arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2012.10604physics.app-ph
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基于悬膜装置的面内导热系数测量方法的数值模拟

Numerical modeling of in-plane thermal conductivity measurement methods based on a suspended membrane setup

Hanfu Wang, Yanjun Guo, Kaiwu Peng, Weiguo Chu, Guangming Chen

摘要:

基于3D有限元法(FEM)模拟和1D解析解的数值模拟研究已经进行了评估的能力的两个交流方法测量面内热导率的薄膜沉积在背面的悬浮氮化硅膜设置。两个平行的金属条存在于电介质膜的顶部上。一个条带(S1)既用作加热器又用作温度计,而另一个条带(S2)仅用作温度计。对于改进的相移法(MPS),从S2上温度振荡的相移中提取面内热扩散率是至关重要的。结果发现,进行数据拟合的频率窗口变得更窄的面内的复合膜(${α_{\parallel ,C}}$)的热扩散率的增加,主要是由于在低频区域的半无限宽度假设的失败。为确保方法的有效性,对于所考虑的特定膜尺寸(1 $\times $ 1 mm 2),${α_{\parallel ,C}}$的上限不应超过约1.8 $ \times $ 10-5 m2 s-1。另一方面,受Zhu最近提出的一种改进的Angstrom方法的启发,我们提出了一种新的数据简化方法,该方法利用了S1和S2上的相移以及S1上的幅度。基于仿真结果,可以预期与三个观测量相关联的非理想性可以至少部分地被抵消,因此,用于执行数据拟合的频率窗口选择对${α_{\parallel ,C}}$的幅度不敏感。对于典型的试样膜,其面内热导率范围从0.84 W m-1 K-1至50 W m-1 K-1,这里提出的方法产生小于5%的理论测量不确定度。

英文摘要:

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%.

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