Numerical aspects of the implementation of effective-medium approximation models in spectroscopic ellipsometry regression software

Results are presented of a study of the numerical aspects of the implementation of different effective-medium approximation models in spectroscopic ellipsometry regression software. Straightforward solution of the refractive index from the equations describing the dielectric constant of mixed layers presented by Bruggeman often requires careful selection of the proper branch from a multivalued inverse of a complex function. Transform methods are applied that considerably simplify the radicand formulations. It is shown that the principal branch of the complex functions involved always yields the correct refractive index for any proportion of the materials mixed, leading to efficient vectorizable computer code.