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The role of surface diffusion of adatoms in the formation of nanowire crystals

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Abstract

A model of the formation of nanowire crystals on surfaces activated by droplets of the catalyst of growth is developed. In the model, the diffusion of adatoms from the surface of the substrate to the lateral surface of the crystals is taken into account. The exact solution of the diffusion problem for the flow of adatoms from the surface to the nanowire crystals is obtained, and the particular cases of the solution for the short and long diffusion lengths of adatoms, λs, are analyzed. A general expression for the length of the nanowire crystals, L, in relation to their radius R and to the conditions of growth is derived. The expression is applicable to a large variety of technologies of growth. The theoretical results are compared with the experimental dependences L(R) in the range of R = 20–250 nm for GaAs nanowire crystals grown by molecular-beam epitaxy on the GaAs (111) V Ga surface activated by Au. It is shown that, in some range of the parameters, the dependence L(R) follows the function 1/R 2ln(λs/R), which is radically different from the classical diffusion dependence 1/R.

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References

  1. G. Zheng, W. Lu, S. Jin, and C. M. Lieber, Adv. Mater. 16, 1890 (2004).

    Article  Google Scholar 

  2. A. B. Greytak, L. J. Lauhon, M. S. Gudiksen, and C. M. Lieber, Appl. Phys. Lett. 84, 4176 (2004).

    Article  ADS  Google Scholar 

  3. M. T. Bjork, B. J. Ohlsson, T. Sass, et al., Appl. Phys. Lett. 80, 1058 (2002).

    Article  ADS  Google Scholar 

  4. Y. Cui and C. M. Lieber, Science 291, 851 (2001).

    Article  ADS  Google Scholar 

  5. S. Gradecak, F. Quin, Y. Li, et al., Appl. Phys. Lett. 87, 173111 (2005).

  6. E. Patolsky, G. Zheng, O. Hayden, et al., Proc. Natl. Acad. Sci. USA 101, 14017 (2004).

    Article  ADS  Google Scholar 

  7. R. S. Friedman, M. C. McAlpine, D. S. Ricketts, et al., Nature 434, 1085 (2005).

    Article  ADS  Google Scholar 

  8. Y. Huang and C. M. Lieber, Pure Appl. Chem. 76, 2051 (2004).

    Google Scholar 

  9. D. Whang, S. Jin, and C. M. Lieber, Jpn. J. Appl. Phys. 43, 4465 (2004).

    Article  Google Scholar 

  10. R. S. Wagner and W. C. Ellis, Appl. Phys. Lett. 4, 89 (1964).

    Article  Google Scholar 

  11. E. I. Givargizov, J. Cryst. Growth 31, 20 (1975).

    Article  Google Scholar 

  12. P. M. Petroff, A. C. Gossard, and W. Wiegmann, Appl. Phys. Lett. 45, 620 (1984).

    Article  ADS  Google Scholar 

  13. R. Bhat, E. Kapon, S. Simhony, et al., J. Cryst. Growth 107, 716 (1991).

    Article  Google Scholar 

  14. K. Hiruma, M. Yazawa, T. Katsuyama, et al., J. Appl. Phys. 77, 447 (1995).

    Article  ADS  Google Scholar 

  15. E. I. Givargizov, Growth of Whisker and Lamellar Crystals from Vapors (Nauka, Moscow, 1977) [in Russian].

    Google Scholar 

  16. D. N. Mcllroy, A. Alkhateeb, D. Zhang, et al., J. Phys.: Condens. Matter 16, R415 (2004).

    Article  ADS  Google Scholar 

  17. A. I. Persson, M. W. Larsson, S. Stengstrom, et al., Nature Mater. 3, 677 (2004).

    Article  Google Scholar 

  18. E. I. Givargizov and A. A. Chernov, Kristallografiya 18, 147 (1973) [Sov. Phys. Crystallogr. 18, 89 (1973)].

    Google Scholar 

  19. D. Kashchiev, Nucleation: Basic Theory with Applications (Butterworth Heinemann, Oxford, 2000).

    Google Scholar 

  20. V. V. Mamutin, Pis’ma Zh. Tekh. Fiz. 25(18), 55 (1999) [Tech. Phys. Lett. 25, 741 (1999)].

    Google Scholar 

  21. V. G. Dubrovskii and N. V. Sibirev, Phys. Rev. E 70, 031604 (2004).

    Google Scholar 

  22. V. G. Dubrovskiĭ, N. V. Sibirev, and G. E. Cirlin, Pis’ma Zh. Tekh. Fiz. 30(16), 41 (2004) [Tech. Phys. Lett. 30, 682 (2004)].

    Google Scholar 

  23. V. Dubrovskii, N. V. Sibirev, G. Cirlin, et al., Proc. SPIE 5946, 594611 (2005).

  24. G. W. Sears, Acta Metall. 3, 367 (1955).

    Article  Google Scholar 

  25. W. Dittmar and K. Neumann, in Crowth and Perfection of Crystals, Ed. by R. H. Doremus, B. W. Roberts, and D. Turnball (Wiley, New York, 1958), p. 121.

    Google Scholar 

  26. V. Ruth and J. R. Hirth, J. Chem. Phys. 41, 31 (1964).

    Google Scholar 

  27. S. Bhunia, T. Kawamura, S. Fujikawa, and Y. Watanabe, Physica E (Amsterdam) 24, 238 (2004).

    Google Scholar 

  28. G. E. Cirlin, V. G. Dubrovskiĭ, N. V. Sibirev, et al., Fiz. Tekh. Poluprovodn. (St. Petersburg) 39, 587 (2005) [Semiconductors 39, 557 (2005)].

    Google Scholar 

  29. V. G. Dubrovskii, G. E. Cirlin, I. P. Soshnikov, et al., Phys. Rev. B 71, 205 325 (2005).

    Google Scholar 

  30. W. Seifert, M. Borgstrom, K. Deppert, et al., J. Cryst. Growth 272, 211 (2004).

    Article  Google Scholar 

  31. L. Schubert, P. Werner, N. D. Zakharov, et al., Appl. Phys. Lett. 84, 4968 (2004).

    Article  ADS  Google Scholar 

  32. V. G. Dubrovskii, I. P. Soshnikov, G. E. Cirlin, et al., J. Cryst. Growth 289, 31 (2006).

    Article  Google Scholar 

  33. G. E. Cirlin, A. A. Tonkikh, Yu. B. Samsonenko, et al., Czech. J. Phys. 56, 13 (2006).

    Article  ADS  Google Scholar 

  34. J. C. Harmand, G. Patriarche, N. Péré-Laperne, et al., Appl. Phys. Lett. 87, 203 101 (2005).

    Google Scholar 

  35. V. G. Dubrovskii, I. P. Soshnikov, G. E. Cirlin, et al., Phys. Status Solidi B 241, R30 (2004).

    Article  ADS  Google Scholar 

  36. Handbook of Mathematical Functions, Ed. by M. Abramowitz and I. A. Stegun, 2nd ed. (Dover, New York, 1971; Nauka, Moscow, 1979).

    Google Scholar 

  37. T. Takebe, M. Fujii, T. Yamamoto, et al., J. Appl. Phys. 81, 7273 (1997).

    Article  ADS  Google Scholar 

  38. S. Koshiba, Y. Nakamura, M. Tsuchhiya, et al., J. Appl. Phys. 76, 4138 (1994).

    Article  ADS  Google Scholar 

  39. V. G. Dubrovskii, Phys. Status Solidi B 171, 345 (1992).

    Google Scholar 

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Authors and Affiliations

  1. St. Petersburg Physicotechnical Center of Science and Education, Russian Academy of Sciences, St. Petersburg, 195220, Russia

    V. G. Dubrovskiĭ, G. É. Cirlin & V. M. Ustinov

  2. Ioffe Physicotechnical Institute, Russian Academy of Sciences, St. Petersburg, 194021, Russia

    V. G. Dubrovskiĭ, R. A. Suris, G. É. Cirlin & V. M. Ustinov

  3. Institute for Analytical Instrumentation, Russian Academy of Sciences, St. Petersburg, 190103, Russia

    N. V. Sibirev & G. É. Cirlin

  4. CNRS-LPN, Route de Nozay, Marcoussis, 91460, France

    M. Tchernysheva & J. C. Harmand

Authors
  1. V. G. Dubrovskiĭ
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  2. N. V. Sibirev
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  3. R. A. Suris
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  4. G. É. Cirlin
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  5. V. M. Ustinov
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  6. M. Tchernysheva
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  7. J. C. Harmand
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Original Russian Text © V.G. Dubrovskiĭ, N.V. Sibirev, R.A. Suris, G.É. Cirlin, V.M. Ustinov, M. Tchernysheva, J.C. Harmand, 2006, published in Fizika i Tekhnika Poluprovodnikov, 2006, Vol. 40, No. 9, pp. 1103–1110.

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Dubrovskiĭ, V.G., Sibirev, N.V., Suris, R.A. et al. The role of surface diffusion of adatoms in the formation of nanowire crystals. Semiconductors 40, 1075–1082 (2006). https://doi.org/10.1134/S1063782606090168

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  • DOI: https://doi.org/10.1134/S1063782606090168

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