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

J 2019

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

OHLÍDAL, Ivan, Jiří VOHÁNKA, Jan MISTRÍK, Martin ČERMÁK, František VIŽĎA et. al.

Basic information

Original name

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

Authors

OHLÍDAL, Ivan (203 Czech Republic, guarantor, belonging to the institution), Jiří VOHÁNKA (203 Czech Republic, belonging to the institution), Jan MISTRÍK (203 Czech Republic, belonging to the institution), Martin ČERMÁK (203 Czech Republic, belonging to the institution), František VIŽĎA (203 Czech Republic) and Daniel FRANTA (203 Czech Republic, belonging to the institution)

Edition

Thin Solid Films, Elsevier, 2019, 0040-6090

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10306 Optics

Country of publisher

Switzerland

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

odkaz na stránku nakladatele

Impact factor

Impact factor: 2.030

RIV identification code

RIV/00216224:14310/19:00112003

Organization unit

Faculty of Science

DOI

http://dx.doi.org/10.1016/j.tsf.2019.03.001

UT WoS

000499678700004

Keywords in English

Reflectance;Transmittance;Ellipsometric parameters;Inhomogeneous thin films

Abstract

V originále

A multiple-beam interference model is used to derive approximate formulae for the reflection and transmission coefficients of inhomogeneous thin films exhibiting large gradients of refractive index profiles. It is shown that these formulae are constituted by series containing the Wentzel-Kramers-Brillouin-Jeffreys term and correction terms with increasing order corresponding to number of considered internal reflections inside the films. A numerical analysis enabling us to show the influence of a degree of inhomogeneity on spectral dependencies of reflectance and ellipsometric parameters of inhomogeneous films is performed. Advantages and disadvantages of our approach compared with other approximate approaches are discussed. The optical characterization of a selected non-stoichiometric silicon nitride film prepared by reactive magnetron sputtering onto silicon single crystal substrate is performed for illustration of using our formulae in practice.

Links

LO1411, research and development project

Name: Rozvoj centra pro nízkonákladové plazmové a nanotechnologické povrchové úpravy (Acronym: CEPLANT plus)

Investor: Ministry of Education, Youth and Sports of the CR

Citovat

OHLÍDAL, Ivan, Jiří VOHÁNKA, Jan MISTRÍK, Martin ČERMÁK, František VIŽĎA and Daniel FRANTA. Approximations of reflection and transmission coefficients of inhomogeneous thin films based on multiple-beam interference model. Thin Solid Films. Elsevier, 2019, vol. 692, 31 December 2019, p. 1-17. ISSN 0040-6090. Available from: https://dx.doi.org/10.1016/j.tsf.2019.03.001.

@article{1598679,
   author = {Ohlídal, Ivan and Vohánka, Jiří and Mistrík, Jan and Čermák, Martin and Vižďa, František and Franta, Daniel},
   article_number = {31 December 2019},
   doi = {http://dx.doi.org/10.1016/j.tsf.2019.03.001},
   keywords = {Reflectance;Transmittance;Ellipsometric parameters;Inhomogeneous thin films},
   language = {eng},
   issn = {0040-6090},
   journal = {Thin Solid Films},
   title = {Approximations of reflection and transmission coefficients of inhomogeneous thin films based on multiple-beam interference model},
   url = {https://www.sciencedirect.com/science/article/pii/S0040609019301385},
   volume = {692},
   year = {2019}
}

TY  - JOUR
ID  - 1598679
AU  - Ohlídal, Ivan - Vohánka, Jiří - Mistrík, Jan - Čermák, Martin - Vižďa, František - Franta, Daniel
PY  - 2019
TI  - Approximations of reflection and transmission coefficients of inhomogeneous thin films based on multiple-beam interference model
JF  - Thin Solid Films
VL  - 692
IS  - 31 December 2019
SP  - 1-17
EP  - 1-17
PB  - Elsevier
SN  - 00406090
KW  - Reflectance;Transmittance;Ellipsometric parameters;Inhomogeneous thin films
UR  - https://www.sciencedirect.com/science/article/pii/S0040609019301385
L2  - https://www.sciencedirect.com/science/article/pii/S0040609019301385
N2  - A multiple-beam interference model is used to derive approximate formulae for the reflection and transmission coefficients of inhomogeneous thin films exhibiting large gradients of refractive index profiles. It is shown that these formulae are constituted by series containing the Wentzel-Kramers-Brillouin-Jeffreys term and correction terms with increasing order corresponding to number of considered internal reflections inside the films. A numerical analysis enabling us to show the influence of a degree of inhomogeneity on spectral dependencies of reflectance and ellipsometric parameters of inhomogeneous films is performed. Advantages and disadvantages of our approach compared with other approximate approaches are discussed. The optical characterization of a selected non-stoichiometric silicon nitride film prepared by reactive magnetron sputtering onto silicon single crystal substrate is performed for illustration of using our formulae in practice.
ER  -

OHLÍDAL, Ivan, Jiří VOHÁNKA, Jan MISTRÍK, Martin ČERMÁK, František VIŽĎA and Daniel FRANTA. Approximations of reflection and transmission coefficients of inhomogeneous thin films based on multiple-beam interference model. \textit{Thin Solid Films}. Elsevier, 2019, vol.~692, 31 December 2019, p.~1-17. ISSN~0040-6090. Available from: https://dx.doi.org/10.1016/j.tsf.2019.03.001.

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