Sensitivity of the Ellipsometric Parameters to Angle-of-Incidence Variations

Formulas by which the partial derivatives of the ellipsometric parameters psi and Delta with respect to the angle of incidence can be calculated are presented. These derivatives are plotted as a function of the angle of incidence, the refractive indices of the film, the substrate, and the immersion medium, and also as a function of film thickness on three-dimensional graphs. These graphs illustrate the angular regions in which angle-of-incidence errors are significant for typical materials. At the angles of incidence at which these derivatives are large, errors due to beam deviation and errors due to the use of noncollimated light or due to the use of specimens with rough or irregular surfaces can be significant. The results illustrate that the errors due to beam deviation are often significant in zone-averaged measurements when standard optical components with wedge angle tolerances of 0 degrees 3' of arc are used.