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Dislocation-Free 3D Islands in Highly Mismatched Epitaxy: An Equilibrium Study With Anharmonic Interactions

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Atomistic Aspects of Epitaxial Growth

Part of the book series: NATO Science Series ((NAII,volume 65))

Abstract

Accounting for the anharmonicity of the real interatomic potentials in a model in 1+1 dimensions shows that coherent three-dimensional (3D) islands can be formed on the wetting layer in a Stranski-Krastanov growth mode predominantly in compressed overlayers. Coherent 3D islanding in expanded overlayers could be expected as an exception rather than as a rule. The thermodynamic driving force of formation of coherent 3D islands on the wetting layer of the same material is the weaker adhesion of the atoms near the island edges. The average adhesion gets weaker with increasing island thickness but reaches a saturation after several monolayers. A misfit greater than a critical value is a necessary condition for coherent 3D islanding. Monolayer height islands with a critical size appear as necessary precursors of the 3D islands. The transformation from monolayer-high islands to three-dimensional pyramids takes place through a series of stable intermediate 3D islands with discretely increasing thickness.

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References

  1. Politi, P., Grenet, G., Marty, A., Ponchet, A. and Villain, J. (2000) Instabilities in crystal growth by atomic or molecular beams, Phys. Rep. 324, pp. 271–404.

    Article  CAS  Google Scholar 

  2. Eaglesham, D.J. and M. Cerullo, M. (1990) Dislocation-free Stranski-Krastanow growth of Ge on Si(100), Phys, Rev. Lett. 64, pp. 1943–1946.

    Article  CAS  Google Scholar 

  3. Leonard, D., Krishnamurthy, M., Reaves, CM., Denbaars, S.P. and Petroff, P.M. (1993) Direct formation of quantum-sized dots from uniform coherent islands of InGaAs on GaAs surfaces, Appl. Phys. Lett. 63, pp, 3203–3205.

    Article  CAS  Google Scholar 

  4. Thanh, V.L., Boucaud, P., Debarre, D., Zheng, Y., Bouchier, D. and Lourtioz, J.-M. (1998) Nucleation and growth of self-assembled Ge/Si(0Ql) quantum dots, Phys. Rev B 58, pp. 13115–13120.

    Article  Google Scholar 

  5. Duport, C., Priester, C. and Villain, J. (1998) in Morphological Organization in Epitaxial Growth and Removal, Vol. 14 of Directions in Condensed Matter Physics, Zhang, Z. and Lagally, M.G., eds. (World Scientific, Singapore).

    Google Scholar 

  6. Spencer, B.J. and Tersoff, J. (1997) Equilibrium shapes and properties of epitaxially strained islands, Phys. Rev. Lett. 79, pp. 4858–4861; Spencer, B.J. (1999) Asymptotic derivation of the glued-wetting-layer model and contact-angle condition for Stranski-Krastanow islands, Phys. Rev. B 59, pp. 2011-2017.

    Article  CAS  Google Scholar 

  7. Liu, Q.K.K., Moll, N., Scheffler, M. and Pehlke, E. (1999) Equilibrium shapes and energies of coherent strained InP islands, Phys. Rev. B 60, pp. 17008–17015.

    Article  CAS  Google Scholar 

  8. Müller, P. and Kern, R. (2000) Equilibrium nano-shape changes induced by epitaxial stress (generalised Wulf-Kaishew theorem), Surf. Sci. 457, pp. 229–253.

    Article  Google Scholar 

  9. Daruka, I., Tersoff, J. and Barabási, A.-L. (1999) Shape transition in growth of strained islands, Phys. Rev. Lett. 82, pp. 2753–2756.

    Article  CAS  Google Scholar 

  10. Ashu, P. and Matthai, C.C (1991) A molecular dynamics study of the critical thickness of Ge layers on Si substrates, Appl. Surf. Sei. 48/49, pp. 39–43.

    Article  Google Scholar 

  11. Orr, B.G., Kessler, D., Snyder, C.W. and Sander, L. (1992) A model for strain-induced roughening and coherent island growth, Europhys. Lett. 19, pp. 33–38.

    Article  CAS  Google Scholar 

  12. Ratsch, C. and Zangwll, A. (1993) Equilibrium theory of the Stranski-Krastanov epitaxial morphology, Surf. Sci. 293, pp. 123–131.

    Article  CAS  Google Scholar 

  13. Tersoff, J. and Tromp, R.M. (1993) Shape transition in growth of strained islands; Spontaneous formation of quantum wires, Phys. Rev. Lett. 70, pp. 2782–2785.

    Article  CAS  Google Scholar 

  14. Priester, C. and Lannoo, M. (1995) Origin of self-assembled quantum dots in highly mismatched heteroepitaxy, Phys. Rev. Lett. 75, pp. 93–96.

    Article  CAS  Google Scholar 

  15. Daruka, I. and Barabasi, A.-L. (1997) Dislocation-free island formation in heteroepi-taxial growth: A study at equilibrium, Phys. Rev. Lett. 79, pp. 3708–3711.

    Article  CAS  Google Scholar 

  16. Shchukin, V.A., Ledentsov, N.N., Kop'ev, P.S. and Bimberg, D. (1995) Spontaneous ordering of arrays of coherent strained islands, Phys. Rev. Lett. 75, pp. 2968–2971.

    Article  CAS  Google Scholar 

  17. Chen, Y. and Washburn, J. (1996) Structural transition in large-lattice-mismatch heteroepitaxy, Phys. Rev. Lett. 77, pp. 4046–4049.

    Article  CAS  Google Scholar 

  18. Freund, L.B., Johnson, H.T. and Kukta, R.V. (1996) Observations on the mechanics of strained epitaxial island growth, in Evolution of Epitaxial Structure and Morphology, Mat. Res. Soc. Syrup. Proc. 399, edited by Zangwill, A., Jesson, D., Chambliss, D.D. and R. Clarke, pp. 359.

    Google Scholar 

  19. Yu, W. and Madhukar, A. (1997) Molecular dynamics study of coherent island energetics, stresses, and strains in highly strained epitaxy, Phys. Rev. Lett. 79, pp. 905–908.

    Article  CAS  Google Scholar 

  20. Wang, L.G., Kratzer, P., Scheffler, M. and Moll, N. (1999) Formation and stability of self-assembled coherent islands in highly mismatched heteroepitaxy, Phys. Rev. Lett. 82, pp. 4042–4045.

    Article  CAS  Google Scholar 

  21. Joyce, B.A., Sudijono, J.L., Belk, J.G., Yamaguchi, H., Zhang, X.M., Dobbs, H.T., Zangwill, A., Vvedensky, D.D. and Jones, T.S. (1997) A scanning tunneling microscopy reflection high energy electron diffraction-rate equation study of the molecular beam epitaxial growth of InAs on GaAs(001), (110) and (111)A—Quantum dots and two-dimensional modes, Jpn. J. Appl. Phys. 36, pp. 4111–4117.

    Article  CAS  Google Scholar 

  22. Dobbs, H.T., Vvedensky, D.D., Zangwill, A., Johansson, J., Carlsson, N. and Seifert, W. (1997) Mean-field theory of quantum dot formation, Phys. Rev. Lett. 79, pp. 897–900.

    Article  CAS  Google Scholar 

  23. Koduvely, H.M. and A. Zangwill, A. (1999) Epitaxial growth kinetics with interacting coherent islands, Phys. Rev. B 60, pp. R2204–R2207.

    Article  CAS  Google Scholar 

  24. Rudra, A., Houdre, R., Carlin, J.F. and Ilegems, M. (1994) Dynamics of island formation in the growth of InAs/InP quantum wells, J. Cryst. Growth 136, pp. 278–281; Houdre, R., Carlin, J.F., Rudra, A., Ling, J. and Ilegems, M. (1993) Formation and optical-properties of islands in ultrarthin InAs/InP quantum-wells grown by chemical beam epitaxy, Superlattices Miarostrnct. 13, pp. 67-70.

    Article  CAS  Google Scholar 

  25. Mo, Y.-W., Savage, D.E., Swartzentruber, B.S. and Lagally, M.G. (1990) Kinetic pathway in Stranski-Krastanov growth of Ge on Si(001), Phys. Rev. Lett. 65, pp. 1020–1023.

    Article  CAS  Google Scholar 

  26. Moison, J.M., Houzay, F., Barthe, F., Leprince, L., André, E. and Vatel, O. (1994) Self-organized growth of regular nanometer-scale InAs dote on GaAs, Appl. Phys. Lett. 64, pp. 196–198.

    Article  CAS  Google Scholar 

  27. Schikora, D., Schwedhelm, S., As, D.J., Lischka, K., Litvinov, D., Rosenauer, A., Gerthsen, D., Strassburg, M., Hoffmann, A. and Bimberg, D. (2000) Investigations on the StransM-Krastanow growth of CdSe quantum dots, Appl. Phys. Lett. 76, pp. 418–420; Strassburg, M., Deniozou, T., Hoffmann, A., Heitz, R., Pohl, U.W., Bimberg, D., Litvinov, D., Rosenauer, A., Gerthsen, D., Schwedhelm, S., Lischka, K. and Schikora, D. (2000) Coexistence of planar and three-dimensional quantum dots in CdSe/ZnSe structure, Appl. Phys. Lett. 76, pp. 685-687.

    Article  CAS  Google Scholar 

  28. Pinczolits, M., Springholz, G. and Bauer, G. (1998) Direct formation of self-assembled quantum dots under tensile strain by heteroepitaxy of PbSe on PbTe (111), Appl. Phys. Lett 73, pp. 250–252.

    Article  CAS  Google Scholar 

  29. Stoyanov, S. and Markov, I. (1982) On the 2D-3D transition in epitaxial thin-film growth, Surf. Sci. 116, pp. 313–337.

    Article  CAS  Google Scholar 

  30. Korutcheva, E., Turiel, A.M. and Markov, I. (2000) Coherent Stranski-Krastanov growth in 1+1 dimensions with anharmonic interactions: An equilibrium study, Phys. Rev. B 61, pp. 16890–16901.

    Article  CAS  Google Scholar 

  31. Kern, R., LeLay, G. and Metois, J.J. (1979) Basic mechanisms in the early stages of epitaxy, in Current Topics in Materials Science, Vol. 3, Kaldis, E. ed., (North-Holland, Amsterdam).

    Google Scholar 

  32. S. Stoyanov, S. (1986) On the theory of epitaxial growth, Surf. Sci. 172, pp. 198–210.

    Article  CAS  Google Scholar 

  33. Markov, I. and Stoyanov, S. (1987) Mechanisms of epitaxial growth, Contemp. Phys. 28, pp. 267–320.

    Article  CAS  Google Scholar 

  34. Kaischew, R. (1950) Commim. Bulg. Acad. Sd. (Ser. Phys.) 1, pp. 100-; Fortschr. Miner, 38, 7 (1960).

    Google Scholar 

  35. Markov, I. (1995) Crystal Growth for Beginners, Ftmdamentab of Nuclation, Crystal Growth and Epitaxy. World Scientific, Singapore.

    Google Scholar 

  36. Bauer, E.G. (1958) Phänomenologische theorie der kristallabscheidung an oberflächen I, Z. Kristallogr. 110, pp. 372–394.

    Article  CAS  Google Scholar 

  37. Grabow, M.H. and Gilmer, G.H. (1988) Thin-film growth modes, wetting and cluster nucleation, Surf, Sci 194, pp. 333–346.

    Article  CAS  Google Scholar 

  38. Matthews, J.W., Jackson, D.C. and Chambers, A. (1975) Effect of coherency strain and misfit dislocations on mode of growth of thin films, Thin Solid Films 29, pp. 129–134.

    Article  Google Scholar 

  39. Kegel, I., Metzger, T.H., Lorke, A., Peisl, J., Stangl, J., Bauer, G., Garcia, J.M. and Petroff, P.M. (2000) Nanometer-scale resolution of strain and interdiffusion in self-assembled InAs/GaAs quantum dots, Phys. Rev. Lett. 85, pp. 1694–1697.

    Article  CAS  Google Scholar 

  40. Stoop, L.C.A. and van der Merwe, J.H. (1973) Thin Solid Films 17, pp. 291.

    Article  Google Scholar 

  41. Frenkel, Ya.I. and Kontorova, T. (1939) J. Phys. Acad. Sci. USSR 1, pp. 137.

    CAS  Google Scholar 

  42. Prank, F.C. and van der Merwe, J.H. (1949) One-dimensional dislocations. I. Static theory, Proc. Roy. Soc. London, Ser. A 198, pp. 205–215; One-dimensional dislocations. II. Misfitting monolayers and oriented overgrowth, 198, 216 (1949).

    Article  Google Scholar 

  43. van der Merwe; J.H., Woltersdorf, J. and Jesser, W.A. (1986) Low-energy dislocation-structures in epitaxy, Mater. Sd. Eng. 81, pp. 1–33.

    Article  Google Scholar 

  44. Tersoff, J. (1986) New empirical model for the structural properties of silicon, Phys. Rev. Lett. 56, pp. 632–635.

    Article  CAS  Google Scholar 

  45. Markov, I. and A. Trayanov, A. (1988) Epitaxial interfaces with realistic interatomic forces, J. Phys. C 21, pp. 2475–2493; (1990) Accommodation of misfit in epitaxial interfaces—discrete Prenkel-Kontorova model with real interatomic forces, J. Phys.; Condens. Mat. 2, 6965-6980.

    Article  Google Scholar 

  46. Markov, I. (1993) Static multikink solutions in a discrete Prenkel-Kontorova model with enharmonic interactions, Phys. Rev. B 48, pp. 14016–14019.

    Article  CAS  Google Scholar 

  47. Stillinger, F.H. and T. A. Weber, T.A. (1985) Computer simulation of local order in condensed phases of silicon, Phys. Rev. B 31, pp. 5262–5271.

    Article  CAS  Google Scholar 

  48. Xie, Y.H., Gilmer, G.H., Roland, C., Silverman, P.J., Buratto, S.K., Cheng, J.Y., Fitzgerald, E.A., Kortan, A.R., Schuppler, S., Marcus, M.A. and Citrin, P.H. (1994) Semiconductor surface roughness: Dependence on sign and magnitude of bulk strain, Phys. Rev. Lett. 73, pp. 3006–3009.

    Article  CAS  Google Scholar 

  49. Walther, T., Cullis, A.G., Norris, D.J. and Hopkinson, M. (2001) Nature of the Stranski-Krastanow transition during epitaxy of InGaAs on GaAs, Phys. Rev. Lett. 86, pp. 2381–2384.

    Article  CAS  Google Scholar 

  50. Shklyaev, A.A., Shibata, M. and Ichikawa, M. (1998) Ge islands on Si(111) at coverages near the transition from two-dimensional to three-dimensional growth, Surf. Sci. 416, pp. 192–199.

    Article  CAS  Google Scholar 

  51. Voigtländer, B. and Zinner, A. (1993) Simultaneous molecular-beam epitaxy growth and scanning-tunneling-microscopy imaging during Ge/Si epitaxy, Appl. Phys. Lett. 63, pp. 3055–3057.

    Article  Google Scholar 

  52. Bhatti, A.S., Grassi Alessi, M., Capizzi, M., Prigeri, P. and Franchi, S. (1999) Optical spectroscopy of quasimonolayer InAs at the onset of quantum-dot nucleation, Phys. Rev. B 60, pp. 2592–2598.

    Article  CAS  Google Scholar 

  53. Polimeni, A., Patane, A., Capizzi, M., Martelli, F., Nasi, L. and Salviati, G. (1996) Self-aggregation of quantum dots for very thin InAs layers grown on GaAs, Phys. Rev. B 53, pp. R4213–R4216.

    Article  CAS  Google Scholar 

  54. Colocci, M., Bogani, F., Carraresi, L., Mattolini, R., Bosacchi, A., Franchi, S., Frigeri, P., Rosa-Clot, M. and Taddei, S. (1997) Growth patterns of self-assembled InAs quantum dots near two-dimensional to three-dimensional transition, Appl. Phys. Lett. 70, pp. 3140–3142.

    Article  CAS  Google Scholar 

  55. Bourret, A., Adelmann, C, Daudin, B., Rouviere, J.-L., Feuillet, G, and Mula, G. (2001) Strain relaxation in (0001) AIN/GaN heterostructures, Phys. Rev. B 63, art. no. 245307.

    Article  Google Scholar 

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Markov, I., Prieto, J.E. (2002). Dislocation-Free 3D Islands in Highly Mismatched Epitaxy: An Equilibrium Study With Anharmonic Interactions. In: Kotrla, M., Papanicolaou, N.I., Vvedensky, D.D., Wille, L.T. (eds) Atomistic Aspects of Epitaxial Growth. NATO Science Series, vol 65. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0391-9_31

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  • DOI: https://doi.org/10.1007/978-94-010-0391-9_31

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