Advertisement

Off-lattice Kinetic Monte Carlo Simulations of Strained Heteroepitaxial Growth

  • Michael Biehl
  • Florian Much
  • Christian Vey
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 149)

Abstract

An off-lattice, continuous space Kinetic Monte Carlo (KMC) algorithm is discussed and applied in the investigation of strained heteroepitaxial crystal growth. As a starting point, we study a simplifying (1+1)-dimensional situation with inter-atomic interactions given by simple pair-potentials. The model exhibits the appearance of strain-induced misfit dislocations at a characteristic film thickness. In our KMC simulations we observe a power law dependence of this critical thickness on the lattice misfit, which is in agreement with experimental results for semiconductor compounds. We furthermore investigate the emergence of strain induced multilayer islands or Dots upon an adsorbate wetting layer in the so-called Stranski-Krastanow (SK) growth mode. At a characteristic kinetic film thickness, a transition from monolayer to multilayer island growth occurs. We discuss the microscopic causes of the SK-transition and its dependence on the model parameters, i.e., lattice misfit, growth rate, and substrate temperature.

Keywords

Heteroepitaxy Off-lattice Kinetic Monte Carlo 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    A. Pimpinelli and J. Villain, Physics of crystal growth. Cambridge University Press (1998).Google Scholar
  2. [2]
    T. Michely and J. Krug, Islands, mounds and atoms. Patterns and Processes in Crystal Growth far from equilibrium. Springer (2004).Google Scholar
  3. [3]
    M.E.J. Newman and G.T. Barkema, Monte Carlo Methods in Statistical Physics, Oxford University Press (1999).Google Scholar
  4. [4]
    M. Kotrla, N.I. Paanicolaou, D.D. Vvedensky, and L.T. Wille, Atomistic Aspects of Epitaxial Growth. Kluwer (2002).Google Scholar
  5. [5]
    M. Biehl, Lattice gas models of epitaxial growth and Kinetic Monte Carlo simulations. This volume.Google Scholar
  6. [6]
    B. Joyce, P. Kelires, A. Naumovets, and D.D. Vvedensky (eds.), Quantum Dots: Fundamentals, Applications, and Frontiers. Kluwer, to be published.Google Scholar
  7. [7]
    D.C. Rapaport, The Art of Molecular Dynamics Simulation. Cambridge University Press (1995).Google Scholar
  8. [8]
    M. Parrinello, Solid State Comm. 102 (1997) 107.CrossRefGoogle Scholar
  9. [9]
    K. Albe, this volume.Google Scholar
  10. [10]
    L. Dong, J. Schnitker, R.W. Smith, D.J. Sroloviy, Stress relaxation and misfit dislocation nucleation in the growth of misfitting films: a molecular dynamics simulation. J. Appl. Phys. 83 (1997) 217.CrossRefGoogle Scholar
  11. [11]
    A.F. Voter, F. Montalenti, and T.C. Germann, Extending the time scale in atomistic simulations of materials. Annu. Rev. Mater. Res. 32 (2002) 321.CrossRefGoogle Scholar
  12. [12]
    A. Madhukar, Far from equilibrium vapor phase growth of lattice matched III–V compound semiconductor interfaces: some basic concepts and Monte Carlo computer simulations. Surf. Sci. 132 (1983) 344.CrossRefGoogle Scholar
  13. [13]
    K.E. Khor and S. Das Sarma, Quantum Dot self-assembly in growth of strained-layer thin films: a kinetic Monte Carlo study. Phys. Rev. B 62 (2000) 16657.Google Scholar
  14. [14]
    C.H. Lam, C.K. Lee, and L.M. Sander, Competing roughening mechanisms in strained heteroepitaxy: A fast kinetic Monte Carlo study. Phys. Rev. Lett. 89 (2002) 216102.PubMedGoogle Scholar
  15. [15]
    M. Meixner, E. Schöll, V.A. Shchukin, and D. Bimberg, Self-assembled quantum dots: crossover from kinetically controlled to thermodynamically limited growth. Phys. Rev. Lett. 87 (2001) 236101.PubMedGoogle Scholar
  16. [16]
    M. Schroeder and D.E. Wolf, Diffusion on strained surfaces. Surf. Sci. 375 (1997) 375.CrossRefGoogle Scholar
  17. [17]
    A.C. Schindler, Theoretical aspects of growth in one and two-dimensional strained crystal surfaces. Dissertation, Univeristät Duisburg (1999).Google Scholar
  18. [18]
    A.C. Schindler and D.E. Wolf, Continuous space Monte Carlo simulations in a model of strained epitaxial growth. Preprint, Universität Duisburg (1999).Google Scholar
  19. [19]
    F. Much, M. Ahr, M. Biehl, and W. Kinzel, Kinetic Monte Carlo simulations of dislocations in heteroepitaxial growth. Europhys. Lett. 56 (2001) 791–796.CrossRefGoogle Scholar
  20. [20]
    F. Much and M. Biehl, Simulation of wetting-layer and island formation in heteroepitaxial growth. Europhys. Lett. 63 (2003) 14–20.CrossRefGoogle Scholar
  21. [21]
    M. Biehl and F. Much, Off-lattice Kinetic Monte Carlo simulations of Stranski-Krastanov-like growth. In [6], in press.Google Scholar
  22. [22]
    F. Much, Modeling and simulation of strained heteroepitaxial growth. Dissertation Universität Würzburg (2003).Google Scholar
  23. [23]
    J. Kew, M.R. Wilby, and D.D. Vvedensky, Continuous-space Monte Carlo simulations of epitaxial growth. J. Cryst. Growth 127 (1993) 508.CrossRefGoogle Scholar
  24. [24]
    H. Spjut and D.A. Faux, Computer simulation of strain-induced diffusion enhancement of Si adatoms on the Si(001) surface. Surf. Sci. 306 (1994) 233.CrossRefGoogle Scholar
  25. [25]
    F. Jensen, Introduction to Computational Chemistry, Wiley (1999).Google Scholar
  26. [26]
    G.T. Barkema and N. Mousseau, Event-based relaxation of continuous disordered systems. Phys. Rev. Lett. 77 (1996) 4358.PubMedGoogle Scholar
  27. [27]
    N. Mousseau and G.T. Barkema, Traveling through potential energy landscapes of disordered materials: the activation relaxation technique. Phys. Rev. E 57 (1998) 2419.Google Scholar
  28. [28]
    R. Malek and N. Mousseau, Dynamics of Lennard-Jones clusters: A characterization fo the activation relaxation technique. Phys. Rev. E 62 (2000) 7723.Google Scholar
  29. [29]
    A.S. Bader, W. Faschinger, C. Schumacher, J. Geurts, and L.W. Molenkamp, Real-time in situ X-ray diffraction as a method to control epitaxial growth. Appl. Phys. Lett. 82 (2003) 4684.CrossRefGoogle Scholar
  30. [30]
    J.W. Matthews and A.E. Blakeslee, Defects in epitaxial multilayers. J. Cryst. Growth 27 (1974) 118.CrossRefGoogle Scholar
  31. [31]
    G. Cohen-Solal, F. Bailly, and M. Barbé, Critical thickness of zinc-blende semiconductor compounds. J. Cryst. Growth 138 (1994) 138.CrossRefGoogle Scholar
  32. [32]
    F. Bailly, M. Barbé, and G. Cohen-Solal, Setting up of misfit dislocations in heteroepitaxial growth and critical thickness. J. Cryst. Growth 153 (1995) 153.CrossRefGoogle Scholar
  33. [33]
    K. Pinardi, U. Jain, S.C. Jain, H.E. Maes, R. Van Overstraeten, and M. Willander, Critical thickness and strain relaxation in lattice mismatched II–VI semiconductor layers. J. Appl. Phys. 83 (1998) 4724.CrossRefGoogle Scholar
  34. [34]
    L. Chkoda, M. Schneider, V. Shklover, L. Kilian, M. Sokolowski, C. Heske, and E. Umbach, Temperature-dependent morphology and structure of ordered 3,4,9,10-perylene-tetracarboxylicacid-dianhydride (PCTDA) thin films on Ag(111), Chem. Phys. Lett. 371 (2003) 548.CrossRefGoogle Scholar
  35. [35]
    Illustrations and movies of our simulations are available at http://physik.uni-wuerzburg.de/~much{biehl}.Google Scholar
  36. [36]
    V. Cherepanov and B. Voigtländer, Influence of strain on diffusion at Ge(111) surfaces, Appl. Phys. Lett. 81 (2002) 4745.CrossRefGoogle Scholar
  37. [37]
    J. Johansson and W. Seifert, Kinetics of self-assembled island formation: Part I — island density, J. Cryst. Growth 234 (2002) 132, and: Part II — island size, same volume, 139.CrossRefGoogle Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2005

Authors and Affiliations

  • Michael Biehl
    • 1
  • Florian Much
    • 2
  • Christian Vey
    • 2
  1. 1.Institute for Mathematics and Computing ScienceUniversity GroningenGroningenThe Netherlands
  2. 2.Institut für Theoretische PhysikUniversität WürzburgWürzburgGermany

Personalised recommendations