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Calculation of the size-distribution function for quantum dots at the kinetic stage of growth

  • Atomic Structure and Nonelectronic Properties of Semiconductors
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Abstract

A theoretical model for calculating the distribution of quantum dots in size in the case of growth according to the Stranski-Krastanow mechanism in the lattice-mismatched heteroepitaxial systems is suggested. The model is based on the general theory of the islands’ nucleation at the first-order phase transition, in which situation the role of the metastable phase is played by the overstressed wetting layer, while the elastically stressed three-dimensional islands act as nuclei of the new phase. The suggested model clarifies and generalizes a number of the results reported previously. The theory can be used at the kinetic stage of formation of quantum dots, in which case their ensemble is noninteracting. An example of calculation of the kinetics for formation of hut-shaped clusters in the heteroepitaxial Ge/Si(100) system is given.

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References

  1. V. M. Ustinov, A. E. Zhukov, A. Yu. Egorov, and N. A. Maleev, Quantum Dot Lasers (Oxford Univ. Press, Oxford, 2003).

    Google Scholar 

  2. D. Bimberg, M. Grundmann, and N. N. Ledentsov, Quantum Dot Heterostructures (Wiley, New York, 1999).

    Google Scholar 

  3. V. A. Shchukin and D. Bimberg, Rev. Mod. Phys. 71, 1125 (1999).

    Article  ADS  Google Scholar 

  4. O. P. Pchelyakov, Yu. B. Bolkhovityanov, A. V. Dvurechenskiĭ, et al., Fiz. Tekh. Poluprovodn. (St. Petersburg) 34, 1281 (2000) [Semiconductors 34, 1229 (2000)].

    Google Scholar 

  5. A.-L. Barabasi, Appl. Phys. Lett. 70, 2562 (1997).

    Article  ADS  Google Scholar 

  6. A. V. Osipov, F. Schmitt, S. A. Kukushkin, and P. Hess, Appl. Surf. Sci. 188, 156 (2002).

    Article  ADS  Google Scholar 

  7. A. V. Osipov, S. A. Kukushkin, F. Schmitt, and P. Hess, Phys. Rev. B 24, 205421 (2001).

    Google Scholar 

  8. V. G. Dubrovskii, G. E. Cirlin, and V. M. Ustinov, Phys. Rev. B 68, 075409 (2003).

    Google Scholar 

  9. V. G. Dubrovskii, G. E. Cirlin, Yu. G. Musikhin, et al., J. Cryst. Growth 267, 47 (2004).

    Article  ADS  Google Scholar 

  10. V. G. Dubrovskiĭ, Yu. G. Musikhin, G. E. Cyrlin, et al., Fiz. Tekh. Poluprovodn. (St. Petersburg) 38, 342 (2004) [Semiconductors 38, 329 (2004)].

    Google Scholar 

  11. V. A. Shchukin, N. N. Ledentsov, P. S. Kop’ev, and D. Bimberg, Phys. Rev. Lett. 75, 2968 (1995).

    Article  ADS  Google Scholar 

  12. V. P. Evtikhiev, A. M. Boiko, I. V. Kudryashov, et al., Semicond. Sci. Technol. 17, 545 (2002).

    Article  ADS  Google Scholar 

  13. V. G. Dubrovskiĭ and N. V. Sibirev, Pis’ma Zh. Tekh. Fiz. 31(4), 58 (2005) [Tech. Phys. Lett. 31, 161 (2005)].

    Google Scholar 

  14. A. A. Tonkikh, V. G. Dubrovskii, G. E. Cirlin, et al., Phys. Status Solidi B 236, R1 (2003).

    Article  ADS  Google Scholar 

  15. Yu. G. Musikhin, G. E. Cyrlin, V. G. Dubrovskiĭ, et al., Fiz. Tekh. Poluprovodn. (St. Petersburg) 39, 853 (2005) [Semiconductors 39, 820 (2005)].

    Google Scholar 

  16. V. G. Dubrovskiĭ, V. A. Egorov, G. E. Cyrlin, et al., Fiz. Tekh. Poluprovodn. (St. Petersburg) 37, 883 (2003) [Semiconductors 37, 855 (2003)].

    Google Scholar 

  17. P. Müller and R. Kern, Appl. Surf. Sci. 102, 6 (1996).

    Article  MATH  Google Scholar 

  18. C. Ratsch and A. Zangwill, Surf. Sci. 293, 123 (1993).

    Article  ADS  Google Scholar 

  19. H. T. Johnson and L. B. Freund, J. Appl. Phys. 81, 6081 (1997).

    Article  ADS  Google Scholar 

  20. F. M. Kuni and A. P. Grinin, Kolloidn. Zh. 46, 460 (1984).

    Google Scholar 

  21. S. A. Kukushkin and A. V. Osipov, Usp. Fiz. Nauk 168, 1083 (1998) [Phys. Usp. 41, 983 (1998)].

    Article  Google Scholar 

  22. M. Grundmann, O. Stier, and D. Bimberg, Phys. Rev. B 52, 11969 (1995).

    Article  ADS  Google Scholar 

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

    Google Scholar 

  24. K.-I. Shiramine, T. Itoh, S. Muto, et al., J. Cryst. Growth 242, 332 (2002).

    Article  ADS  Google Scholar 

  25. V. G. Dubrovskii, G. E. Cirlin, and V. M. Ustinov, Phys. Status Solidi B 241, R42 (2004).

    Article  ADS  Google Scholar 

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Original Russian Text © V.G. Dubrovskiĭ, 2006, published in Fizika i Tekhnika Poluprovodnikov, 2006, Vol. 40, No. 10, pp. 1153–1160.

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Dubrovskiĭ, V.G. Calculation of the size-distribution function for quantum dots at the kinetic stage of growth. Semiconductors 40, 1123–1130 (2006). https://doi.org/10.1134/S1063782606100010

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  • DOI: https://doi.org/10.1134/S1063782606100010

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