Approximations of reflection and transmission coefficients of inhomogeneous thin films based on multiple-beam interference model

Ohlı́dal, Ivan; Vohánka, Jiří; Mistrı́k, Jan; Čermák, Martin; Vižd'a, František; Franta, Daniel

doi:10.1016/j.tsf.2019.03.001

Cited by 16 publications

(18 citation statements)

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“…Thus, it can be employed for characterizing the films with large gradients of the refractive index profiles and complicated profiles. The method is based on calculating corrections to the WKBJ formula corresponding to single, double, triple and multiple internal reflections inside the structure of the inhomogeneous film connected with the profile of the refractive index (see [33]). These corrections contain multiple integrals similar to those obtained in paper [20].…”

Section: Approximate Methods Based On Multiple Beam Inter-mentioning

confidence: 99%

“…A multiplicity of the integrals is again given by the numbers of the considered internal reflections inside the film. After using the mathematical procedure presented in [33] one then derives the following formula for r…”

Section: Approximate Methods Based On Multiple Beam Inter-mentioning

confidence: 99%

“…where ∆r n denotes the individual correction of the order n and M is the maximum order needed for obtaining a required precision of calculations. The correction of the n-th order is expressed as follows [33] ∆r n =…”

Section: Approximate Methods Based On Multiple Beam Inter-mentioning

confidence: 99%

“…n,R represent the partial corrections of the n-th order (see [33]). The partial corrections of the first order are expressed as follows [33]…”

Section: Approximate Methods Based On Multiple Beam Inter-mentioning

confidence: 99%

“…for p-polarization with C 0 = cos ϕ 0 and C U = cos ϕ U . The partial corrections of the second order are given in this way [33]…”

Section: Approximate Methods Based On Multiple Beam Inter-mentioning

confidence: 99%

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Approximate methods for the optical characterization of inhomogeneous thin films: Applications to silicon nitride films

Ohlı́dal

Vohánka

Franta

et al. 2019

Journal of Electrical Engineering

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In this paper the overview of the most important approximate methods for the optical characterization of inhomogeneous thin films is presented. The following approximate methods are introduced: Wentzel–Kramers–Brillouin–Jeffreys approximation, method based on substituting inhomogeneous thin films by multilayer systems, method based on modifying recursive approach and method utilizing multiple-beam interference model. Principles and mathematical formulations of these methods are described. A comparison of these methods is carried out from the practical point of view, ie advantages and disadvantages of individual methods are discussed. Examples of the optical characterization of three inhomogeneous thin films consisting of non-stoichiometric silicon nitride are introduced in order to illustrate efficiency and practical meaning of the presented approximate methods.

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Section: Approximate Methods Based On Multiple Beam Inter-mentioning

confidence: 99%

Section: Approximate Methods Based On Multiple Beam Inter-mentioning

confidence: 99%

Section: Approximate Methods Based On Multiple Beam Inter-mentioning

confidence: 99%

“…n,R represent the partial corrections of the n-th order (see [33]). The partial corrections of the first order are expressed as follows [33]…”

Section: Approximate Methods Based On Multiple Beam Inter-mentioning

confidence: 99%

“…for p-polarization with C 0 = cos ϕ 0 and C U = cos ϕ U . The partial corrections of the second order are given in this way [33]…”

Section: Approximate Methods Based On Multiple Beam Inter-mentioning