Substrate Effect on the Optical Reflectance and Transmittance of Thin-Film Structures

Abstract

A rigorous and consistent approach is demonstrated to develop a model of the 4M structure (the four-media structure of a film on a substrate of finite thickness). The general equations obtained for the reflectance and transmittance spectra of the 4M structure are simplified by employing a procedure of the so-called device averaging to reduce them to a succinct form convenient for processing of experimental spectra for the structures with a thick substrate. The newly derived equations are applied to two special cases: (i) an arbitrary film on highly absorbing substrates and (ii) a slightly absorbing film on transparent substrates. The reflectance and transmittance spectra represented in the simplified (with the device averaging) form have a practical application for determining the film thickness and optical constants from experimental spectra by using the known techniques.

Analysis of Optical Properties of SiO<sub>2</sub> Thin Films for Various Thicknesses and Substrate Material Using Matlab Code

“…The difference in the optical thickness and therefore, the thickness of the layer causes the shift of the wavelength at which the reflectance would be maximal. As seen from this figure, when the period number increases the spectra become sharper, narrower, and the refractivity increased, and this result is complies with the results of Barybin and shapovalov [18], and Wen-Hao Cho [19] It is obvious that the reflectance of the layer, in this case, is independent on the thickness of the coatings at shorter wavelength. With the thickness of SiO2 in stack increasing, the reflectance changes correspondingly.…”

Comparison of the heat-treatment effect on carrier dynamics in TiO2 thin films deposited by different methods

“…The steady state spectra of the samples can be analysed to reveal the film thickness and porosity. The interference of the monitoring light reflected from the front and back film surface results in a specific spectral features which depend on the film refractive index and thickness 30,31 . These features are most pronounced when the film thickness is in the order of magnitude of the monitoring wavelength, but can be applied to thinner films, though with lower accuracy.…”

Optimum excitation wavelength and photon energy threshold for spintronic terahertz emission from Fe/Pt bilayer

“…Consequently, the influence of the pump wavelength on the spintronic THz emission can be properly elucidated in terms of the absorbed laser power in the metallic heterostructure. The absorptance values from 100 to 4000 nm were obtained based on the appropriate relevant formulae ( Tomlin, 1972 ; Barybin and Shapovalov, 2010 ) for the double thin film structure of the Fe/Pt that is bounded by ambient air on the Pt side and by 500-μm MgO substrate on the Fe side. The calculations, which take into consideration that the pump beam enters the metallic heterostructure at normal incidence by penetrating the 3-nm Pt film first before reaching the 2-nm Fe, are described further in the STAR Methods Section.…”

“…The absorptance values were obtained by first determining the transmittance and reflectance values of the metallic heterostructure, then by computing for the absorptance values using α = 1 – τ – ρ, where α is the absorptance, τ is the transmittance (the ratio of transmitted optical power to the incident optical power), and ρ is the reflectance (the ratio of the reflected optical power to the incident optical power). The formulae for calculating the pump wavelength-dependent transmittance and reflectance are found in literature ( Tomlin, 1972 ; Barybin and Shapovalov, 2010 ), and allow for proper consideration of parameters and conditions that are consistent with the experimental configuration for the optical excitation of the spintronic THz emitter. The optical constants, which are necessary inputs for the computation, are based on published information on the wavelength-dependent refractive indices and absorption coefficients of Pt ( Rakic et al., 1998 ) and Fe ( Ordal et al., 1988 ; Johnson and Christy, 1974 ; Werner et al., 2009 ) as well as on the refractive indices of air ( Ciddor, 1996 ; Mathar, 2007 ) and MgO ( Stephens and Malitson, 1952 ).…”