)导热系数的已知值的热扩散方程的解析解进行比较来验证拟合程序。然后,我们展示了它在蚀刻成具有泵浦光束半径的微柱时提取Si热特性的能力。具有圆形截面的硅微柱的实验测量提供和拟合使用数值拟合程序建立作为这项工作的一部分。同样地,我们表明,当几何形状明显偏离标准半无限情况时,解析解不适用于热性质的提取。这项工作对于测量具有任意几何形状的材料的热性能至关重要,包括超拉伸玻璃纤维和激光增益介质。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A numerical fitting routine for frequency-domain thermoreflectance measurements of nanoscale material systems having arbitrary geometries
In this work, we develop a numerical fitting routine to extract multiple thermal parameters using frequency-domain thermoreflectance (FDTR) for materials having non-standard, non-semi-infinite geometries. The numerical fitting routine is predicated on either a 2-D or 3-D finite element analysis that permits the inclusion of non semi-infinite boundary conditions, which can not be considered in the analytical solution to the heat diffusion equation in the frequency domain. We validate the fitting routine by comparing it to the analytical solution to the heat diffusion equation used within the wider literature for FDTR and known values of thermal conductivity for semi-infinite substrates (SiO2, Al2O3 and Si). We then demonstrate its capacity to extract the thermal properties of Si when etched into micropillars that have radii on the order of the pump beam. Experimental measurements of Si micropillars with circular cross-sections are provided and fit using the numerical fitting routine established as part of this work. Likewise, we show that the analytical solution is unsuitable for the extraction of thermal properties when the geometry deviates significantly from the standard semi-infinite case. This work is critical for measuring the thermal properties of materials having arbitrary geometries, including ultra-drawn glass fibers and laser gain media.
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