A Sellmeier extended empirical model for the spectral dependence of the refractive index applied to the case of thin-film silicon and some of its more common alloys
Through modeling thin-film silicon’s refractive index’s spectral dependence, a hybridized empirical approach has been developed. Noting that the empirical polynomial fit paradigm of Moghaddam and O’Leary (J Mater Sci: Mater Electron 30:1637–1646, 2019) has a spectral range of validity that is limited to the exact spectral range over which the primary experimental data set is available, we suggest a means whereby this spectral range may be extended. In particular, by splining a first-order Sellmeier equation onto the long-wavelength side of such a polynomial fit, we have been able to increase the spectral range over which our empirical approach to modeling the refractive index’s spectral dependence is valid. The Sellmeier coefficients corresponding to this first-order Sellmeier ‘extension’ are selected so as to ensure continuity in the refractive index’s spectral dependence, and in that of its derivative, across the boundary between the two regimes, i.e., the polynomial fit regime and the Sellmeier ‘extension’ regime. We then apply this approach to a number of thin-film silicon cases, as well as to two of its more common alloys with other materials, and have found that it adequately captures the experimentally observed spectral dependencies. The coefficients associated with these polynomial fits, as well as that associated with the corresponding first-order Sellmeier equations, are presented in tabular form. We believe that the simplicity of this model offers the thin-film silicon community with a distinct advantage when compared with other approaches to modeling thin-film silicon’s refractive index’s spectral dependence.
The authors gratefully acknowledge financial support from the Natural Sciences and Engineering Research Council of Canada and MITACS. Inspiring discussions with Mr. Calum Hughes, of Advanced Micro Biosciences, Inc., are also acknowledged. We would also like to thank the anonymous referees, whose constructive criticisms helped shape the final form of this manuscript.
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