Numerical Ellipsometry: Ellipsometer analysis in the n–k plane for growing films on unknown homogeneous, isotropic substrates and unknown, layered substrates

Ellipsometry is an optical analytical method based on measuring the change in polarization state of reflected or transmitted polarized light. A major challenge of the method has been the computation of reflecting surface physical parameters of interest from the raw measured data. These methods in common use are plagued by local minima and algorithm performance. The mathematics of the light reflection has long taken advantage of some aspects of Complex Analysis. The authors have used much more of Complex Analysis to treat growing films on homogeneous, isotropic substrates. The work presented here explores this advanced treatment for unknown homogeneous, isotropic substrates and for unknown layered substrates. The results lay the groundwork for a set of solution algorithms which are much more powerful and convenient than existing algorithms. Such algorithms eliminate the multiple solution problems inherent in least squares methods.