论文标题

具有任意几何形状的纳米级材料系统的频率域热反射测量值的数值拟合程序

A Numerical Fitting Routine for Frequency-domain Thermoreflectance Measurements of Nanoscale Material Systems having Arbitrary Geometries

论文作者

Warzoha, Ronald J., Wilson, Adam A., Donovan, Brian F., Smith, Andrew N., Vu, Nicholas T., Perry, Trent, Li, Longnan, Miljkovic, Nenad, Getto, Elizabeth

论文摘要

在这项工作中,我们开发了一种数值拟合程序,以使用频域热素感域(FDTR)提取多个热参数,用于非标准,非符号侵入的几何形状。数值拟合程序是基于2-D有限元分析,该分析允许包含非半无限边界条件,这在频域中的热扩散方程的分析解决方案中无法考虑。我们通过将拟合程序与分析溶液与较宽的文献中用于FDTR中使用的热扩散方程进行比较来验证拟合程序,并将其用于FDTR和半无限底物的热导率的已知值值(SIO2,AL2O3和SI)。然后,我们证明了其在将泵束序列的半径蚀刻到具有半径的微柱中时提取Si的热性能的能力。提供了具有圆形横截面的Si微柱的实验测量,并使用作为这项工作的一部分建立的数值拟合程序进行拟合。同样,我们表明,当几何形状显着偏离标准的半无限情况时,分析解决方案不适合提取热性能。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,包括超吸玻璃纤维和激光增益培养基。

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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