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

J 2019

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

VOHÁNKA, Jiří, David NEČAS a Daniel FRANTA

Základní údaje

Originální název

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

Autoři

VOHÁNKA, Jiří (203 Česká republika, garant, domácí), David NEČAS (203 Česká republika, domácí) a Daniel FRANTA (203 Česká republika, domácí)

Vydání

Journal of Vacuum Science & Technology B, 2019, 2166-2746

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10306 Optics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 1.511

Kód RIV

RIV/00216224:14310/19:00112014

Organizační jednotka

Přírodovědecká fakulta

DOI

http://dx.doi.org/10.1116/1.5122276

UT WoS

000522021700060

Klíčová slova anglicky

Spectroscopy; Series expansion; Density of states; Phonons; Optical properties; Optical constants; Gaussian broadening

Štítky

rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 17. 4. 2020 17:17, Mgr. Marie Šípková, DiS.

Anotace

V originále

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.

Návaznosti

LO1411, projekt VaV

Název: Rozvoj centra pro nízkonákladové plazmové a nanotechnologické povrchové úpravy (Akronym: CEPLANT plus)

Investor: Ministerstvo školství, mládeže a tělovýchovy ČR, Rozvoj centra pro nízkonákladové plazmové a nanotechnologické povrchové úpravy

LQ1601, projekt VaV

Název: CEITEC 2020 (Akronym: CEITEC2020)

Investor: Ministerstvo školství, mládeže a tělovýchovy ČR, CEITEC 2020

Citovat

VOHÁNKA, Jiří, David NEČAS a Daniel FRANTA. Evaluation of the Dawson function and its antiderivative needed for the Gaussian broadening of piecewise polynomial functions. Journal of Vacuum Science & Technology B. 2019, roč. 37, č. 6, s. "062909-1"-"062909-7", 7 s. ISSN 2166-2746. Dostupné z: https://dx.doi.org/10.1116/1.5122276.

@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 a 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, roč.~37, č.~6, s.~''062909-1''-''062909-7'', 7 s. ISSN~2166-2746. Dostupné z: https://dx.doi.org/10.1116/1.5122276.

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