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利用单波长椭偏仪对各向异性薄膜光学常数和欧拉角的研究

冀丽娜 邓剑勋 汪娟 黄佐华

冀丽娜, 邓剑勋, 汪娟, 黄佐华. 利用单波长椭偏仪对各向异性薄膜光学常数和欧拉角的研究[J]. 华南师范大学学报(自然科学版), 2019, 51(4): 14-20. doi: 10.6054/j.jscnun.2019058
引用本文: 冀丽娜, 邓剑勋, 汪娟, 黄佐华. 利用单波长椭偏仪对各向异性薄膜光学常数和欧拉角的研究[J]. 华南师范大学学报(自然科学版), 2019, 51(4): 14-20. doi: 10.6054/j.jscnun.2019058
JI Lina, DENG Jianxun, WANG Juan, HUANG Zuohua. A Study of the Optical Constants and Euler Angle of Anisotropic Thin Film with the Single-wavelength Ellipsometer[J]. Journal of South China normal University (Natural Science Edition), 2019, 51(4): 14-20. doi: 10.6054/j.jscnun.2019058
Citation: JI Lina, DENG Jianxun, WANG Juan, HUANG Zuohua. A Study of the Optical Constants and Euler Angle of Anisotropic Thin Film with the Single-wavelength Ellipsometer[J]. Journal of South China normal University (Natural Science Edition), 2019, 51(4): 14-20. doi: 10.6054/j.jscnun.2019058

利用单波长椭偏仪对各向异性薄膜光学常数和欧拉角的研究

doi: 10.6054/j.jscnun.2019058
基金项目: 

国家自然科学基金项目 61704031

广州市科学研究专项资助项目 2014J4100130

详细信息
    通讯作者:

    黄佐华,教授,Email:zuohuah@scnu.edu.cn

  • 中图分类号: O436.3

A Study of the Optical Constants and Euler Angle of Anisotropic Thin Film with the Single-wavelength Ellipsometer

  • 摘要: 基于椭偏测量原理和4×4矩阵法原理,提出了利用单波长椭偏仪在光轴平行于薄膜表面方向上测量各向异性薄膜的薄膜参数(包括双折射率、厚度及欧拉角)的方法.通过转动待测样品90°的方法,得到2组椭偏参数,利用反演算法对2组椭偏参数进行反演,得到各向异性薄膜的4个薄膜参数;采用数值模拟分析了入射角、薄膜厚度、欧拉角及其定位误差对测量结果的影响;实验测量了光轴平行于样品表面的各向异性聚酰亚胺薄膜样品在转动前后的椭偏参数,并进行反演.结果表明:该方法提出的算法反演稳定性好、精度高;该方法测得各向异性薄膜的寻常光折射率、非寻常光折射率、厚度以及欧拉角的精度分别达到0.000 1、0.000 1、0.1 nm及0.03°;寻常光折射率、非寻常光折射率、厚度的最大测量误差分别为0.001 2,0.004 4以及4.57 nm;该方法具有较好的测量稳定性、自洽性及可靠性.文中提出的方法具有测量过程简单、对实验仪器要求低的优点,拓展了单波长椭偏仪的测量范围,提出了各向异性薄膜参数的测量方法,具有实际应用意义.
  • 图  1  在环境介质/各向异性薄膜/各向同性衬底结构中入射、反射和透射电场

    Figure  1.  The representation of the electric fields for incident, reflected and transmitted waves in an ambient/anisotropic thin film/isotropic substrate structure

    图  2  模拟退火单纯形联合算法流程图

    Figure  2.  The flow chart of the simulated annealing-simplex algorithm

    图  3  PI /Si样品椭偏参数随入射角的变化

    a: no=1.547 3, ne=1.530 1, d=195 nm; b: no=1.557 3, ne=1.540 1, d=200 nm; c: no=1.567 3, ne=1.550 1, d=205 nm.

    Figure  3.  The ellipsometric parameters of PI/Si plotted as a function of incident angle

    图  4  SiO2/Si样品椭偏参数随入射角的变化

    a: no=1.37, ne=1.49, d=195 nm; b: no=1.38, ne=1.50, d=200 nm; c: no=1.39, ne=1.51, d=205 nm.

    Figure  4.  The ellipsometric parameters of SiO2/Si plotted as a function of incident angle

    图  5  椭偏参数随薄膜厚度的变化曲线

    Figure  5.  The ellipsometric parameters plotted as a function of film thickness

    图  6  PI/Si样品椭偏参数随欧拉角的变化曲线

    a: no=1.547 3, ne=1.530 1, d=195 nm; b: no=1.557 3, ne=1.540 1, d=200 nm; c: no=1.567 3, ne=1.550 1, d=205 nm.

    Figure  6.  The ellipsometric parameters plotted as a function of Euler angle of PI/Si

    图  7  SiO2/Si样品椭偏参数随欧拉角的变化曲线

    a: no=1.37, ne=1.49, d=195 nm; b: no=1.38, ne=1.50, d=200 nm; c: no=1.39, ne=1.51, d=205 nm.

    Figure  7.  The ellipsometric parameters plotted as a function of Euler angle of SiO2/Si

    图  8  PI/Si样品椭偏参数的测量误差在特定厚度处的大小

    Figure  8.  The error of ellipsometric parameters plotted as a function of thickness

    表  1  不同厚度PI/Si薄膜的反演结果

    Table  1.   The inversion results of different thickness of PI/Si films

    厚度d/nm no ne 反演厚度d/nm φE/(°)
    50 1.555 0±0.001 0 1.539 4±0.000 5 50.11±0.08 59.0±2.0
    100 1.557 3±0.000 2 1.540 4±0.000 1 99.98±0.02 59.2±0.7
    150 1.557 4±0.000 1 1.540 2±0.000 1 149.97±0.02 60.1±0.5
    200 1.557 9±0.000 8 1.540 7±0.000 6 199.90±0.10 59.8±0.1
    下载: 导出CSV

    表  2  不同厚度SiO2/Si薄膜的反演结果

    Table  2.   The inversion results of different thickness of SiO2/Si films

    厚度d/nm no ne 反演厚度d/nm φE/(°)
    50 1.380 0±0.001 0 1.501 0±0.001 0 49.97±0.09 60.30±0.30
    100 1.379 7±0.000 2 1.500 2±0.000 2 100.04±0.03 60.07±0.03
    150 1.380 0±0.000 1 1.500 1±0.000 1 150.05±0.02 59.97±0.03
    200 1.380 1±0.000 1 1.499 7±0.000 2 199.96±0.04 60.00±0.01
    下载: 导出CSV

    表  3  样品椭偏参数(Ψ1, Δ1)、(Ψ2, Δ2)的重复测量及反演结果

    Table  3.   The repeated measurement results of (Ψ1, Δ1), (Ψ2, Δ2) and the inversion results

    测量及反演量 平均值
    转动前Ψ1/(°) 21.63±0.01
    Δ1/(°) 97.26±0.02
    转动后Ψ2/(°) 19.16±0.01
    Δ2/(°) 103.67±0.02
    no 1.527 3±0.000 1
    ne 1.519 5±0.000 1
    d/nm 750.0±0.1
    φE/(°) 120.19±0.03
    下载: 导出CSV

    表  4  样品光学参数3次测量及反演结果

    Table  4.   The three measurements of sample parameters and the inversion results

    转盘始刻度/(°) 转盘末刻度/(°) no ne d/nm
    0 90 1.519 4 1.510 7 752.48
    105 195 1.520 2 1.513 3 752.84
    210 300 1.519 0 1.515 1 757.05
    下载: 导出CSV
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出版历程
  • 收稿日期:  2019-01-07
  • 刊出日期:  2019-08-25

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