椭偏参数测量误差对薄膜参数测试精度的影响

Impact of ellipsometric parameters measurement error on measurement accuracy of thin film parameters

为了分析透明均匀介质膜的椭偏方程中所隐含的椭偏参数和薄膜参数(膜厚、折射率)之间的误差关系,提出基于误差传递公式和反函数组定理,通过求出椭偏参数对薄膜参数的偏导在名义膜厚和名义折射率处的值来反求后者对前者的偏导值,进而绘出不同入射角下膜厚和折射率误差与椭偏参数测量误差之间的关系曲线的方法.该法所得结果表明,椭偏参数测量误差导致的膜厚误差和折射率误差并非在同一入射角下达到最小;它们最小时所分别对应的最佳入射角随着入射光波长、薄膜名义膜厚、名义折射率和基片折射率变化而变化;若以各自最佳入射角时所对应测得的膜厚和折射率作为薄膜参数测试值,则能有效提高测量精度.该结论与在激光椭偏仪上的实际测量结果相符.文中方法对分析其他超越方程中多个变量之间的误差关系以及各变量值的优化选取有一定参考价值.

The error relationship between ellipsometric parameters and thin film parameters（i.e.,film thickness and refractive index） contained implicitly in the ellipsometric equation of a transparent homogenous dielectric thin film was analyzed based on the error transfer formula and the inverse functions theorem.Partial derivatives of ellipsometric parameters to thin film parameters at nominal thickness and refractive index were found so as to reverse their partial derivatives to ellipsometric parameters.Relationship curves of the thickness error as well as the refractive index error versus the ellipsometric parameters measurement error under different incident angles were drawn.The curves show that the above two errors caused by the ellipsometric parameters measurement error aren＇t the minimum at a same incident angle.The optimal incident angle corresponding to their respective minimum error varies with the incident wavelength,the nominal thickness,the nominal refractive index and the substrate refractive index.The measurement accuracy can be improved effectively if the measured thickness and refractive index under their respective optimal incident angles are taken as thin film parameters measurements.The above analysis is in accordance with experimental results measured on a laser ellipsometer.The above method has certain reference to the analysis of multiple variables error relationship and the optimal selection of their values in other transcendental equations.