论文标题
基于悬浮膜设置的平面内电导率测量方法的数值建模
Numerical modeling of in-plane thermal conductivity measurement methods based on a suspended membrane setup
论文作者
论文摘要
已经进行了基于3D有限元方法（FEM）模拟和1D分析溶液的数值建模研究，以评估两种AC方法的能力，用于测量沉积在悬浮的Sinx Membrane Setup的背面的薄膜的平面内电导率。介电膜的顶部有两个平行的金属条。一条带（S1）既用作加热器又是温度计，而另一条（S2）仅充当温度计。对于修改的相移（MPS）方法，至关重要的是从S2上温度振荡的相移中提取平面内热扩散率。发现执行数据拟合的频率窗口变得更窄，因为复合膜的平面内热扩散率（$ {a {α_ {\ parallel，c}} $）主要是由于低频区域中半企业宽度假设的失败。为了确保该方法的有效性，对于所考虑的特定膜尺寸（1 $ \ tims $ 1 mm2），$ {α_ {\ parallel，c}} $的上限不应超过〜1.8 $ \ times $ 10-5 m2 s-1。另一方面，受朱最近提出的修改后的Angstrom方法的启发，我们建议一种新的数据还原方法，它利用S1和S2的相移以及S1上的振幅。基于仿真结果，预计与三个可观测值相关的非理想性至少可以部分取消。对于典型的标本膜的平面导热率范围从0.84 W m-1 K-1到50 W m-1 K-1，此处提出的方法产生的理论测量不确定性小于5％。
A numerical modeling study based on 3D finite element method (FEM) simulation and 1D analytical solutions has been carried out to evaluate the capabilities of two ac methods for measuring in-plane thermal conductivity of thin film deposited on the back of a suspended SiNx membrane setup. Two parallel metal strips are present on the top of the dielectric membrane. One strip (S1) serves as both heater and thermometer, while another one (S2) acts as thermometer only. For a modified phase shift (MPS) method, it is crucial to extract the in-plane thermal diffusivity from the phase shift of the temperature oscillation on S2. It was found that the frequency window for carrying out the data fitting became narrower as the in-plane thermal diffusivity of the composite membrane (${α_{\parallel ,C}}$) increased, primarily due to the failure of the semi-infinite width assumption in the low frequency region. To ensure the validity of the method, the upper limit of ${α_{\parallel ,C}}$ should not exceed ~1.8$ \times $10-5 m2 s-1 for the specific membrane dimension under consideration (1$\times $1 mm2). On the other hand, inspired by a modified Angstrom method proposed by Zhu recently, we suggest a new data reduction methodology which takes advantage of the phase shift on both S1 and S2 as well as the amplitude on S1. Based on the simulation results, it is expected that the non-ideality associated with the three observables may be at least partially cancelled out.Therefore, the frequency window selection for carrying out the data fitting is not sensitive to the magnitude of ${α_{\parallel ,C}}$. For typical specimen films whose in-plane thermal conductivity ranges from 0.84 W m-1 K-1 to 50 W m-1 K-1, the method proposed here yields a theoretical measurement uncertainty of less than 5%.
