Publication detail

Simultaneous determination of dispersion model parameters and local thickness of thin films by imaging spectrophotometry

NEČAS, D. VODÁK, J. OHLÍDAL, I. OHLÍDAL, M. MAJUMDAR, A. ZAJÍČKOVÁ, L.

Original Title

Simultaneous determination of dispersion model parameters and local thickness of thin films by imaging spectrophotometry

English Title

Simultaneous determination of dispersion model parameters and local thickness of thin films by imaging spectrophotometry

Type

journal article in Web of Science

Language

en

Original Abstract

A least-squares data fitting procedure is developed for the analysis of measurements of thin films non-uniform in thickness by imaging spectroscopic reflectometry. It solves the problem of simultaneous least-squares fitting of film thicknesses in all image pixels together with shared dispersion model parameters. Since the huge number of mutually correlated fitting parameters prevents a straightforward application of the standard Levenberg–Marquardt algorithm, the presented procedure exploits the special structure of the specific least-squares problem. The free parameters are split into thicknesses and dispersion model parameters. Both groups of parameters are fitted alternately, utilising an unmodified Levenberg–Marquardt algorithm, correcting however the thicknesses during the dispersion model fitting step to preserve effective optical thicknesses. The behaviour of the algorithm is studied using experimental data of two highly non-uniform thin films of different materials, SiOxCyHz and CNx:H, and by numerical simulations using artificial data. It is found that the optical thickness correction enables the procedure to converge rapidly, permitting the analysis of large imaging spectroscopic reflectometry data sets with reasonable computational resources.

English abstract

A least-squares data fitting procedure is developed for the analysis of measurements of thin films non-uniform in thickness by imaging spectroscopic reflectometry. It solves the problem of simultaneous least-squares fitting of film thicknesses in all image pixels together with shared dispersion model parameters. Since the huge number of mutually correlated fitting parameters prevents a straightforward application of the standard Levenberg–Marquardt algorithm, the presented procedure exploits the special structure of the specific least-squares problem. The free parameters are split into thicknesses and dispersion model parameters. Both groups of parameters are fitted alternately, utilising an unmodified Levenberg–Marquardt algorithm, correcting however the thicknesses during the dispersion model fitting step to preserve effective optical thicknesses. The behaviour of the algorithm is studied using experimental data of two highly non-uniform thin films of different materials, SiOxCyHz and CNx:H, and by numerical simulations using artificial data. It is found that the optical thickness correction enables the procedure to converge rapidly, permitting the analysis of large imaging spectroscopic reflectometry data sets with reasonable computational resources.

Keywords

Imaging spectrophotometry; Thin films; Optical properties; Thickness mapping; Non-linear least-squares; Levenberg–Marquardt

RIV year

2015

Released

23.01.2015

Publisher

Applied Surface Science

Pages from

149

Pages to

155

Pages count

7

URL

BibTex


@article{BUT115038,
  author="David {Nečas} and Jiří {Vodák} and Ivan {Ohlídal} and Miloslav {Ohlídal} and Abhijit {Majumdar} and Lenka {Zajíčková}",
  title="Simultaneous determination of dispersion model parameters and local thickness of thin films by imaging spectrophotometry",
  annote="A least-squares data fitting procedure is developed for the analysis of measurements of thin films non-uniform in thickness by imaging spectroscopic reflectometry. It solves the problem of simultaneous least-squares fitting of film thicknesses in all image pixels together with shared dispersion model parameters. Since the huge number of mutually correlated fitting parameters prevents a straightforward application of the standard Levenberg–Marquardt algorithm, the presented procedure exploits the special structure of the specific least-squares problem. The free parameters are split into thicknesses and dispersion model parameters. Both groups of parameters are fitted alternately, utilising an unmodified Levenberg–Marquardt algorithm, correcting however the thicknesses during the dispersion model fitting step to preserve effective optical thicknesses. The behaviour of the algorithm is studied using experimental data of two highly non-uniform thin films of different materials, SiOxCyHz and CNx:H, and by numerical simulations using artificial data. It is found that the optical thickness correction enables the procedure to converge rapidly, permitting the analysis of large imaging spectroscopic reflectometry data sets with reasonable computational resources.",
  address="Applied Surface Science",
  chapter="115038",
  doi="10.1016/j.apsusc.2015.01.093",
  howpublished="online",
  institution="Applied Surface Science",
  number="350",
  year="2015",
  month="january",
  pages="149--155",
  publisher="Applied Surface Science",
  type="journal article in Web of Science"
}