Abstract

Reflectometric and ellipsometric methods for the measurement of the dielectric permittivity and thickness of a film deposited onto an isotropic substrate with a known dielectric permittivity encounter significant difficulties since the parameters of the film enter into the measured quantities in an involved form. Abelés has shown that the processes of determination of the film’s refractive index and thickness may be completely separated [1]. When the relative reflectances of p - polarized light at the film-covered and uncovered surfaces are equal, the angle of incidence is equal to the Brewster angle of the ambient-film interface. On the other hand, for a film with non-uniform thickness (such as a wedge-shape film or film during the growth process) under variation of the angle of incidence at this “shadow” Brewster angle (where the sample’s reflectance is not equal zero!) the interference fringes of all interference patterns corresponding to the different thicknesses of the film disappear. Moreover, there is another shadow Brewster angle where the sample’s reflectance ceases to depend on the film’s thickness and the interference fringes disappear. Indeed, the intensity reflection coefficient for p - polarized light of an ambient -film - substrate system has the form: $R(\theta )={\left|\frac{r_{01}(\theta )+r_{12}(\theta )e^{-i\delta }}{1+r_{01}(\theta )r_{12}(\theta )e^{-i\delta }}\right|}^2$, where r₀₁, r₁₂ are Fresnel reflection coefficients at ambient - film and film - substrate interfaces, $\delta =\frac{4\pi d}{\lambda }\sqrt{{\epsilon }_1-{\sin }^2\theta }$, d and ε₁ are the thickness and dielectric permittivity of the film, λ is the free-space-wavelength and θ is the angle of incidence. Abelés angle (first shadow Brewster angle) θ_B1 is defined by the relation $r_{01}\left({\theta }_{B1}\right)=0$. At the point ${\theta }_{B2}$ where $r_{12p}\left({\theta }_{B2}\right)$ turns to zero (second shadow Brewster angle) the coefficient R, just as in the previous case, does not depend on the film’s thickness. Therefore, the reflectances of films of different thickness (or from different places in the case of a wedge film) will have the same value at the angles ${\theta }_{B1}$ and ${\theta }_{B2}$ and so the interference patterns should intersect each other at these points.

© 1998 Optical Society of America