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 imple mentation of different effective-medium approximation models in spectr oscopic ellipsometry regression software. Straightforward solution of the refractive index from the equations describing the dielectric cons tant of mixed layers presented by Bruggeman often requires careful sel ection of the proper branch from a multivalued inverse of a complex fu nction. Transform methods are applied that considerably simplify the r adicand formulations. It is shown that the principal branch of the com plex functions involved always yields the correct refractive index for any proportion of the materials mixed, leading to efficient vectoriza ble computer code.