基于严格耦合波理论的光栅结构参数测量方法

发布时间：2018-07-20 21:18

【摘要】：衍射光栅作为一种重要的光学元件,在诸多领域具有不可替代的重要作用,其结构参数的测量具有重要意义。随着光栅制造技术和应用领域的不断发展,现有的原子力显微镜、扫描隧道显微镜、扫描电子显微镜和透射电子显微镜等光栅结构参数测量方法已经无法兼顾快速、低成本、非破坏和高精度的测量需求。近年来,光学散射测量法为同时兼顾上述测量需求提供了全新的解决方案。该方法在实际应用中需解决两个重要问题,分别是正问题光栅衍射建模和逆问题结构参数求解。针对上述问题,本文提出了基于严格耦合波理论的光栅结构参数测量方法,对光栅衍射建模及参数求解两个关键问题着手进行分析,并结合实验验证,实现了光栅结构参数的测量。论文的主要研究内容如下:(1)基于严格耦合波理论的光栅衍射建模研究。严格耦合波理论作为矢量衍射理论,能够精确建立光栅的光学特性模型并计算衍射效率。针对一维任意结构的光栅,将其近似为数学等效模型,并基于严格耦合波理论建立光栅的衍射特性模型,通过该模型可实现光栅衍射效率的精确求解。基于上述模型仿真分析了不同入射条件、不同光栅结构参数下衍射效率变化情况,为光栅结构参数的反演模型提供了理论依据。(2)光栅衍射效率反演光栅结构参数的研究。光栅衍射场的模型十分复杂,衍射效率的计算没有解析函数,需要基于逆问题分析方法建模,本文选择BP神经网络构建反演模型,探究光栅衍射效率与结构参数的映射关系。采用典型的三层结构,确定6个输入变量,分别为不同入射条件下衍射效率,2个输出变量,分别为槽深和占空比,分析输入和输出变量之间的非线性映射,并采用了Levenberg-Marquardt算法优化训练过程,在提高精度的同时加快了收敛速度,建立了衍射效率反演光栅结构参数的模型,并对模型进行相关性分析,验证了模型具有很强的泛化能力和学习能力。(3)光栅结构参数测量的实验验证。本文建立了光栅衍射效率测量系统,测量了多种光栅的衍射效率,其测量结果与仿真结果比较在±3%误差以内。结合上述光栅光学特性模型以及结构参数反演模型,通过测量得到的衍射效率反演光栅的结构参数。与AFM测量结果光栅槽深434nm和占空比0.325相比,本文测量方法得到的槽深相对误差为0.23%,占空比相对误差为0.92%。实验结果表明,基于光栅衍射效率反演结构参数的方法,能够实现光栅结构参数快速、低成本、非破坏和高精度的测量。
[Abstract]:As an important optical element, diffraction grating plays an irreplaceable role in many fields, and the measurement of its structural parameters is of great significance. With the continuous development of grating manufacturing technology and applications, the existing measurement methods of grating structure parameters, such as atomic force microscope, scanning tunneling microscope, scanning electron microscope and transmission electron microscope, have been unable to take account of fast and low cost. Non-destructive and high-precision measurement requirements. In recent years, optical scattering measurement method has provided a new solution to meet the above measurement requirements at the same time. There are two important problems to be solved in the practical application of this method, namely, the forward problem grating diffraction modeling and the inverse problem structure parameter solution. In order to solve the above problems, a grating structure parameter measurement method based on strictly coupled wave theory is proposed in this paper. The two key problems of grating diffraction modeling and parameter solving are analyzed and verified by experiments. The measurement of grating structure parameters is realized. The main research contents are as follows: (1) grating diffraction modeling based on strictly coupled wave theory. As a vector diffraction theory, the strictly coupled wave theory can accurately establish the optical characteristic model of the grating and calculate the diffraction efficiency. The grating with one dimensional arbitrary structure is approximated as a mathematical equivalent model, and the diffraction characteristic model of the grating is established based on the strictly coupled wave theory, by which the diffraction efficiency of the grating can be solved accurately. Based on the above model, the variation of diffraction efficiency under different incident conditions and different grating structure parameters is simulated and analyzed, which provides a theoretical basis for the inversion model of grating structure parameters. (2) the research of grating diffraction efficiency inversion grating structural parameters. The model of grating diffraction field is very complicated, the calculation of diffraction efficiency has no analytic function, it needs to be modeled based on inverse problem analysis method. In this paper, BP neural network is selected to construct the inversion model, and the mapping relationship between grating diffraction efficiency and structural parameters is explored. Using a typical three-layer structure, six input variables are determined, one is diffraction efficiency under different incident conditions, the other is two output variables, which are groove depth and duty cycle, respectively. The nonlinear mapping between input and output variables is analyzed. The Levenberg-Marquardt algorithm is used to optimize the training process, which improves the accuracy and accelerates the convergence speed. The model of diffraction efficiency inversion of grating structure parameters is established, and the correlation of the model is analyzed. The model has strong generalization ability and learning ability. (3) Experimental verification of grating structure parameter measurement. In this paper, a grating diffraction efficiency measurement system is established, and the diffraction efficiency of various gratings is measured. The comparison between the measured results and the simulation results is within 卤3% error. Based on the above optical characteristic model and the inversion model of the structure parameters, the structural parameters of the grating are retrieved by measuring the diffraction efficiency. Compared with 434nm and duty cycle 0.325, the relative error of groove depth and duty cycle obtained by this method is 0.23 and 0.92 respectively. The experimental results show that the method based on grating diffraction efficiency can achieve fast, low cost, non-destructive and high precision measurement of grating structure parameters.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN25

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