角分辨光谱干涉薄膜多参数测量方法研究

The accurate measurement of thickness and optical constants of thin films is crucial to preparing thin film materials with high performance. While there are challenges to measuring all these parameters simultaneously and accurately with existing spectrophotometry for the reasons of the parameter correlation and fewer measurement data than unknowns, which may lead to local solutions. To tackle this problem, a thin film multiparameter measurement system based on the angle-resolved spectral interferometry is proposed to significantly increase the amount of measurement data. An original method for the reduction of the parameter correlation is presented based on the response of the interferometric phase to the change of thin film parameters. With this method, the problem of local solutions can be solved and the measurement accuracy of thin film multiparameter is improved. In this project, the measurement principle of the angle-resolved spectral interferometry based on the back focal plane interference of the objective and the spectral imaging is studied systematically to reduce the noise and the distortion of the interferogram. The analytical model of the first-order partial derivatives of the phase of the complex amplitude is established with respect to the thin film parameters to reveal the monotonicity of the interferometric phase and the corresponding preconditions as well as the scope of applications. By removing the ambiguity from the unwrapped phase of the interferogram, the reduction of the parameter correlation can be achieved based on the monotonicity of the unwrapped phase. The investigation provides a new perspective for analyzing the interference signal of thin films and opens up a new way for the simultaneous and accurate measurement of thickness and optical constants of thin films.

薄膜厚度和光学常数的准确测量对制备高性能薄膜材料至关重要。利用现有光度法同时准确测量薄膜厚度和光学常数存在一定挑战，主要因为薄膜参数的相关性和测量数据少于未知参数，导致了测量结果易陷入局部极值的问题。为此，拟提出一种大幅提高测量数据量的角分辨光谱干涉薄膜多参数测量技术，从干涉相位对薄膜参数变化响应机理的独特视角研究降低薄膜参数相关性的新方法，解决局部极值问题，提高薄膜参数测量准确度。项目系统地研究基于物镜后焦面干涉和光谱成像的角分辨光谱干涉测量原理，研究干涉数据畸变校正和降噪方法，建立复振幅相位关于薄膜参数一阶偏导的解析模型，揭示干涉相位关于薄膜参数的单调特性及其先决条件和适用范围，研究绝对相位恢复算法，建立利用解包裹相位单调特性降低薄膜参数相关性的理论方法。研究成果有利于为薄膜干涉信号的分析提供一种新的视角，为薄膜厚度和光学常数的同时准确测量提供一种新的技术途径。

项目开展了基于角分辨光谱干涉原理的光学薄膜厚度d和光学常数n(λ)、κ(λ)多参数测量方法研究。针对薄膜多参数之间的相关性和测量数据少于未知参数使得测量结果易陷入局部极值的问题，提出了一种基于物镜后焦面干涉原理结合光谱成像的角分辨光谱干涉技术。首先，研究了干涉相位对薄膜参数变化的响应机理，建立了薄膜复振幅反射系数的相位关于薄膜参数一阶偏导数的解析模型，重点针对解包裹相位的单调特性进行了研究，建立了基于解包裹相位的目标函数。其次，设计并搭建了物镜后焦面干涉系统，重点优化了物镜后焦面的位置误差，提高了像面干涉信号的信噪比，通过在像面位置放置光谱成像模块，成功地将谱域和角域干涉信号分别成像在面阵探测器的行和列上，实现了单次测量获得 N×M 个有效数据点。在此基础上，利用角分辨光谱干涉实验系统对蓝宝石基底上制备的厚度为1.12 μm的GaN薄膜进行了实验测试和比对测试，结果表明该方法能够成功实现薄膜厚度d和光学常数n(λ)、κ(λ)的解耦和准确测量。薄膜厚度相对于SEM结果的误差为3 nm，折射率与Sellmeier色散方程拟合吻合度达0.9984，消光系数与文献数值基本吻合。最后，详细分析了膜厚测量范围、对多层膜结构测量的潜力以及测量数据的误差敏感性，并指出了角分辨光谱干涉方法对弱吸收光学材料的测量局限性，拓展性地研究了基于光热效应的弱吸收测量方法，为后续研究开拓了新思路。本项目的研究成果，为薄膜厚度和光学常数的同时准确测量提供了新的技术途径。

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