GENERALIZED MATRIX-METHOD FOR ANALYSIS OF COHERENT AND INCOHERENT REFLECTANCE AND TRANSMITTANCE OF MULTILAYER STRUCTURES WITH ROUGH SURFACES, INTERFACES, AND FINITE SUBSTRATES

A generalized matrix method is presented for calculating the optical r eflectance and transmittance of an arbitrary thin-solid-him multilayer structure on very thick substrates with rough surfaces and interfaces . We show that the effect of roughness and the influence of incoherent ly reflected light on the back side of a thick. layer can be accounted for with a more general transfer matrix that enables the inclusion of modified complex Fresnel coefficients. Coherent, partially coherent, and incoherent multiply reflected light inside the multilayer structur e is treated in the same way. We demonstrate the method by applying it to simulated and experimental reflectance spectra of thin epitaxial S i overlayers on very thick SiO2 substrates and on a separation by ion implantation of oxygen structure with a SiO2 buried layer exhibiting s ubstantial roughness on both of its interfaces (Si/SiO2 and SiO2/Si).