46 - Ellipsometry

Summary

The goal of ellipsometry is to determine the optical and structural constants of thin films and flat surfaces from the measurements of the ellipse of polarization in reflected or transmitted light. In the absence of birefringence and optical activity a flat surface, a single-layer film, or a thin-film stack may be characterized by the complex reflection coefficients r_p = |r_p|exp(iφ_rp) and r_s = |r_s|exp(iφ_rs) for p- and s-polarized incident beams, as well as by the corresponding transmission coefficients t_p = |t_p|exp(iφ_tp) and t_s = |t_s|exp(iφ_ts).

Strictly speaking, an ellipsometer is a device that measures the complex ratios r_p /r_s and/or t_p /t_s. The amplitude ratios are usually deduced from the angles ψ_r and ψ_t, which are defined by tan ψ_r = |r_p|/|r_s| and tan ψ_t = |t_p|/|t_s|. In practice, measuring the individual reflectivities R_p = |r_p|², R_s = |r_s|² or transmissivities T_p = |t_p|², T_s = |t_s|² does not require much additional effort. Measuring the individual phases, of course, is difficult, but the relative phase angles φ_rp − φ_rs and φ_tp − φ_ts can be readily obtained by ellipsometric methods. The values of R_p, R_s, φ_rp − φ_rs, ψ_r, T_p, T_s, φ_tp − φ_ts and ψ_t may be measured as functions of the angle of incidence, θ, or as functions of the wavelength of the light, λ, or both.

The results of ellipsometric measurements are fed to a computer program that searches the space of unknown parameters to find agreement between the measured data points and theoretical calculations.