Correction of large retardation window effect for ellipsometry measurements using quasi-Newton method.
Optical windows attached to the sample chamber for ellipsometry measurements often manifest stress-induced retardation. In reality, the retardation is not always small enough to be simplified with the small angle approximation, varies within the optical beam, and furthermore may change with the evolution of the environmental conditions of the chamber. Large retardations and retardation distributions result in complicated Mueller matrices of the input window-sample-output window system. Consequently, extensive computation is required to obtain the true ellipsometric parameters (Δ,Ψ) of the sample. In this paper, we show that the quasi-Newton method can be used to simultaneously obtain 14 unknown parameters (including ellipsometric parameters) from the Mueller matrix, with a single measurement under conditions of large and inhomogeneous window retardation. A limitation of the method is that it is valid only for isotropic samples. The validity of the method has been tested using a set of samples: a silicon substrate, a TiN-coated silicon wafer, and a thermally grown silicon dioxide film. Measurements were done under the window effect and corrected using the proposed method. The corrected results showed excellent agreement with ellipsometric parameters obtained without window effect.