Ellipsometric calculations for nonabsorbing thin films with linear refractive-index gradients

The measurement of the refractive index n and the physical thickness t of a homogeneous thin film by ellipsometry is a well-established technique. Ellipsometry also opens up the possibility of characterizing inhomogeneous thin films. This paper deals with the theoretical analysis of the sensitivity of ellipsometry to a linear refractive index gradient within a single-layer thin film. A major result is that, to a first approximation, the ellipsometric data for a film at a wavelength that is an odd multiple of four times the optical thickness (i.e., at the odd quarter-wave points) are unaffected by the inhomogeneity of the film but depend only on the average refractive index of the film. Ellipsometric data for wavelengths that are multiples of twice the optical thickness (the half-wave points) are strongly affected by the inhomogeneity of the films. Results are presented relative to the sensitivity of ellipsometric measurements for the determination of the average index and the degree of inhomogeneity of a film.