Evaluation of the Dawson function and its antiderivative needed for the Gaussian broadening of piecewise polynomial functions

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Authors

VOHÁNKA Jiří NEČAS David FRANTA Daniel

Year of publication 2019
Type Article in Periodical
Magazine / Source Journal of Vacuum Science & Technology B
MU Faculty or unit

Faculty of Science

Citation
Web https://doi.org/10.1116/1.5122276
Doi http://dx.doi.org/10.1116/1.5122276
Keywords Spectroscopy; Series expansion; Density of states; Phonons; Optical properties; Optical constants; Gaussian broadening
Description The broadening of a sharp (unbroadened) dielectric function is a fruitful approach to the construction of models of dielectric response of materials. It naturally includes structural disorder or finite state lifetime and allows parameterization of such effects. The unbroadened function is often taken as a piecewise polynomial. Broadening it with the Lorentzian then leads to relatively simple analytical formulae. The Gaussian broadening, however, requires evaluation of several special functions, including the antiderivative of the Dawson function which is not generally available in mathematical libraries. Recently, the authors described the simple recurrent formulae for the construction of a Gaussian-broadened piecewise polynomial model of a complex dielectric function using three special functions, the error function, the Dawson function, and its antiderivative. In this paper, for the Dawson function and its antiderivative an efficient evaluation method is developed enabling the utilization of this model in optical spectra fitting. The effectiveness of this approach is illustrated using elementary and real-world examples of complex dielectric function models.
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