基于嚴(yán)格耦合波理論的光柵結(jié)構(gòu)參數(shù)測量方法
發(fā)布時間：2018-07-20 21:18
【摘要】：衍射光柵作為一種重要的光學(xué)元件,在諸多領(lǐng)域具有不可替代的重要作用,其結(jié)構(gòu)參數(shù)的測量具有重要意義。隨著光柵制造技術(shù)和應(yīng)用領(lǐng)域的不斷發(fā)展,現(xiàn)有的原子力顯微鏡、掃描隧道顯微鏡、掃描電子顯微鏡和透射電子顯微鏡等光柵結(jié)構(gòu)參數(shù)測量方法已經(jīng)無法兼顧快速、低成本、非破壞和高精度的測量需求。近年來,光學(xué)散射測量法為同時兼顧上述測量需求提供了全新的解決方案。該方法在實(shí)際應(yīng)用中需解決兩個重要問題,分別是正問題光柵衍射建模和逆問題結(jié)構(gòu)參數(shù)求解。針對上述問題,本文提出了基于嚴(yán)格耦合波理論的光柵結(jié)構(gòu)參數(shù)測量方法,對光柵衍射建模及參數(shù)求解兩個關(guān)鍵問題著手進(jìn)行分析,并結(jié)合實(shí)驗(yàn)驗(yàn)證,實(shí)現(xiàn)了光柵結(jié)構(gòu)參數(shù)的測量。論文的主要研究內(nèi)容如下:(1)基于嚴(yán)格耦合波理論的光柵衍射建模研究。嚴(yán)格耦合波理論作為矢量衍射理論,能夠精確建立光柵的光學(xué)特性模型并計算衍射效率。針對一維任意結(jié)構(gòu)的光柵,將其近似為數(shù)學(xué)等效模型,并基于嚴(yán)格耦合波理論建立光柵的衍射特性模型,通過該模型可實(shí)現(xiàn)光柵衍射效率的精確求解。基于上述模型仿真分析了不同入射條件、不同光柵結(jié)構(gòu)參數(shù)下衍射效率變化情況,為光柵結(jié)構(gòu)參數(shù)的反演模型提供了理論依據(jù)。(2)光柵衍射效率反演光柵結(jié)構(gòu)參數(shù)的研究。光柵衍射場的模型十分復(fù)雜,衍射效率的計算沒有解析函數(shù),需要基于逆問題分析方法建模,本文選擇BP神經(jīng)網(wǎng)絡(luò)構(gòu)建反演模型,探究光柵衍射效率與結(jié)構(gòu)參數(shù)的映射關(guān)系。采用典型的三層結(jié)構(gòu),確定6個輸入變量,分別為不同入射條件下衍射效率,2個輸出變量,分別為槽深和占空比,分析輸入和輸出變量之間的非線性映射,并采用了Levenberg-Marquardt算法優(yōu)化訓(xùn)練過程,在提高精度的同時加快了收斂速度,建立了衍射效率反演光柵結(jié)構(gòu)參數(shù)的模型,并對模型進(jìn)行相關(guān)性分析,驗(yàn)證了模型具有很強(qiáng)的泛化能力和學(xué)習(xí)能力。(3)光柵結(jié)構(gòu)參數(shù)測量的實(shí)驗(yàn)驗(yàn)證。本文建立了光柵衍射效率測量系統(tǒng),測量了多種光柵的衍射效率,其測量結(jié)果與仿真結(jié)果比較在±3%誤差以內(nèi)。結(jié)合上述光柵光學(xué)特性模型以及結(jié)構(gòu)參數(shù)反演模型,通過測量得到的衍射效率反演光柵的結(jié)構(gòu)參數(shù)。與AFM測量結(jié)果光柵槽深434nm和占空比0.325相比,本文測量方法得到的槽深相對誤差為0.23%,占空比相對誤差為0.92%。實(shí)驗(yàn)結(jié)果表明,基于光柵衍射效率反演結(jié)構(gòu)參數(shù)的方法,能夠?qū)崿F(xiàn)光柵結(jié)構(gòu)參數(shù)快速、低成本、非破壞和高精度的測量。
[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 鹵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.
【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TN25
本文編號：2134809
[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 鹵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.
【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TN25
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