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Regularities of the formation of fractal porous clusters in silicon

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Abstract

Using the experimental results and computer simulation data, we demonstrate the existence of technological regimes of pore formation in the electrolyte-silicon system that are controlled by the delivery of holes to the interface between the two media. We develop a dynamic sequential 3D computer model for describing the formation of porous clusters in silicon with regard to different aspects of anodization, including the electric potential variation in the system at the change in configuration of the interface between the crystal and electrolyte. We investigate features of the hole transport regime described by equations scale-invariant relative to the affine transformation of space and time variables. Porous clusters formed using such technological regimes are characterized by the fractal self-similarity.

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References

  1. Smith, R.L. and Collins, S.D., J. Appl. Phys., 1992, vol. 71, no. 8, pp. R1–R22.

    Article  Google Scholar 

  2. John, Y.C. and Singh, V.A., Phys. Rep., 1995, vol. 263, pp. 93–151.

    Article  Google Scholar 

  3. Buchin, E.Yu., Churilov, A.B., and Prokaznikov, A.V., Appl. Surf. Sci., 1996, vol. 102, pp. 431–435.

    Article  Google Scholar 

  4. Wesolowsky, M., Phys. Rev. B, 2002, vol. 66, p. 205207.

    Article  Google Scholar 

  5. Nychyporuk, T., Lysenko, V., and Barbier, D., Phys. Rev. B, 2005, vol. 71, p. 115402.

    Article  Google Scholar 

  6. Zhong, J.X. and Mosserii, R., J. Non-Crystalline Solids, 1993, vols. 162–164, pp. 969–972.

    Article  Google Scholar 

  7. Huang, Y. M., Zhai, B. G., and Zhou, F. F., Appl. Surf. Sci., 2008, vol. 254, no. 13, pp. 4139–4143.

    Article  Google Scholar 

  8. Ben-Chorin, M., Moller, F., Koch, F., Schirmacher, W., and Eberhard, M., Phys. Rev. B, 1995, vol. 51, no. 4, pp. 2199–2213.

    Article  Google Scholar 

  9. Smith, R.L., Chuang, S.-F., and Collins, S.D., J. Electron. Mater., 1988, vol. 17, no. 6, pp. 533–541.

    Article  Google Scholar 

  10. Chuang, S.-F., Collins, S.D., and Smith, R.L., Appl. Phys. Lett., 1989, vol. 55, no. 7, pp. 675–677.

    Article  Google Scholar 

  11. Erlebacher, J., Sieradzki, K., and Searson, P.C., J. Appl. Phys., 1994, vol. 76, no. 1, pp. 182–187.

    Article  Google Scholar 

  12. Yan, H. and Hu, X., J. Appl. Phys., 1993, vol. 73, no. 9, pp. 4324–4331.

    Article  Google Scholar 

  13. Weng, Y.M., Qiu, J.Y., Zhou, Y.H., and Zong, X.F., J. Vac. Sci. Technol., vol. 14, no. 4, pp. 2505–2509.

  14. Kang, Y. and Jorne, J., J. Electrochem. Soc., 1993, vol. 140, no. 8, pp. 2258–2265.

    Article  Google Scholar 

  15. Valance, A., Phys. Rev. B, 1995, vol. 52, no. 11, pp. 8323–8336.

    Article  Google Scholar 

  16. Mullins, W.W. and Sekerka, R.F., J. Appl. Phys., 1964, vol. 35, no. 2, pp. 444–451.

    Article  Google Scholar 

  17. Buchin, E.Yu. and Prokaznikov, A.V., Tech. Phys. Lett., 1997, vol. 23, no. 3, pp. 244–245.

    Article  Google Scholar 

  18. Buchin, E.Yu. and Prokaznikov, A.V., Russ. Microelectron., 1998, vol. 27, no. 2, p. 86.

    Google Scholar 

  19. Prokaznikov, A.V. and Buchin, E.Yu., Phys. Low-Dim. Struct., 1997, vol. 5/6, pp. 47–52.

    Google Scholar 

  20. Kochergin, V. and Foell, H., Porous Semiconductors. Optical Properties and Applications, London: Springer-Verlag, 2009.

    Book  Google Scholar 

  21. Lashin, A.M., Preprint of Inst. of Appl. Math., Russ. Acad. Sci., Moscow, 2001.

    Google Scholar 

  22. Lehmann, V. and Gosele, U., Appl. Phys. Lett., 1991, vol. 58, no. 8, pp. 856–858.

    Article  Google Scholar 

  23. Zhang, X.G., J. Electrochem. Soc., 1991, vol. 138, no. 12, pp. 3750–3756.

    Article  Google Scholar 

  24. Trucks, G.W., Raghavachari, K., Higashi, G.S., and Chabal, Y.J., Phys. Rev. Lett., 1990, vol. 65, no. 4, pp. 504–507.

    Article  Google Scholar 

  25. Volkov, V.T., Kryuchkov, S.V., Obukhov, I.A., and Rumyantsev, S.V., USSR Comput. Math. Math. Phys., 1989, vol. 29, no. 4, pp. 132–138.

    Article  MathSciNet  Google Scholar 

  26. Engle, V.L., Dirks, H.K., and Meinertzhagen, B., Proc. IEEE, Moscow, 1983, vol. 71, no 1, pp. 14–42.

    Google Scholar 

  27. Klyatskin, V.I. and Gurarii, D., Phys.-Uspekhi, 1999, vol. 42, no. 2, pp. 165–198.

    Article  Google Scholar 

  28. Klyatskin, V.I., Ocherki po dinamike stokhasticheskikh system (On the Dynamics of Stochastic Systems), Moscow: Krasand, 2012 [in Russian].

    Google Scholar 

  29. Allen, E., Modelling with Ito Stochastic Differential Equation, New York: Springer, 2007, p. 230.

    Google Scholar 

  30. Zel’dovich, Ya.B. and Myshkis, A.D., Elementy matematicheskoi fiziki. Sreda iz nevzaimodeistvuyushchikh chastits (Elements of Mathematical Physics. A Medium for Noninteracting Particles), Moscow: Nauka, 1973 [in Russian].

    Google Scholar 

  31. Feder, J., Fractals, New York: Plenum Press, 1988.

    Book  MATH  Google Scholar 

  32. Kvasnikov, I.A., Termodinamika i statisticheskaya fizika. Teoriya neravnovesnykh system (Thermodynamics and Statistical Physics. Theory of Nonequilibrium Systems), Moscow: Editorial URSS, 2003 [in Russian].

    Google Scholar 

  33. Isikhara, A., Statistical Physics, London-New York: Academic Press, 1971.

    Google Scholar 

  34. Landau, L.D. and Lifshits, E.M., Gidrodinamika (Hydrodynamics), Moscow: Nauka, 1986, vol. 6 [in Russian].

    Google Scholar 

  35. Pogorelov, A.V., Differentsial’naya geometriya (Differential Geometry), Moscow: Nauka, 1974 [in Russain].

    Google Scholar 

  36. Dubrovin, B.A., Novikov, S.P., and Fomenko, F.T., Sovremennaya geometriya (Modern Geometry), Moscow: Nauka, 1979 [in Russian].

    Google Scholar 

  37. Jackson, J.-D., Classical Electrodynamics, New York: John Wiley & Sons, 1962.

    Google Scholar 

  38. Fractals in Physics, Pietronero, E. and Tozatti, L., Eds., Amsterdam: North-Holland., 1986.

    Google Scholar 

  39. Turkevich, L.A. and Scher, H., Phys. Rev. Lett., 1985, vol. 55, no. 9, pp. 1026–1029.

    Article  MathSciNet  Google Scholar 

  40. Mozhaev, A.V., Buchin, E.Yu., and Prokaznikov, A.V., Tech. Phys. Lett., 2008, vol. 34, p. 431.

    Article  Google Scholar 

  41. Mozhaev, A.V., Buchin, E.Yu., and Prokaznikov, A.V., J. Tech. Phys., 2009, vol. 54, no. 3, pp. 327–332.

    Article  Google Scholar 

  42. Mozhaev, A.V. and Prokaznikov, A.V., Russ. Microelectron., 2009, vol. 38, no. 5, p. 291.

    Article  Google Scholar 

  43. Aravamudhan, S., Luongo, K., Poddar, P., Srikanth, H., and Bhatsali, S., Appl. Phys. A, 2007, vol. 83, pp. 773–780.

    Article  Google Scholar 

  44. Nittmann, I., Daccord, G., Stanley, H., In Fractals in Physics, Pietronero, E. and Tozatti, L., Eds., Amsterdam: North-Holland., 1986.

  45. Happo, N., Fujiwara, N., Iwamatsu, M., and Horii, K., Jpn. J. Appl. Phys., 1998, vol. 37, pp. 3951–3953.

    Article  Google Scholar 

  46. Malyutin, V.M. and Sklyarova, E.A., Komp’yuternoe modelirovanie fizicheskikh yavlenii (Computer Simulation of Physical Phenomena), Tomsk: Izd. TPU, 2004 [in Russian].

    Google Scholar 

  47. Averkiev, N.S., Pikus, G.E., and Shmatov, M.L., Sov. Phys. Solid State, 1988, vol. 30, p. 1884.

    Google Scholar 

  48. Buchin, E.Yu. and Prokaznikov, A.V., Tech. Phys. Lett., 1997, vol. 23, no. 3, pp. 244–245.

    Article  Google Scholar 

  49. Da, Costa, R.C.T., Phys. Rev. A, 1981, vol. 23, no. 4, pp. 1982–1987.

    Article  MathSciNet  Google Scholar 

  50. Magarill, L.I., Chaplik, A.V., and Entin, M.V., Phys.-Uspekhi, 2005, vol. 48, no. 9, pp. 953–958.

    Article  Google Scholar 

  51. Randrianalisoa, J. and Baillis, D., J. Appl. Phys., 2008, vol. 103, p. 053052.

    Article  Google Scholar 

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Authors and Affiliations

  1. Yaroslavl State University, ul. Sovetskaya 10, Yaroslavl, 150000, Russia

    N. A. Arzhanova, A. V. Mozhaev & A. V. Prokaznikov

  2. Institute of Physics and Technology, Russian Academy of Sciences, Yaroslavl Branch, ul. Universitetskaya 21, Yaroslavl, 150007, Russia

    A. V. Prokaznikov

Authors
  1. N. A. Arzhanova
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  2. A. V. Mozhaev
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  3. A. V. Prokaznikov
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Correspondence to A. V. Prokaznikov.

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Original Russian Text © N.A. Arzhanova, A.V. Mozhaev, A.V. Prokaznikov, 2014, published in Mikroelektronika, 2014, Vol. 43, No. 3, pp. 212–227.

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Arzhanova, N.A., Mozhaev, A.V. & Prokaznikov, A.V. Regularities of the formation of fractal porous clusters in silicon. Russ Microelectron 43, 212–225 (2014). https://doi.org/10.1134/S1063739714030032

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