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Cellular Automata Model of Electrons and Holes Annihilation in an Inhomogeneous Semiconductor

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9251))

Abstract

An asynchronous CA model of annihilation of electrons and holes in an inhomogeneous semiconductor is presented. The model is based on the Monte Carlo algorithm of electron-hole annihilation. CA model allows us to study the dynamics of electron-hole spatial distribution. The annihilation process is simulated for different values of the modeling parameters. The spatial distributions of particles are analyzed. It is found out that a segregation, i.e., a spatial separation of electron and hole clusters occurs. This happens under certain conditions on the diffusion and tunneling rates. In addition, the parallel implementation of the CA model of the annihilation is performed using OpenMP standard. The parallel implementation makes it possible to perform averaging over a rich ensemble of initial distributions of particles.

Supported by Russian Science Foundation under Grant 14-11-00083.

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References

  1. DenBaars, S.P.: Gallium-nitride-based materials for blue to ultraviolet optoelectronics devices. Proc. IEEE 85(11), 1740–1749 (1997). doi:10.1109/5.649651

    Article  Google Scholar 

  2. Brosseau, C.-N., Perrin, M., Silva, C., Lenonelli, R.: Carrier recombination dynamics in \(In_xGa_{1-x}N/GaN\) multiple quantum wells, Phys. Rev. B 88 (2010), Article ID 085305

    Google Scholar 

  3. Caro, M., Schulz, S., and O’Reilly, E.: Theory of local electric polarization and its relation to internal strain: Impact on polarization potential and electronic properties of group-III nitrides, Phys. Rev. B, vol. 88 (2013), Article ID 214103

    Google Scholar 

  4. Sabelfeld, K.K., Brandt, O., Kaganer, V.M.: Stochastic model for the fluctuation-limited reaction-diffusion kinetics in inhomogeneous media based on the nonlinear Smoluchowski equations. J. Math. Chem 53(2), 651–669 (2015)

    Article  MathSciNet  Google Scholar 

  5. Sabelfeld, K.K., Levykin, A.I., Kireeva, A.E.: Stochastic simulation of fluctuation-induced reaction-diffusion kinetics governed by Smoluchowski equations. Monte Carlo Methods Appl. 21(1), 33–48 (2015)

    Article  MathSciNet  Google Scholar 

  6. Sabelfeld, K.K., Kolodko, A.A.: Stochastic Lagrangian models and algorithms for spatially inhomogeneous Smoluchowski equation. Math. Comput. Simul. 61, 115–137 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  7. Toffoli, T., Margolus N.: Cellular Automata Machines: A New Environment for Modeling. MIT Press, USA (1987)

    Google Scholar 

  8. Weimar, J.R., Tyson, J.J.W., Layne, T.: Diffusion and wave propagation in cellular automaton model of excitable media. Physica D 55, 309–327 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  9. Bandman, O.L.: Mapping physical phenomena onto CA-models, AUTOMATA-2008. In: Adamatzky, A., Alonso-Sanz, R., Lawniczak, A., Martinez, G.J., Morita, K., Worsch, T. (eds.) Theory and Applications of Cellular Automata, pp. 381–397. Luniver Press, UK (2008)

    Google Scholar 

  10. Bandman, O.L.: Cellular automatic models of spatial dynamics. Syst. Inform. Methods Models Mod. Program. 10, 59–113 (2006). (In Russian)

    Google Scholar 

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Correspondence to A. E. Kireeva .

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© 2015 Springer International Publishing Switzerland

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Kireeva, A.E., Sabelfeld, K.K. (2015). Cellular Automata Model of Electrons and Holes Annihilation in an Inhomogeneous Semiconductor. In: Malyshkin, V. (eds) Parallel Computing Technologies. PaCT 2015. Lecture Notes in Computer Science(), vol 9251. Springer, Cham. https://doi.org/10.1007/978-3-319-21909-7_18

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  • DOI: https://doi.org/10.1007/978-3-319-21909-7_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21908-0

  • Online ISBN: 978-3-319-21909-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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