摘要
红外干涉法测量外延层厚度时，多光束效应会导致双光束模型产生系统性偏差。针对现有模型有效性验证方法计算复杂的问题，本研究提出一种基于残差分析的快速判断方法。以SiC外延层10°和15°入射角红外反射光谱为研究对象，采用双光束模型进行非线性拟合，通过分析拟合残差的周期性、符号规律和幅度特征，建立多光束效应的判据。结果表明：10°入射角下残差范围-0.6~+0.2、均方根0.32，15°入射角下残差范围-0.55~+0.18、均方根0.30；残差呈现与干涉条纹同频的周期性振荡，频谱相关系数>0.95；所有波峰处残差为负、波谷处残差为正，峰负谷正比例均为100%。归纳出多光束效应判据：残差与干涉条纹同频振荡、波峰处残差为负且波谷处残差为正、残差均方根>0.2。该方法仅需模型拟合结果即可完成分析，无需额外材料参数，为双光束模型的适用性判断提供依据。
关键词： 残差分析；红外干涉；双光束模型；多光束效应
Abstract
When measuring epitaxial layer thickness using infrared interferometry, the multi-beam effect can lead to systematic deviations in the two-beam model. To address the computational complexity of existing model validity verification methods, this study proposes a rapid judgment approach based on residual analysis. Taking the infrared reflectance spectra of SiC epitaxial layers at incident angles of 10°and 15°as the research object, nonlinear fitting is performed using the two-beam model. By analyzing the periodicity, sign pattern, and amplitude characteristics of the fitting residuals, criteria for identifying the multi-beam effect are established. The results indicate that at a 10° incident angle, the residual ranges from -0.6 to +0.2 with an RMS of 0.32; at a 15° incident angle, the residual ranges from -0.55 to +0.18 with an RMS of 0.30. The residuals exhibit periodic oscillations at the same frequency as the interference fringes, with a spectral correlation coefficient exceeding 0.95. At all peak positions, the residuals are negative, while at all valley positions, they are positive, with both the negative-at-peak and positive-at-valley proportions reaching 100%. The criteria for the multi-beam effect are summarized as follows: the residuals oscillate at the same frequency as the interference fringes, residuals are negative at peaks and positive at valleys, and the RMS of residuals exceeds 0.2. This method requires only the model fitting results for analysis, without the need for additional material parameters, providing a basis for assessing the applicability of the two-beam model.
Key words： Residual analysis; Infrared interferometry; Dual-beam model; Multi-beam effects
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