Exact polynomial inversion for top transparent layer parameters on an arbitrary substrate in ellipsometry

摘要

We consider the inverse ellipsometric problem for a transparent layer on top of an isotropic substrate, which may consist of an arbitrary number of plane parallel homogeneous layers with complex refractive indexes, or have an arbitrary depth profile variation of the complex refractive index. It is shown that the task of finding the top layer parameters can be split into two. First, the top layer dielectric constant is determined by the roots of a fifth degree polynomial and then the layer thickness is found. Error propagation analysis is provided on a sample system and the stability of the method is estimated.