Generalized matrix method for analysis of coherent and incoherent reflectance and transmittance of multilayer structures with rough surfaces, interfaces, and finite substrates

Abstract

A generalized matrix method is presented for calculating the optical reflectance and transmittance of an arbitrary thin-solid-film multilayer structure on very thick substrates with rough surfaces and interfaces. We show that the effect of roughness and the influence of incoherently 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 structure is treated in the same way. We demonstrate the method by applying it to simulated and experimental reflectance spectra of thin epitaxial Si overlayers on very thick SiO(2) substrates and on a separation by ion implantation of oxygen structure with a SiO(2) buried layer exhibiting substantial roughness on both of its interfaces (Si/SiO(2) and SiO(2)/Si).

Experimental and theoretical demonstration of acoustic Bloch oscillations in porous silicon structures

“…The frequency x of the acoustic wave is related to the wave vector via x ¼ v j k j , where v j is the speed of sound in the j-th layer and x ¼ 2pf, with f being the frequency in s À1 . Using the matrix method, 27 we can relate the amplitudes of the waves A þ j (traveling to the right) and A À j (traveling to the left) in the j-th layer of the system with the amplitudes of the waves in the j þ 1-th layer according to…”

Rapid Detection and Recognition of Organic Pollutants at Trace Levels by Surface-Enhanced Raman Scattering

“…With a transfer matrix method, we can calculate the reflectivity of those films. [35,36] Figure 5(a) shows the calculated reflectivity spectra of 100 nm Ag, Al, Si, and Ti films. In general, the reflectivity, R Ag > R Al > R Ti > R Si , except that at λ ~ 600 nm where the Si film has a large constructive interference.…”

Multi-objective optimization of microcavity OLEDs with DBR mirror

“…where z + is the dipoles' distance from the top mirror, z − is the dipoles' distance from the bottom mirror and r is the amplitude reflection coefficient of the top and bottom mirrors calculated using the modified transfer matrix approach of Katsidis and Siapkas [27][28] .…”