Numerical modeling of high-energy ion implantation using Fokker – Planck equations

Authors

  • Viktor I. Belko Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus
  • Sergey V. Lemeshevsky Institute of Mathematics, National Academy of Sciences of Belarus, Surhanava Street, 11, 220072, Minsk, Belarus
  • Mikhail M. Chuiko Institute of Mathematics, National Academy of Sciences of Belarus, Surhanava Street, 11, 220072, Minsk, Belarus

Keywords:

the high-energy ion implantation, the Fokker – Planck equation, difference schemes, stability

Abstract

The model of transport for high energetic ions in solids based on numerical solving of the boundary value problem for the Fokker – Planck equation is considered. The Fokker – Planck equation has a second order both on energetic and angular variables. We derived the difference scheme approximating the boundary value problem. It was shown, that the difference scheme is satisfied the grid maximum principle. There is estimated the stability of the difference solutions with respect to the initial data. We present the results of computational experiments on modeling of bismuth and phosphorus ion transport under ion implantation into the silicon with the initial energy of 1 and 50 MeV. We compared depth distribution profiles of stopped particles obtained using both the presented model and the model without angular scatte ring with the data of statistical simulations. 

Author Biographies

  • Viktor I. Belko, Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus

    PhD (physics and mathematics); head of the department of mathematical modeling and control, faculty of applied mathematics and computer sciences

  • Sergey V. Lemeshevsky, Institute of Mathematics, National Academy of Sciences of Belarus, Surhanava Street, 11, 220072, Minsk, Belarus

    PhD (physics and mathematics); deputy director

  • Mikhail M. Chuiko, Institute of Mathematics, National Academy of Sciences of Belarus, Surhanava Street, 11, 220072, Minsk, Belarus

    PhD (physics and mathematics); leading researcher

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Published

2018-01-24

Issue

No. 2 (2017): Journal of the Belarusian State University. Mathematics and Informatics

Section

Computational Mathematics

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How to Cite

[1]
Belko, V.I. et al. 2018. Numerical modeling of high-energy ion implantation using Fokker – Planck equations. Journal of the Belarusian State University. Mathematics and Informatics. 2 (Jan. 2018), 28–36.