GENERALIZED MATRIX-METHOD FOR ANALYSIS OF COHERENT AND INCOHERENT REFLECTANCE AND TRANSMITTANCE OF MULTILAYER STRUCTURES WITH ROUGH SURFACES, INTERFACES, AND FINITE SUBSTRATES
Cl. Mitsas et Di. Siapkas, GENERALIZED MATRIX-METHOD FOR ANALYSIS OF COHERENT AND INCOHERENT REFLECTANCE AND TRANSMITTANCE OF MULTILAYER STRUCTURES WITH ROUGH SURFACES, INTERFACES, AND FINITE SUBSTRATES, Applied optics, 34(10), 1995, pp. 1678-1683
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).