Study on LM algorithm in Mueller's ellipsometry calibration method

被引：0

作者：

Guan Y. ^{[1
,2
]}

Tang D. ^{[2
]}

Fu Y. ^{[2
]}

Sun J. ^{[2
]}

Han Z. ^{[3
]}

Zhang B. ^{[2
]}

Kong M. ^{[1
]}

Cao C. ^{[2
]}

Lei L. ^{[1
,2
]}

机构：

[1] College of Metrology and Measurement Engineering, China Jiliang University, Hangzhou

[2] Shanghai Institute of Measurement and Testing Technology, Shanghai

[3] The 13th Research Institute of CETC, Shijiazhuang

来源：

Hongwai yu Jiguang Gongcheng/Infrared and Laser Engineering | 2020年 / 49卷 / 08期

关键词：

Ellipsometry; LM algorithm; Mueller matrix; Parameter calibration; Standard sample;

D O I：

10.3788/IRLA20200204

中图分类号：

学科分类号：

摘要：

According to the transmission method of polarized light in Mueller ellipsometry method, this paper presented a method for calibrating the optical element parameters in ellipsometry system. By establishing a nonlinear least squares model of outgoing light intensity with respect to orientations of transmission axis of the polarizer and analyzer and orientations and retardation of the rotation compensator, the initial parameters were iterated with Levenberg-Marquardt (LM) algorithm. Accurate values of optical element parameters could be obtained, so as to achieve the calibration of components. Through the simulation experiment, using the SiO2/Si standard sample with the known Mueller matrix and the calibration value of (24.90 ± 0.30) nm, the residual square sum of the light intensity value was calculated based on LM algorithm. When numbers of iterations accumulate to 50, the sum of squares converges of the residuals of the measurement and calculation was limited to 0.24. Then compared with the traditional multi-point calibration method, the feasibility of solving optical parameters based on LM algorithm was verified. Fitting results were validated by SiO2/Si standard sample with calibration value of (91.21±0.36) nm. Calculated film thickness was 91.53 nm and the relative error is 0.35%. Results proved that LM algorithm has advantages of rapidly converging and high precision in the parameter calibration of the Mueller ellipsometry system. © 2020, Editorial Board of Journal of Infrared and Laser Engineering. All right reserved.

引用

共 16 条

[1]

Liu Ninglin, Research on mid-infrared mull-er matrix spectroscopic ellipsometer, (2019)

[2]

Wu Suyong, Long Xingwu, Yang Kaiyong, An error processing technique for ellipsometry measurement system which minimizes the error of optical parameter characterization of thin films, Acta Optica Sinica, 32, 6, (2012)

[3]

Fan Zhentao, Research on the advanced parameters problem of muller matrix ellipsometry system, (2019)

[4]

Li W, Zhang C, Jiang H, Et al., Depolarization artifacts in dual rotating compensator Mueller matrix ellipsometry, Journal of Optics, 18, 5, (2016)

[5]

Liu S Y, Chen X G, Zhang C W., Development of a broadband Mueller matrix ellipsometer as a powerful tool for nano structure metrology, Thin Solid Films, 584, 1, pp. 176-185, (2015)

[6]

Dai Lina, Deng Jianxun, Wang Juan, Et al., The optical constants and Euler angles of anisotropic thin films were studied by using a single wavelength ellipsometer, Journal of South China Normal University (Natural Science Edition), 51, 4, pp. 14-20, (2019)

[7]

Zhen Tang, Mul-tipoint calibration method based on stok-es ellipsometry measurement system [J], Chinese Journal of Lasers, 39, 11, pp. 163-167, (2012)

[8]

Urban F K I, Barton D., Numerical ellipsometry: Use of parameter sensitivity to guide measurement selection for transparent anisotropic films, Thin Solid Films, 663, 10, pp. 116-125, (2018)

[9]

Meng Fanxue, A hybrid algorithm for solving nonlinear least squares problems, (2011)

[10]

Yang Liu, Chen Yanping, A new globally con-vergent levenberg-marquardt method for sovling nonlinear system of equations, Mathematica Numerica Sinica, 30, 4, pp. 388-396, (2008)

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