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

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Authors

NEČAS David VODÁK Jiří OHLÍDAL Ivan OHLÍDAL Miloslav MAJUMDAR Abhijit ZAJÍČKOVÁ Lenka

Year of publication 2015
Type Article in Periodical
Magazine / Source Applied Surface Science
MU Faculty or unit

Central European Institute of Technology

Citation
Doi http://dx.doi.org/10.1016/j.apsusc.2015.01.093
Field Optics, masers and lasers
Keywords Imaging spectrophotometry; Levenberg-Marquardt; Non-linear least-squares; Optical properties; Thickness mapping; Thin films
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Description 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. © 2015 Elsevier B.V. All rights reserved.
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