张曌一1 何东升2,3 叶沁州2 刘让雄2 罗海凹4
（1.华中科技大学物理学院物理系，湖北 武汉 430074
2.广州铁路职业技术学院，广东 广州 511300
3.清华大学深圳国际研究生院，广东 深圳 518055
4.国家智能电网输配电设备质量检验检测中心，广东 东莞 523325）
摘要：针对碳化硅外延层厚度测量因传统的双光束干涉模型折射率常数简化与忽略载流子-声子耦合效应导致误差偏大的问题，提出一种基于Drude-Lorentz模型与红外反射光谱干涉条纹的碳化硅外延层厚度反演方法。该方法以n型4H-SiC同质外延片为研究对象，基于集成载流子-声子耦合效应的复折射率色散模型，描述其在红外波段的色散特性；通过对预处理后红外反射光谱曲线中的干涉条纹提取极值点，获取其波数序列，并建立碳化硅外延层厚度与干涉相位的物理关联；通过将预设的碳化硅外延层厚度区间离散化为若干个节点，计算各节点对应的理论折射率，并通过最小化理论折射率与极值点实验折射率的残差平方和，实现对n型4H-SiC外延层厚度的精准确定。实验结果表明，该方法得到的n型4H-SiC外延层厚度的反演结果残差分布近似正态且无明显的系统性偏差，综合不确定性标准差为0.061 μm，为半导体薄膜材料的厚度测量提供了一种高精度、高效率的解决方案。
关键词：碳化硅外延层厚度；红外反射光谱；Drude-Lorentz模型；干涉条纹；复折射率；反演
中图分类号：O433.4 文献标志码：A 文章编号：1674-2605(2026)02-0003-08
DOI：10.12475/aie.20260203 开放获取
Thickness Inversion Method of Silicon Carbide Epitaxial Layers Based on the Drude-Lorentz Model and Interference Fringes in Infrared Reflectance Spectra
ZHANG Zhaoyi1 HE Dongsheng2,3 YE Qinzhou2 LIU Rangxiong2 LUO Haiao4
(1.Department of Physics, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
2.Guangzhou Railway Polytechnic, Guangzhou 511300, China
3.Shenzhen International Graduate School (SIGS), Tsinghua University, Shenzhen 518055, China
4.National Quality Inspection and Testing Center for Smart Grid Transmission and Distribution Equipment, Dongguan 523325, China)
Abstract: To address the problem of large errors in SiC epitaxial layer thickness measurement caused by the simplified constant refractive index in traditional double-beam interference models and the neglect of carrier-phonon coupling effects, this paper proposes a thickness inversion method based on the Drude-Lorentz model and interference fringes in infrared reflectance spectra. The method takes n-type 4H-SiC homoepitaxial wafers as the research object. A complex refractive index dispersion model incorporating carrier-phonon coupling is employed to describe the dispersion characteristics in the infrared band. After preprocessing the infrared reflectance spectrum, extreme points of the interference fringes are extracted to obtain their wavenumber sequence, and the physical relationship between the SiC epitaxial layer thickness and the interference phase is established. By discretizing a preset thickness interval intoseveral nodes, the theoretical refractive index corresponding to each node is calculated. The n-type 4H-SiC epitaxial layer thickness is accurately determined by minimizing the residual sum of squares between the theoretical refractive index and the experimental refractive index at the extreme points. Experimental results show that the residual distribution of the inverted thickness obtained by this method is approximately normal without significant systematic deviation, with a combined uncertainty standard deviation of 0.061 μm. This provides a high-precision and high-efficiency solution for thickness measurement of semiconductor thin-film materials.
Keywords: SiC epitaxial layer thickness; infrared reflectance spectroscopy; Drude-Lorentz model; interference fringes; complex refractive index; inversion
