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@article{1598856, author = {Vohánka, Jiří and Nečas, David and Franta, Daniel}, article_number = {6}, doi = {http://dx.doi.org/10.1116/1.5122276}, keywords = {Spectroscopy; Series expansion; Density of states; Phonons; Optical properties; Optical constants; Gaussian broadening}, language = {eng}, issn = {2166-2746}, journal = {Journal of Vacuum Science & Technology B}, title = {Evaluation of the Dawson function and its antiderivative needed for the Gaussian broadening of piecewise polynomial functions}, url = {https://doi.org/10.1116/1.5122276}, volume = {37}, year = {2019} }
TY - JOUR ID - 1598856 AU - Vohánka, Jiří - Nečas, David - Franta, Daniel PY - 2019 TI - Evaluation of the Dawson function and its antiderivative needed for the Gaussian broadening of piecewise polynomial functions JF - Journal of Vacuum Science & Technology B VL - 37 IS - 6 SP - "062909-1"-"062909-7" EP - "062909-1"-"062909-7" SN - 21662746 KW - Spectroscopy KW - Series expansion KW - Density of states KW - Phonons KW - Optical properties KW - Optical constants KW - Gaussian broadening UR - https://doi.org/10.1116/1.5122276 L2 - https://doi.org/10.1116/1.5122276 N2 - 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. ER -
VOHÁNKA, Jiří, David NEČAS and Daniel FRANTA. Evaluation of the Dawson function and its antiderivative needed for the Gaussian broadening of piecewise polynomial functions. \textit{Journal of Vacuum Science \&{} Technology B}. 2019, vol.~37, No~6, p.~''062909-1''-''062909-7'', 7 pp. ISSN~2166-2746. Available from: https://dx.doi.org/10.1116/1.5122276.
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