Bu-Abbud G H, Bashara N M
Appl Opt. 1981 Sep 1;20(17):3020-6. doi: 10.1364/AO.20.003020.
A general procedure for the characterization of the optical parameters of a given surface using fixed wavelength multiple-angle-of-incidence ellipsometry is developed. Quantitative evaluation of estimated parameter precision is studied considering the sum of errors squared of a least squares fit, the parameter cross-correlation at this minimum, and the confidence limits of the parameters from variance-covariance relations. Most significantly, it is shown numerically that precision is improved when the solutions exhibit a lower correlation to the remaining parameters when a correct system model is used. Using the silicon dioxide-silicon substrate system we were able to determine the complex index of silicon and the extinction coefficient of the oxide with high precision. Once this was done it was possible to estimate with reasonable confidence the refractive index and particularly the thickness of the oxide despite an observed large cross-correlation coefficient between them. A wide range of starting values for the film refractive index n(f) and thickness t(f) always converged to a small sum of errors squared, and nearly identical values for n(f) and t(f) after accurate estimates were obtained for the other parameters of the system.
开发了一种使用固定波长多入射角椭偏仪表征给定表面光学参数的通用程序。考虑最小二乘拟合误差平方和、此最小值处的参数互相关性以及方差协方差关系得出的参数置信限，研究了估计参数精度的定量评估。最显著的是，数值结果表明，当使用正确的系统模型时，若解与其余参数的相关性较低，则精度会提高。利用二氧化硅 - 硅衬底系统，我们能够高精度地确定硅的复折射率和氧化物的消光系数。完成此操作后，尽管观察到它们之间存在较大的互相关系数，但仍有可能合理地置信估计折射率，尤其是氧化物的厚度。对于薄膜折射率n(f)和厚度t(f)的广泛起始值，总是收敛到一个小的误差平方和，并且在对系统的其他参数进行准确估计后，n(f)和t(f)的值几乎相同。
