Advertisement

Russian Microelectronics

, Volume 38, Issue 5, pp 291–298 | Cite as

Computer simulation of the processes of formation of microclusters on the basis of scaling invariance of random walk

  • A. V. Mozhaev
  • A. V. ProkaznikovEmail author
Micro- and Nanostructure Modeling and Simulation

Abstract

On the basis of scaling invariance of the process of random walk, a discrete three-dimensional algorithm is developed and implemented for computer simulation of the multistage processes of formation of porous clusters in a crystal matrix. A software package is worked out that provides the simulation of dynamic processes of clustering deep in the crystals with allowance for surface processes, applied external fields, and chemical reactions accompanying the processes of clustering. The morphological pattern of pores formed by the simulation is correlated with the behavior of the current-voltage characteristic of anodizing.

PACS

82.75.-z 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Nallet, P., Chassaing, E., Walls, M.G., and Hytch, M.J., Interface Characterization in Electrodeposited Cu-Co Multilayers, J. Appl. Phys., 1996, vol. 79, no. 9, pp. 6884–6889.CrossRefGoogle Scholar
  2. 2.
    Aravamudhan, S., Luongo, K., Poddar, P., Srikanth, H., and Bhatsali, S., Porous Silicon Templates for Electrodeposition of Nanostructures, Appl. Phys., A, 2007, vol. 83, no. 4, pp. 773–780.CrossRefGoogle Scholar
  3. 3.
    Feder, J., Fractals, New-York: Plenum, 1988.zbMATHGoogle Scholar
  4. 4.
    Fractals in Physics. Pietronero, L. and Tosatti, E., Eds., Amsterdam: North Holland, 1986.Google Scholar
  5. 5.
    Peitgen, H.-O. and Richter, P.H., The Beauty of Fractals. Images of Complex Dynamical Systems. Berlin: Springer-Verlag, 1986.zbMATHGoogle Scholar
  6. 6.
    Ross, J.C., Fractal Surfaces, New-York: Plenum, 1994.Google Scholar
  7. 7.
    Hockney, R.W., and Eastwood, J.W., Computer Simulation Using Particles, New York: McGraw-Hill, 1981.Google Scholar
  8. 8.
    Fujita, H., Kobayashi, K., Kawai, T., and Shiga, K., Hall Effect of Photoelectrons in Cadmium Sulfide, J. Phys. Soc. Jpn., 1965, vol. 20, no. 1, pp. 109–122.CrossRefGoogle Scholar
  9. 9.
    Gould, H. and Tobochnik, J., An Introduction to Computer Simulation Methods: Applications to Physical Systems, Reading, Mass.: Addison-Wesley, 1988.Google Scholar
  10. 10.
    Smith, R.L., Chuang, S.-F., and Collins, S.D., A Theoretical Model of the Formation Morphologies of Porous Silicon, J. Electr. Mater., 1988, vol. 17, no. 6, pp. 533–541.CrossRefGoogle Scholar
  11. 11.
    Smith, R.L. and Collins, S.D., Porous Silicon Formation Mechanisms, J. Appl. Phys., 1992, vol. 71, no. 8, pp. R1–R22.CrossRefGoogle Scholar
  12. 12.
    Chuang, S.-F., Collins, S.D., and Smith, R.L., Preferential Propagation of Pores During the Formation of Porous Silicon: a Transmission Electron Microscopy Study, Appl. Phys. Lett., 1989, vol. 55, no. 7, pp. 675–677.CrossRefGoogle Scholar
  13. 13.
    Kaplii, S.A., Prokaznikov, A.V., and Rud’, N.A., Clustering in determinate and stochastic fields, Zh. Tekh. Fiz., 2004, vol. 74, no. 5, pp. 6–11 [Tech. Phys. (Engl. Transl.), vol. 49, no. 5, pp. 526–531].Google Scholar
  14. 14.
    Kaplii, S.A., Prokaznikov, A.V., and Rud’, N.A., Clusterization of Stochastically Wandering Particles in Potential Fields, Izv. Vyssh. Uch. Zaved. Fiz., 2004, no. 6, pp. 31–38 [Russ. Phys. J. (Engl. Transl.), vol. 47, no. 6, pp. 609–616].Google Scholar
  15. 15.
    Kvasnikov, I. A., Termodinamika i Statisticheskaya Fizika. Teoriya Neravnovesnykh sistem (Thermodynamics and Statistical Physics. Theory of Nonequilibrium Systems), Moscow: Mosk. Gos. Univ., 1987.Google Scholar
  16. 16.
    Isihara, A., Statistical Physics, New York: Academic, 1971.Google Scholar
  17. 17.
    Landau, L.D. and Lifshits, E.M., Gidrodinamika (Hydrodynamics), Moscow: Nauka, 1988 [Hydrodynamics (Engl. Transl.), Oxford: Pergamon, 1990)].Google Scholar
  18. 18.
    Mozhaev, A.V., Buchin, E.Yu., and Prokaznikov, A.V., Dynamic Model of Three-Dimensional Cluster Formation, Pis’ma Zh. Tekh. Fiz., 2008, vol. 34, no.10, pp. 53–60 [Tech. Phys. Lett. (Engl. Transl.), vol. 34, no. 5, pp. 431–434].Google Scholar
  19. 19.
    Klyatskin, V.I. and Gurarie, D., Coherent Phenomena in Stochastic Dynamical Systems, Usp. Fiz. Nauk, 1999, vol. 169, no. 2, 171–207 [Phys.-Usp. (Engl. Transl.), vol. 42, no. 2, pp. 165–198].CrossRefGoogle Scholar
  20. 20.
    Kaplii, S. A., Prokaznikov, A.V., and Rud’, N.A., A Discrete Model of Adsorption with Three States, Pis’ma Zh. Tekh. Fiz., 2004, vol. 30, no.14, pp. 46–52 [Tech. Phys. Lett. (Engl. Transl.), vol. 30, no. 7, pp. 595–597].Google Scholar
  21. 21.
    Kaplii, S.A., Prokaznikov, A.V., and Rud’, N.A., Discrete Model of Adsorption with a Finite Number of States, Zh. Tekh. Fiz., 2005, vol. 75, no. 12, pp. 1–9 [Tech. Phys. (Engl. Transl.), vol. 50, no. 12, pp. 1535–1543].Google Scholar
  22. 22.
    Vanag, V.K., Study of Spatially Extended Dynamical Systems Using Probabilistic Cellular Automata, Usp. Fiz. Nauk, 1999, vol. 169, no. 5, 481–505 [Phys.-Usp. (Engl. Transl.), vol. 42, no. 5, p. 413–434, 1999].CrossRefGoogle Scholar
  23. 23.
    Prokaznikov, A.V. and Svetovoy, V.B., Fluorine Penetration through the Whole Silicon Wafer during Anodization in HF Solution, Phys. Low-Dim. Structures, 2002, vol. 9/10, pp. 65–69.Google Scholar
  24. 24.
    Lehmann, V., The Physics of Macropore Formation in Low-Doped n-Type Silicon, J. Electrochem. Soc., 1993, vol. 140, no. 10, pp. 2836–2843.CrossRefGoogle Scholar
  25. 25.
    Buchin, E.Yu. and Prokaznikov, A.V., The Mechanisms of Formation of Pores of Different Morphology, Mikroelectronika, 1998, vol. 27, no. 2, pp. 107–113.Google Scholar
  26. 26.
    Sokolov, A.V., Mathematical Models and Algorithms of Optimal Control of Dynamic Data Structures, Extended Abstract of Doctoral (Phys.-Math.) Dissertation, Saint Petersburg, St. Petersburg Gos. Univ., 2006.Google Scholar
  27. 27.
    Shkarupa, E.V., Error Estimation and Optimization of the Functional Algorithms of a Random Walk on a Grid Which Are Applied to Solving the Dirichlet Problem for the Helmholtz Equation, Sibir. Math. Zh., 2003, vol. 44, no. 5, pp. 1163–1182 [Siber. Math. J. (Engl. Transl.), vol. 44, no. 5, pp. 908–925].zbMATHMathSciNetGoogle Scholar
  28. 28.
    Bisi, O., Osicini, S., and Pavesi, L., Porous Silicon: a Quantum Sponge Structure for Silicon Based Electronics, Surf. Sci. Reports, 2000, vol. 38, no.1–3, pp. 1–126.CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  1. 1.Yaroslavl State UniversityYaroslavlRussia
  2. 2.Institute of Physics and Technology (Yaroslavl Branch)Russian Academy of SciencesMoscowRussia

Personalised recommendations