Modification of the Scharfetter–Gummel method for calculating the flux of charged particles for simulation of a radio-frequency capacitive coupled discharge

V.S. Zheltukhin^a*, M.S. Fadeeva^b**, V.Ju. Chebakova^b***

^a Kazan National Research Technological University, Kazan, 420015 Russia

^b Kazan Federal University, Kazan, 420008 Russia

 E-mail: *vzheltukhin@gmail.com, **manysha-98@mail.ru, ***vchebakova@mail.ru

Received January 15, 2017

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Abstract

A numerical method of solving of nonstationary convection-diffusion equation for charged particle densities in capacitive coupled RF discharge is presented. The method allows us to calculate the particle concentration together with the flux density simultaneously at very rapid changes of particle density and electrical field in the electrode sheath. The method is a modification of the Scharfetter–Gummel algorithm. Firstly, implicit difference approximation of the equation constructed by the integro-interpolation method is used for calculating the charged particles density. Then the flux density of charged particles is calculated. Our modification allows to carry out the calculation at milder restriction on the time step than the Courant condition. In addition, diffusion coefficient may be variable unlike with the original Scharfetter–Gummel algorithm.

Keywords: mathematical modeling, radio-frequency capacitive coupled discharge, modified Scharfetter–Gummel method, convection-diffusion equation, flux density of charged particles

Acknowledgments. The study was supported by the Russian Science Foundation (project no. 16-11-10299).

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For citation: Zheltukhin V.S., Fadeeva M.S., Chebakova V.Ju. Modification of the Scharfetter–Gummel method for calculating the flux of charged particles for simulation of a radio-frequency capacitive coupled discharge. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2017, vol. 159, no. 4, pp. 444–457. (In Russian)

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