减小由光谱测量数据误差造成的薄膜光学参数反演不确定度的方法

吴素勇; 龙兴武; 黄云; 杨开勇

中国激光, 2009, 36 (8): 2171, 网络出版: 2009-08-13

减小由光谱测量数据误差造成的薄膜光学参数反演不确定度的方法

Methods for Decreasing Optical Parameters Reverse Determination Uncertainty of Thin Films Caused by Spectral Measurement Errors

论文大纲

吴素勇 ^*龙兴武黄云杨开勇

作者单位

国防科技大学光电科学与工程学院光电工程系, 湖南长沙 410073

摘要

基于对光谱测量数据中系统误差和随机误差的不同特性分析, 提出了两种方法来分别减小其对薄膜光学参数反演测量精度的影响。方法一是利用薄膜光谱系数关于薄膜光学参数的一阶偏导数信息筛选数据点, 选取偏导数符号相反的波段或入射角区域作为最佳测量数据点采集区域, 以最小化系统误差引起的薄膜光学参数相对真实值的偏差大小。方法二是在实测光谱数据中注入独立同分布的随机噪声, 利用基于偏差函数最小化方法的混合优化算法多次进行反演计算, 将每次反演得到的薄膜光学参数估计值的统计均值作为薄膜真实光学参数的估计值, 以减小甚至消除随机误差引起的薄膜光学参数不确定度。这两种方法不仅在提高薄膜光学参数测量精度上具有明显的实用价值, 而且物理意义明确, 可操作性强, 不局限于特定波段和特定材料的薄膜光学参数测量, 具有良好的普适性, 可望在薄膜光学参数的准确测量技术中发挥重要作用。

Abstract

Based on different characteristics analysis of the systematic and random errors found in the spectral measurement data, two methods are put forward to diminish their impacts on the reverse determination accuracy of thin films’ respectively optical parameters. The first method uses spectral coefficient’s first order partial derivatives of thin films with respect to layer optical parameters to select measurement data. The spectral region or incident angle region characterized with opposite operation symbol of partial derivatives is chosen as the optimal measurement data region to minimize the deviations from the real optical parameters of thin films caused by systematic measurement errors. The second method injects independent random noise of same distribution to the actual measurement data. The data with noise are utilized as the real spectral coefficients of the thin film being measured in the reverse determination for many times. The reverse determination algorithm used is a mixed optimization method based on the discrepancy function minimization technique. The statistics mean values of all fit optical parameters obtained each time by the mixed optimization method are chosen as estimates of the real optical parameters of the measured thin film to diminish or eliminate the uncertainty of optical parameters caused by random measurement errors. These two methods are of obviously practical value to improve the determination accuracy of thins films’ optical parameters. And they also characterize with concise and definite physical meaning, expedient manipulation ability and good universality, not restricted to specific spectral regions or specific materials. They are of promising importance in the accurate reverse determination techniques of thins films’ optical parameters.

参考文献

[1] . Analytical method of determination optical constants of a weekly absorbing thin film[J]. Appl. Opt., 1997, 36(25): 6325-6328.

[2] . Swanepoel. Determination of the thickness and optical constants of amorphous silicon[J]. J. Phys. E, 1983, 16: 1214-1222.

[3] 王胭脂, 张伟丽, 范正修等. SiO2薄膜折射率的准确拟合分析[J]. 中国激光, 2008, 35(5)： 760～763

Wang Yanzhi, Zhang Weili, Fan Zhengxiu et al.. Analysis for accurately fitting the refractive index of SiO2 thin film[J]. Chinese J. Lasers, 2008, 35(5)： 760～763

[4] 顾培夫, 陈海星, 艾曼灵等. TiO2膜消光系数的确定及制备参量的影响[J]. 光学学报, 2005, 25(7)： 1005～1008

Gu, Peifu, Chen Haixing, Ai Manling et al.. Determination of the extinction coefficient of TiO2 and effect of preparation parameters[J]. Acta Optica Sinica, 2005, 25(7)： 1005～1008

[5] . A. Dobrowoski, F. C. Ho, A. Waldorf. Determination of optical constants of thin film coating materials based on inverse synthesis[J]. Appl. Opt., 1983, 22: 3191-3200.

[6] . P. Arndt, R. M. A. Azzam, J. M. Bennett et al.. Multiple determination of the optical constants of thin-film coating materials[J]. Appl. Opt., 1984, 23: 3571-3596.

[7] . B. Djurisic, J. M. Elazar, A. D. Ratic. Simulated-annealing-based genetic algorithm for modeling the optical constants of solids[J]. Appl. Opt., 1997, 36(28): 7097-7103.

[8] . S. Parramon, J. F. Borrull, Salvador Bosch et al.. Use of information on the manufacture of samples for the optical characterization of multilayers through a global optimization[J]. Appl. Opt., 2003, 42(7): 1325-1328.

[9] . P. Chen, J. M. Chen. Use of surface plasma waves for determination of the thickness and optical constants of thin metallic films[J]. J. Opt. Soc. Am., 1981, 71: 189-191.

[10] F. Abeles. Methods for determining optical parameters of thin films[C] . Progress in Optics ed by E. Wolf, 1963. 251～288

[11] . Ulrich, K. Torge. Measurements of thin film parameter with a prism coupler[J]. Appl. Opt., 1973, 12: 2901-2908.

[12] . Determination of refractive index , thickness, and the optical losses of thin films from prism-film coupling measurements[J]. Appl. Opt., 2008, 47(7): 894-900.

[13] . P. de Lariviere, J.M. Frigerio, J. Rivory et al.. Estimate of the degree of inhomogeneity of the refractive index of dielectric films from spectroscopic ellipsometry[J]. Appl. Opt., 1992, 31: 6056-6061.

[14] . Chindaudom, K. Vedam. Characterization of inhomogeneous transparent substrates by spectroscopic ellipsometry: refractive indices n(λ) of some fluoride-coating materials[J]. Appl. Opt., 1994, 33: 2664-2671.

[15] . P. Borgogno, P. Bousquet, F. Flory et al.. Inhomogeneity in films: limitation of the accuracy of optical monitoring of thin films[J]. Appl. Opt., 1981, 20: 90-94.

[16] . P. Borgogno, P. Bousquet, E. Pelletier. Automatic determination of optical constants of inhomogeneous thin films[J]. Appl. Opt., 1982, 21: 4020-4029.

[17] . P. Borgogno, F. Flory, P. Roche et al.. Refractive index and inhomogeneity of thin films[J]. Appl. Opt., 1984, 23: 3567-3570.

[18] . V. Tikhonravov, M. K. Trubetskov, M. A. Kokarev et al.. Effect of systematic errors in spectral photometric data on the accuracy of determination of optical parameters of dielectric thin films[J]. Appl. Opt., 2002, 41(19): 2555-2560.

[19] . M. del Pozo, L. Diaz. Metheod for the determination of optical constants of thin films: dependence on experimental uncertainties[J]. Appl. Opt., 1992, 31(22): 4474-4481.

[20] . Konstantinov, T. Babeva, S. Kitova. Analysis of errors in the thin-film optical parameters derived from spectrophotometric measurements at normal light incidence[J]. Appl. Opt., 1998, 37(19): 4260-4267.

[21] 吴素勇. 遗传算法在膜系设计中的应用[D]. 长沙：国防科技大学, 2007. 16～32

Wu Suyong. Application of genetic algorithm in the design of optical coatings[D]. Changsha：National University of Defense Technology, 2007. 16～32

[22] Sh. Furman, A.V. Tikhonravov. Basics of Optics of Multilayer Systems[M]. France：Editions Frontieres, 1992. 58～64

吴素勇, 龙兴武, 黄云, 杨开勇. 减小由光谱测量数据误差造成的薄膜光学参数反演不确定度的方法[J]. 中国激光, 2009, 36(8): 2171. Wu Suyong, Long Xingwu, Huang Yun, Yang Kaiyong. Methods for Decreasing Optical Parameters Reverse Determination Uncertainty of Thin Films Caused by Spectral Measurement Errors[J]. Chinese Journal of Lasers, 2009, 36(8): 2171.

减小由光谱测量数据误差造成的薄膜光学参数反演不确定度的方法

关于本站 Cookie 的使用提示

全站搜索

减小由光谱测量数据误差造成的薄膜光学参数反演不确定度的方法

相关论文

相关资讯

关于本站 Cookie 的使用提示

全站搜索