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Supercomputer Stochastic Simulation of Transient Anisotropic Diffusion-Reaction Processes with Application in Cathodoluminescence Imaging

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Parallel Computational Technologies (PCT 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1063))

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Abstract

This paper is devoted to supercomputer simulations of transient anisotropic diffusion processes with recombination in GaN semiconductors containing a set of threading dislocations. The random walk on arbitrary parallelepipeds and cubes based on a Monte Carlo algorithm suggested by K. K. Sabelfeld is here applied to a cathodoluminescence imaging problem. The computational time for large diffusion lengths and large numbers of dislocations is of several hours. For this reason, we carried out a parallel implementation of the code by distributing diffusion particle trajectories among several MPI processes and OpenMP threads. The parallel code made it possible to obtain the transient cathodoluminescence intensity, the concentration of survived particles, and the flux to the dislocation surfaces. To verify the algorithm implementation, we compared the simulation results with those obtained in the isotropic case by means of the random-walk-on-spheres algorithm and also with the exact solution of the isotropic diffusion-reaction equation.

The work was supported by the ICMMG SB RAS (budget project No. 0315-2019-0002).

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References

  1. Kalceff, M.A.S., Phillips, M.R.: Cathodoluminescence microcharacterization of the defect structure of quartz. Phys. Rev. B 52(5), 3122–3135 (1995). https://doi.org/10.1103/PhysRevB.52.3122

    Article  Google Scholar 

  2. Liu, W., Carlin, J.F., Grandjean, N., Deveaud, B., Jacopin, G.: Exciton dynamics at a single dislocation in GaN probed by picosecond time-resolved cathodoluminescence. Appl. Phys. Lett. 109(4), 042101-1–042101-5 (2016). https://doi.org/10.1063/1.4959832

    Article  Google Scholar 

  3. Hauser, A.J., et al.: Characterization of electronic structure and defect states of thin epitaxial \({\rm BiFeO}_3\) films by UV-visible absorption and cathodoluminescence spectroscopies. Appl. Phys. Lett. 92, 222901 (2008). https://doi.org/10.1063/1.2939101

    Article  Google Scholar 

  4. Boggs, S., Krinsley, D.: Application of Cathodoluminescence Imaging to the Study of Sedimentary Rocks. Cambridge University Press, New York (2006). https://doi.org/10.1017/cbo9780511535475.008

    Book  Google Scholar 

  5. Weisbuch, C., Piccardo, M., Martinelli, L., Iveland, J., Peretti, J., Speck, J.S.: The efficiency challenge of nitride light-emitting diodes for lighting. Phys. Status Solidi A 212(5), 885–1176 (2015). https://doi.org/10.1002/pssa.201570427

    Article  Google Scholar 

  6. Edwards, P.R., Martin, R.W.: Cathodoluminescence nano-characterization of semiconductors. Semicond. Sci. Technol. 26, 064005 (8 p.) (2011) https://doi.org/10.1088/0268-1242/26/6/064005

    Article  Google Scholar 

  7. Sabelfeld, K.K., Kaganer, V.M., Pfüller, C., Brandt, O.: Dislocation contrast in cathodoluminescence and electron-beam induced current maps on GaN(0001). J. Phys. D 50, 405101 (2017). https://doi.org/10.1088/1361-6463/aa85c8

    Article  Google Scholar 

  8. Rosner, S.J., Carr, E.C., Ludowise, M.J., Girolami, G., Erikson, H.I.: Correlation of cathodoluminescence inhomogeneity with microstructural defects in epitaxial GaN grown by metalorganic chemical-vapor deposition. Appl. Phys. Lett. 70(4), 420–422 (1997). https://doi.org/10.1063/1.118322

    Article  Google Scholar 

  9. Higgs, V., Lightowlers, E.C., Tajbakhsh, S., Wright, P.J.: Cathodoluminescence imaging and spectroscopy of dislocations in Si and \({\rm Si}_{1-x}Ge_x\) alloys. Appl. Phys. Lett. 61, 1087–1089 (1992). https://doi.org/10.1063/1.107676

    Article  Google Scholar 

  10. Phang, J.C.H., Pey, K.L., Chang, D.S.H.: A simulation model for cathodoluminescence in the scanning electron microscope. IEEE Transact. Electron Devices 39(4), 782–791 (1992). https://doi.org/10.1109/16.127466

    Article  Google Scholar 

  11. Sabelfeld, K.K.: Splitting and survival probabilities in stochastic random walk methods and applications. Monte Carlo Methods Appl. 22(1), 55–72 (2016). https://doi.org/10.1515/mcma-2016-0103

    Article  MathSciNet  MATH  Google Scholar 

  12. Sabelfeld, K.K.: Random walk on spheres method for solving drift-diffusion problems. Monte Carlo Methods Appl. 22(4), 265–275 (2016). https://doi.org/10.1515/mcma-2016-0118

    Article  MathSciNet  MATH  Google Scholar 

  13. Sabelfeld, K.K.: Random walk on spheres algorithm for solving transient drift-diffusion-reaction problems. Monte Carlo Methods Appl. 23(3), 189–212 (2017). https://doi.org/10.1515/mcma-2017-0113

    Article  MathSciNet  MATH  Google Scholar 

  14. Sabelfeld, K.K.: Monte Carlo Methods in Boundary Value Problems. Springer, Berlin (1991)

    Google Scholar 

  15. Irkhin, P., Biaggio, I.: Direct imaging of anisotropic exciton diffusion and triplet diffusion length in rubrene single crystals. Phys. Rev. Lett. 107, 017402 (2011). https://doi.org/10.1103/PhysRevLett.107.017402

    Article  Google Scholar 

  16. Lin, J.D.A., et al.: Systematic study of exciton diffusion length in organic semiconductors by six experimental methods. Mater. Horiz. 1, 280–285 (2014). https://doi.org/10.1039/c3mh00089c

    Article  Google Scholar 

  17. Sabelfeld, K.: Stochastic simulation methods for solving systems of isotropic and anisotropic drift-diffusion-reaction equations and applications in cathodoluminescence imaging, submitted to Probabilistic Engineering Mechanics (2018)

    Google Scholar 

  18. Milstein, G.N., Tretyakov, M.V.: Simulation of a space-time bounded diffusion. Ann. Appl. Probab. 9(3), 732–779 (1999)

    Article  MathSciNet  Google Scholar 

  19. Deaconu, M., Lejay, A.: A random walk on rectangles algorithm. Method. Comput. Appl. Probab. 8(1), 135–151 (2006). https://doi.org/10.1007/s11009-006-7292-3

    Article  MathSciNet  MATH  Google Scholar 

  20. Campillo, F., Lejay, A.: A Monte Carlo method without grid for a fractured porous domain model. Monte Carlo Methods Appli. De Gruyter 8(2), 129–147 (2002). https://doi.org/10.1515/mcma.2002.8.2.129

    Article  MathSciNet  MATH  Google Scholar 

  21. Sabelfeld, K.K., Kireeva, A.: Probability distribution of the life time of a drift-diffusion-reaction process inside a sphere with applications to transient cathodoluminescence imaging. Monte Carlo Methods Appl. 24(2), 79–92 (2018). https://doi.org/10.1515/mcma-2018-0007

    Article  MathSciNet  MATH  Google Scholar 

  22. Sabelfeld, K.K., Kireeva, A.E.: A meshless random walk on parallelepipeds algorithm for solving transient anisotropic diffusion-recombination equations and applications to cathodoluminescence imaging, submitted to Numerische Mathematik, (2018)

    Google Scholar 

  23. Walker, A.J.: An efficient method for generating discrete random variables with general distributions. ACM Transact. Math. Softw. 3(3), 253–256 (1977). https://doi.org/10.1145/355744.355749

    Article  MATH  Google Scholar 

  24. Rosenthal, J.S.: Parallel computing and Monte Carlo algorithms. Far East J. Theor. Stat. 4, 207–236 (2000)

    MathSciNet  MATH  Google Scholar 

  25. Esselink, K., Loyens, L.D.J.C., Smit, B.: Parallel Monte Carlo Simulations. Phys. Rev. E 51(2), 1560–1568 (1995). https://doi.org/10.1103/physreve.51.1560

    Article  Google Scholar 

  26. MVS-10P cluster, JSCC RAS. http://www.jscc.ru

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Authors and Affiliations

  1. Institute of Computational Mathematics and Mathematical Geophysics, Novosibirsk, Russia

    Anastasiya Kireeva & Karl K. Sabelfeld

Authors
  1. Anastasiya Kireeva
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  2. Karl K. Sabelfeld
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Correspondence to Anastasiya Kireeva .

Editor information

Editors and Affiliations

  1. South Ural State University, Chelyabinsk, Russia

    Leonid Sokolinsky

  2. South Ural State University, Chelyabinsk, Russia

    Mikhail Zymbler

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Kireeva, A., Sabelfeld, K.K. (2019). Supercomputer Stochastic Simulation of Transient Anisotropic Diffusion-Reaction Processes with Application in Cathodoluminescence Imaging. In: Sokolinsky, L., Zymbler, M. (eds) Parallel Computational Technologies. PCT 2019. Communications in Computer and Information Science, vol 1063. Springer, Cham. https://doi.org/10.1007/978-3-030-28163-2_19

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  • DOI: https://doi.org/10.1007/978-3-030-28163-2_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-28162-5

  • Online ISBN: 978-3-030-28163-2

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