Simultaneous Measurement of Thickness and Group Refractive Index Based on Differential White Light Interferometry
Simultaneous Measurement of Thickness and Group Refractive Index Based on Differential White Light Interferometry
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DOI：
10.1109/tim.2023.3265747
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发表时间：
2023
影响因子：
5.6
通讯作者：
Xu Lu;Xinkai Wang;Yunlong Zhu;Yonggui Yuan;Fanyang Dang;Yao Zhu;Zhangjun Yu;Jun Yang
中科院分区：
文献类型：
--
作者：
Xu Lu;Xinkai Wang;Yunlong Zhu;Yonggui Yuan;Fanyang Dang;Yao Zhu;Zhangjun Yu;Jun Yang
厚度和折射率的同时测量是高端制造中重要的质量控制方案。然而，大范围厚度的精确测量在技术上仍然是困难的。本文提出了一种利用差分白色光干涉法同时测量薄膜厚度和群折射率的高精度方法。利用高动态范围的双向白色光干涉仪，可以同时获得样品两侧的光路。我们评估所提出的方法的性能，通过测量三种不同材料的试样，不同的厚度范围从200到2000\ \mu \text{m}$。测量结果与标称厚度吻合良好，厚度和群折射率的重复测量标准偏差分别为0. 009 μ m和1. 63 × 10 - 4折射率单位（RIU）。此外，我们评估了温度变化对群折射率的影响。在1310 nm处，硅样品的群折射率与温度呈准线性关系，在20 °C附近的线性拟合斜率约为3.29 × 10^{-4}$ RIU/°C.分析总结了影响测量结果不确定度的主要因素。测量厚度和群折射率的扩展不确定度（k =2）分别为4.21 × 10 - 2 μ m和7.84 × 10 - 4 RIU。随着样品厚度的增加，群折射率测量的重复性和不确定度均降低。
Simultaneous measurement of thickness and refractive index is an important quality control scheme in high-end fabrication. However, the precise measurement of large-range thickness is still technically difficult. In this article, we propose a high-precision simultaneous measurement method of thickness and group refractive index using differential white light interferometry. Using the bi-directional white light interferometer with a high dynamic range, we can get access to the optical paths on both sides of the specimen. We evaluate the performance of the proposed method by measuring specimens of three different materials, with different thicknesses ranging from 200 to $2000 \ \mu \text{m}$ . The measurement data are in good agreement with the nominal thickness, and the standard deviations of repeated measurements are $\le 0.009 \ \mu \text{m}$ and $\le 1.63\times 10^{-4}$ refractive index unit (RIU) for thickness and group refractive index, respectively. In addition, we evaluate the impact of the temperature change on the group refractive index. A quasi-linear relationship between group refractive index and temperature is observed, and the slope of the linear fit of silicon (Si) specimen around 20 °C is about $3.29\times 10^{-4}$ RIU/°C at 1310 nm. We also analyze and summarize the main factors which may introduce uncertainty in the measurement results. The expanded uncertainties ( $k =2$ ) of measured thickness and group refractive index are $\le 4.21\times 10^{-2} \ \mu \text{m}$ and $\le 7.84\times 10^{-4}$ RIU, respectively. The repeatability and uncertainty of group refractive index measurement both decrease as the thickness of the specimen increases.