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Equilibrium shape and size of supported heteroepitaxial nanoislands

  • Solid State and Materials
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Abstract

We study the equilibrium shape, shape transitions and optimal size of strained heteroepitaxial nanoislands with a two-dimensional atomistic model using simply adjustable interatomic pair potentials. We map out the global phase diagram as a function of substrate-adsorbate misfit and interaction. This phase diagram reveals all the phases corresponding to different well-known growth modes. In particular, for large enough misfits and attractive substrate there is a Stranski-Krastanow regime, where nano-sized islands grow on top of wetting films. We analyze the various terms contributing to the total island energy in detail, and show how the competition between them leads to the optimal shape and size of the islands. Finally, we also develop an analytic interpolation formula for the various contributions to the total energy of strained nanoislands.

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References

  • P. Politi, G. Grenet, A. Marty, A. Ponchet, J. Villain, Phys. Rep. 324, 271 (2000)

    Google Scholar 

  • I. Daruka, J. Tersoff, A.-L. Barabási, Phys. Rev. Lett. 82, 2753 (1999)

    Google Scholar 

  • I. Daruka, A.-L. Barabási, Appl. Phys. Lett. 72, 2102 (1998)

    Google Scholar 

  • I. Daruka, J. Tersoff, Phys. Rev. B 66, 132104 (2002)

    Google Scholar 

  • I. Daruka, A.-L. Barabási, Phys. Rev. Lett. 79, 3708 (1997)

    Google Scholar 

  • N. Moll, M. Scheffler, E. Pehlke, Phys. Rev. B, 58, 4566 (1998)

    Google Scholar 

  • L.G. Wang, P. Kratzer, N. Moll, M. Scheffler, Phys. Rev. B 62, 1897 (2000)

    Google Scholar 

  • L.G. Wang, P. Kratzer, M. Scheffler, N. Moll, Phys. Rev. Lett. 82, 4042 (1999)

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • B.J. Spencer, J. Tersoff, Phys. Rev. B 63, 205424 (2001)

    Google Scholar 

  • J. Tersoff, F.K. LeGoues, Phys. Rev. Lett. 72, 3570 (1994)

    Google Scholar 

  • R.A. Budiman, H.E. Ruda, J. Appl. Phys. 88, 4586 (2000)

    Google Scholar 

  • A. Ponchet, A. Le Corre, H. L’Haridon, B. Lambert, S. Salan, D. Alquier, D. Lacombe, L. Durand, Appl. Surf. Sci. 123, 751 (1998)

    Google Scholar 

  • H. Uemura, M. Uwaha, Y. Saito, J. Phys. Soc. Jpn 71, 1296 (2002)

    Google Scholar 

  • H. Katsuno, H. Uemura, M. Uwaha, Y. Saito, J. Crystal Growth 275, 283 (2005)

    Google Scholar 

  • S. Zhen, G.J. Davies, Phys. Stat. Sol. A78, 595 (1983)

    Google Scholar 

  • O. Trushin, E. Granato, S.-C. Ying, P. Salo, T. Ala-Nissila, Phys. Stat. Sol. B, 232, 100 (2002)

    Google Scholar 

  • O. Trushin, E. Granato, S.-C. Ying, P. Salo, T. Ala-Nissila, Phys. Rev. B 65, 241408(R) (2002); O. Trushin, E. Granato, S.-C. Ying, P. Salo, T. Ala-Nissila, Phys. Rev. B 68, 155413 (2003)

    Google Scholar 

  • J. Jalkanen, O. Trushin, E. Granato, S.C. Ying, T. Ala-Nissila, Phys. Rev. B 72, 081403(R) (2005)

  • O. Trushin et al., unpublished (2008)

  • N. Combe, P. Jensen, J.-L. Barrat, Surf. Sci. 490, 351 (2001)

    Google Scholar 

  • D.J. Eaglesham, M. Cerullo, Phys. Rev. Lett. 64, 1943 (1990)

  • V.A. Shchukin, A.I. Borovkov, N.N. Ledentsov, P.S. Kop’ev, Phys. Rev. B 51, 17767 (1995)

    Google Scholar 

  • A.A. Golovin, M.S. Levine, T.V. Savina, S.H. Davis, Phys. Rev. B 70, 235342 (2004)

  • C.H. Chiu, Phys. Rev. B 69, 165413 (2004)

    Google Scholar 

  • P. Thibault, L.J. Lewis, Phys. Rev. B 70, 035415 (2004)

    Google Scholar 

  • E. Pehlke, N. Moll, A. Kley, M. Scheffler, Appl. Phys. A 65, 525 (1997)

    Google Scholar 

  • C.D. Rudin, B.J. Spencer, J. Appl. Phys. 86, 5530 (1999)

    Google Scholar 

  • V.M. Kaganer, K.H. Ploog, Phys. Rev. B 64, 205301 (2001)

    Google Scholar 

  • P.O. Jubert, O. Fruchartn, C. Meyer, Phys. Rev. B 64, 115419 (2001)

    Google Scholar 

  • O. Fruchart, P.O. Jubert, M. Eleoui, B. Borca, P. David, V. Santonacci, A. Liènard, M. Hasegawa, C. Meyer, J. Phys.: Condens. Matter 19, 053001 (2007)

    Google Scholar 

  • B.J. Spencer, P.W. Voorhees, J. Tersoff, Phys. Rev. Lett. 84, 2449 (2000)

    Google Scholar 

  • F. Silly, M.R. Castell, Phys. Rev. Lett. 94, 046103 (2005)

    Google Scholar 

  • K.H. Hansen, T. Worren, S. Stempel, E. Lægsgaard, M. Bäumer, H.-J. Freund, F. Besenbacher, I. Stensgaard, Phys. Rev. Lett. 83, 4120 (1999)

    Google Scholar 

  • G. Parry, A. Cimetière, C. Coupeau, J. Colin, J. Grilhé, Phys. Rev. E 74, 066601 (2006)

    Google Scholar 

  • B.J. Spencer, J. Tersoff, Appl. Phys. Lett. 77, 2533 (2000)

    Google Scholar 

  • A.C. Schindler, M.F. Gyure, G.D. Simms, D.D. Vvedensky, R.E. Caflisch, C. Connell, E. Luo, Phys. Rev. B 67, 075316 (2003)

    Google Scholar 

  • R.E. Miller, V.B. Shenoy, Nanotechnology 11, 139 (2000)

  • By calculating Ω for several values of li, hi and f we saw that the misfit-dependence of Ω is essentially a shape-independent prefactor. Furthermore, we verified that other terms than f2 can be safely omitted. It is possible that this kind of misfit scaling is a feature of the present model. We also varied κ and found that the dependence of Ω on κ is orders of magnitude too small to have any relevance here

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Authors and Affiliations

  1. Department of Engineering Physics, Helsinki University of Technology, P.O. Box 1100, FIN-02015 TKK, Espoo, Finland

    J. Jalkanen & T. Ala-Nissila

  2. Institute of Physics and Technology, Yaroslavl Branch, Academy of Sciences of Russia, Yaroslavl, 150007, Russia

    O. Trushin

  3. Laboratório Associado de Sensores e Materiais, Instituto Nacional de Pesquisas Espaciais, 12245-970, São José dos Campos, SP, Brasil

    E. Granato

  4. Department of Physics, Brown University, P.O. Box 1843, Providence, RI, 02912-1843, USA

    E. Granato, S. C. Ying & T. Ala-Nissila

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  1. J. Jalkanen
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  2. O. Trushin
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  3. E. Granato
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  4. S. C. Ying
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  5. T. Ala-Nissila
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Correspondence to J. Jalkanen.

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Jalkanen, J., Trushin, O., Granato, E. et al. Equilibrium shape and size of supported heteroepitaxial nanoislands. Eur. Phys. J. B 66, 175–183 (2008). https://doi.org/10.1140/epjb/e2008-00410-8

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  • DOI: https://doi.org/10.1140/epjb/e2008-00410-8

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