Transmission ellipsometry of transparent-film transparent-substrate systems: Polynomial inversion for the substrate optical constant

摘要

A polynomial inversion for the substrate optical constant of a transparent-film transparent-substrate system is analytically derived and presented. The reader is spared the derivation procedure which includes involved numerous transformations and algebraic manipulations. Also, closed-form formulae are given to calculate the film thickness of the system. The closed-form formulae are algebraically accurate and introduce no errors. A study of the effects of the experimental random and systematic errors of modern-day ellipsometers is presented which proves the very high accuracy of the method. The method does not need a guessed starting solution and it always provides the correct answer with no divergence. Those are important advantages over the widely used, manufacturer supplied, fitting routines.