Ellipsometry is a method of characterizing thin films and material optical properties by measuring the complex ratio ( \(\rho\) ) of the reflected Fresnel coefficients for different polarizations: $$ \rho = \frac{r_p}{r_s} = \tan(\Psi)e^{i\Delta} $$ In contrast to reflectometry, which mainly measures the reflected intensity, ellipsometry encodes the relative amplitude ( \(\tan(\Psi)\) ) and phase difference ( \(\Delta\) ) between the reflected p- and s-polarized components. This method is widely used in semiconductor manufacturing due to its ability to measure extremely thin layers with very high precision. The use of low-intensity light is also ideal for probing a wafer wthout significantly altering the material.
Ψ : Angular representation of the relative amplitude ratio between polarizations. $$\psi = \arctan\left|\frac{r_p}{r_s}\right|$$ Δ : Phase difference between reflected p- and s-polarized light. $$\Delta = \arg\left(\frac{|r_p|e^{i\phi_p}}{|r_s|e^{i\phi_s}}\right) = \phi_p - \phi_s$$ φ : Phase shift accumulated propagating through thin film at the transmitted angle. $$\phi = \frac{4\pi nt\cos(\theta_t)}{\lambda}$$ rs : Complex reflection coefficient for s-polarization. $$r_s = \frac{r_{s01} + r_{s12}~e^{i\phi}}{1+r_{s01}\cdot r_{s12}~e^{i\phi}}$$ rp : Complex reflection coefficient for p-polarization. $$r_p = \frac{r_{p01} + r_{p12}~e^{i\phi}}{1+r_{p01}\cdot r_{p12}~e^{i\phi}}$$ Rs : Reflectance power for s-polarization. $$R_s = |r_s|^2$$ Rp : Reflectance power for p-polarization. $$R_p = |r_p|^2$$