Ellipsometric characterization of highly non-uniform thin films
with the shape of thickness non-uniformity modeled by
polynomials

J 2020

Ellipsometric characterization of highly non-uniform thin films with the shape of thickness non-uniformity modeled by polynomials

VOHÁNKA, Jiří, Daniel FRANTA, Martin ČERMÁK, Vojtěch HOMOLA, Vilma BURŠÍKOVÁ et. al.

Basic information

Original name

Ellipsometric characterization of highly non-uniform thin films with the shape of thickness non-uniformity modeled by polynomials

Authors

VOHÁNKA, Jiří (203 Czech Republic, guarantor, belonging to the institution), Daniel FRANTA (203 Czech Republic, belonging to the institution), Martin ČERMÁK (203 Czech Republic, belonging to the institution), Vojtěch HOMOLA (203 Czech Republic, belonging to the institution), Vilma BURŠÍKOVÁ (203 Czech Republic, belonging to the institution) and Ivan OHLÍDAL (203 Czech Republic, belonging to the institution)

Edition

Optics Express, Washington, D.C. Optical Society of America, 2020, 1094-4087

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10306 Optics

Country of publisher

United States of America

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

Přeměruje na stránku u nakladatele

Impact factor

Impact factor: 3.894

RIV identification code

RIV/00216224:14310/20:00114443

Organization unit

Faculty of Science

DOI

http://dx.doi.org/10.1364/OE.380657

UT WoS

000514575500095

Keywords in English

optical characterization;thickness non-uniform films;ellipsometry

Abstract

V originále

A common approach to non-uniformity is to assume that the local thicknesses inside the light spot are distributed according to a certain distribution, such as the uniform distribution or the Wigner semicircle distribution. A model considered in this work uses a different approach in which the local thicknesses are given by a polynomial in the coordinates x and y along the surface of the film. An approach using the Gaussian quadrature is very efficient for including the influence of the non-uniformity on the measured ellipsometric quantities. However, the nodes and weights for the Gaussian quadrature must be calculated numerically if the non-uniformity is parameterized by the second or higher degree polynomial. A method for calculating these nodes and weights which is both efficient and numerically stable is presented. The presented method with a model using a second-degree polynomial is demonstrated on the sample of highly non-uniform polymer-like thin film characterized using variable-angle spectroscopic ellipsometry. The results are compared with those obtained using a model assuming the Wigner semicircle distribution.

Links

GA19-15240S, research and development project

Name: Multifunkční nanokompozitní polymerní tenké vrstvy s řízenými povrchovými a mechanickými vlastnostmi připravené v RF prachovém plazmatu

Investor: Czech Science Foundation

LM2018097, research and development project

Name: Centrum výzkumu a vývoje plazmatu a nanotechnologických povrchových úprav (Acronym: CEPLANT)

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

Citovat

VOHÁNKA, Jiří, Daniel FRANTA, Martin ČERMÁK, Vojtěch HOMOLA, Vilma BURŠÍKOVÁ and Ivan OHLÍDAL. Ellipsometric characterization of highly non-uniform thin films with the shape of thickness non-uniformity modeled by polynomials. Optics Express. Washington, D.C.: Optical Society of America, 2020, vol. 28, No 4, p. 5492-5506. ISSN 1094-4087. Available from: https://dx.doi.org/10.1364/OE.380657.

@article{1692056,
   author = {Vohánka, Jiří and Franta, Daniel and Čermák, Martin and Homola, Vojtěch and Buršíková, Vilma and Ohlídal, Ivan},
   article_location = {Washington, D.C.},
   article_number = {4},
   doi = {http://dx.doi.org/10.1364/OE.380657},
   keywords = {optical characterization;thickness non-uniform films;ellipsometry},
   language = {eng},
   issn = {1094-4087},
   journal = {Optics Express},
   title = {Ellipsometric characterization of highly non-uniform thin films with the shape of thickness non-uniformity modeled by polynomials},
   url = {https://doi.org/10.1364/OE.380657},
   volume = {28},
   year = {2020}
}

TY  - JOUR
ID  - 1692056
AU  - Vohánka, Jiří - Franta, Daniel - Čermák, Martin - Homola, Vojtěch - Buršíková, Vilma - Ohlídal, Ivan
PY  - 2020
TI  - Ellipsometric characterization of highly non-uniform thin films with the shape of thickness non-uniformity modeled by polynomials
JF  - Optics Express
VL  - 28
IS  - 4
SP  - 5492-5506
EP  - 5492-5506
PB  - Optical Society of America
SN  - 10944087
KW  - optical characterization;thickness non-uniform films;ellipsometry
UR  - https://doi.org/10.1364/OE.380657
L2  - https://doi.org/10.1364/OE.380657
N2  - A common approach to non-uniformity is to assume that the local thicknesses inside the light spot are distributed according to a certain distribution, such as the uniform distribution or the Wigner semicircle distribution. A model considered in this work uses a different approach in which the local thicknesses are given by a polynomial in the coordinates x and y along the surface of the film. An approach using the Gaussian quadrature is very efficient for including the influence of the non-uniformity on the measured ellipsometric quantities. However, the nodes and weights for the Gaussian quadrature must be calculated numerically if the non-uniformity is parameterized by the second or higher degree polynomial. A method for calculating these nodes and weights which is both efficient and numerically stable is presented. The presented method with a model using a second-degree polynomial is demonstrated on the sample of highly non-uniform polymer-like thin film characterized using variable-angle spectroscopic ellipsometry. The results are compared with those obtained using a model assuming the Wigner semicircle distribution.
ER  -

VOHÁNKA, Jiří, Daniel FRANTA, Martin ČERMÁK, Vojtěch HOMOLA, Vilma BURŠÍKOVÁ and Ivan OHLÍDAL. Ellipsometric characterization of highly non-uniform thin films with the shape of thickness non-uniformity modeled by polynomials. \textit{Optics Express}. Washington, D.C.: Optical Society of America, 2020, vol.~28, No~4, p.~5492-5506. ISSN~1094-4087. Available from: https://dx.doi.org/10.1364/OE.380657.

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