Toward multiscale modeling of thin-film growth processes using SLKMC

Abstract

The self-learning kinetic Monte Carlo method has been shown to be suitable for examining the temporal and spatial evolution of adatom islands on the (111) surface of several fcc metals, unbiased by diffusion processes chosen a priori. A pattern-recognition scheme and a diffusion path finder scheme enable collection of a large database of diffusion processes and their energetics. A variety of mechanisms involving single and multiple atoms, and concerted island motion are uncovered in long-time simulations. In this contribution, after reviewing the methodology, we present results comparing the diffusion kinetics of two sets of homo-epitaxial and hetero-epitaxial systems: small (2–8 atom) Pd and Ag islands on the respective (111) surfaces and small Cu islands on Ni(111) and Ni islands on Cu(111). We trace the dominance of concerted motion in Pd/Pd(111) and Ni/Cu(111) and competition among concerted, multiatom and single-atom processes in Ag/Ag(111) and Cu/Ni(111) to the strength of the lateral interaction among adatoms in these systems.

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References

  1. 1.

    H. Brune, C. Romainczyk, H. Röder, and K. Kern: Mechanism of the transition from fractal to dendritic growth of surface aggregates. Nature 369, 469 (1994).

    CAS  Article  Google Scholar 

  2. 2.

    M. Mulazzi, S. Stanescu, J. Fujii, I. Vobornik, C. Boeglin, R. Belkhou, G. Rossi, and A. Barbier: Structural and electronic properties of thin Ni layers on Cu(111) as investigated by ARPES, STM and GIXD. Surf. Sci. 600, 3938 (2006).

    CAS  Article  Google Scholar 

  3. 3.

    B. Fischer, H. Brune, J.V. Barth, A. Fricke, and K. Kern: Nucleation kinetics on inhomogeneous substrates: Al/Au(111). Phys. Rev. Lett. 82, 1732 (1999).

    CAS  Article  Google Scholar 

  4. 4.

    P. Meakin: Formation of fractal clusters and networks by irreversible diffusion-limited aggregation. Phys. Rev. Lett. 51, 1119 (1983).

    Article  Google Scholar 

  5. 5.

    S. Liu, L. Bönig, and H. Metiu: Effect of small-cluster mobility and dissociation on the island density in epitaxial growth. Phys. Rev. B 52, 2907 (1995).

    CAS  Article  Google Scholar 

  6. 6.

    W. Feng-Min, L. Qiao-Wen, and W. Zi-Qin: Effect of small cluster diffusion during two-dimensional thin film growth on metal surface. Chin. Phys 9, 672 (2000).

    Article  Google Scholar 

  7. 7.

    M. Bowker and F. Leibsle: The importance of diffusion in surface reactions demonstrated with STM. Catal. Lett. 38, 123 (1996).

    CAS  Article  Google Scholar 

  8. 8.

    Y. Malmejac and G. Frohberg: Mass Transport by Diffusion, in Fluid Sciences and Materials Science in Space (Springer, 1987); p. 159.

  9. 9.

    C. Woo: Theory of irradiation deformation in non-cubic metals: Effects of anisotropic diffusion. J. Nucl. Mater. 159, 237 (1988).

    CAS  Article  Google Scholar 

  10. 10.

    J-M. Wen, J.W. Evans, M. Bartelt, J.W. Burnett, and P.A. Thiel: Coarsening mechanisms in a metal film: From cluster diffusion to vacancy ripening. Phys. Rev. Lett. 76, 652 (1996).

    CAS  Article  Google Scholar 

  11. 11.

    S. Wang, U. Kürpick, and G. Ehrlich: Surface diffusion of compact and other clusters: Irx on Ir(111). Phys. Rev. Lett. 81, 4923 (1998).

    CAS  Article  Google Scholar 

  12. 12.

    D.C. Schlößer, K. Morgenstern, L.K. Verheij, G. Rosenfeld, F. Besenbacher, and G. Comsa: Kinetics of island diffusion on Cu(111) and Ag(111) studied with variable-temperature STM. Surf. Sci. 465, 19 (2000).

    Article  Google Scholar 

  13. 13.

    G. Kellogg: Oscillatory behavior in the size dependence of cluster mobility on metal surfaces: Rh on Rh(100). Phys. Rev. Lett. 73, 1833 (1994).

    CAS  Article  Google Scholar 

  14. 14.

    Z. Zhang and M.G. Lagally: Atomistic processes in the early stages of thin-film growth. Science 276, 377 (1997).

    CAS  Article  Google Scholar 

  15. 15.

    S. Wang and G. Ehrlich: Diffusion of large surface clusters: Direct observations on Ir(111). Phys. Rev. Lett. 79, 4234 (1997).

    CAS  Article  Google Scholar 

  16. 16.

    A. Signor, H.H. Wu, and D.R. Trinkle: Misfit-dislocation-mediated heteroepitaxial island diffusion. Surf. Sci. 604, L67 (2010).

    CAS  Article  Google Scholar 

  17. 17.

    B.J. Alder and T. Wainwright: Studies in molecular dynamics. I. General method. J. Chem. Phys. 31, 459 (1959).

    CAS  Article  Google Scholar 

  18. 18.

    G.H. Vineyard: Frequency factors and isotope effects in solid state rate processes. J. Phys. Chem. Solid. 3, 121 (1957).

    CAS  Article  Google Scholar 

  19. 19.

    A.F. Voter and J.D. Doll: Dynamical corrections to transition state theory for multistate systems: Surface self-diffusion in the rare-event regime. J. Chem. Phys. 82, 80 (1985).

    CAS  Article  Google Scholar 

  20. 20.

    A.B. Bortz, M.H. Kalos, and J.L. Lebowitz: A new algorithm for Monte Carlo simulation of Ising spin systems. J. Comput. Phys. 17, 10 (1975).

    Article  Google Scholar 

  21. 21.

    A.F. Voter: Classically exact overlayer dynamics: Diffusion of rhodium clusters on Rh(100). Phys. Rev. B 34, 6819 (1986).

    CAS  Article  Google Scholar 

  22. 22.

    G. Henkelman and H. Jónsson: Long time scale kinetic Monte Carlo simulations without lattice approximation and predefined event table. J. Chem. Phys. 115, 9657 (2001).

    CAS  Article  Google Scholar 

  23. 23.

    O. Trushin, A. Karim, A. Kara, and T. Rahman: Self-learning kinetic Monte Carlo method: Application to Cu(111). Phys. Rev. B 72 (2005).

  24. 24.

    S.I. Shah, G. Nandipati, A. Kara, and T.S. Rahman: Extended pattern recognition scheme for self-learning kinetic Monte Carlo simulations. J. Phys.: Condens. Matter 24, 354004 (2012).

    Google Scholar 

  25. 25.

    A. Karim, A. Al-Rawi, A. Kara, T. Rahman, O. Trushin, and T. Ala-Nissila: Diffusion of small two-dimensional Cu islands on Cu(111) studied with a kinetic Monte Carlo method. Phys. Rev. B 73, (2006).

  26. 26.

    S.I. Shah, G. Nandipati, A. Kara, and T.S. Rahman: Self-diffusion of small Ni clusters on the Ni(111) surface: A self-learning kinetic Monte Carlo study. Phys. Rev. B 88, 035414 (2013).

    Article  CAS  Google Scholar 

  27. 27.

    S.I. Shah, G. Nandipati, A. Karim, and T.S. Rahman: Self-learning kinetic Monte Carlo simulations of self-diffusion of small Ag islands on the Ag(111) surface. J. Phys.: Condens. Matter 28, 025001 (2015).

    Google Scholar 

  28. 28.

    S.R. Acharya, S.I. Shah, and T.S. Rahman: Diffusion of small Cu islands on the Ni(111) surface: A self-learning kinetic Monte Carlo study. Surf. Sci. 662, 42 (2017).

    CAS  Article  Google Scholar 

  29. 29.

    A. Kara, O. Trushin, H. Yildirim, and T.S. Rahman: Off-lattice self-learning kinetic Monte Carlo: Application to 2D cluster diffusion on the fcc(111) surface. J. Phys.: Condens. Matter 21, 084213 (2009).

    Google Scholar 

  30. 30.

    H.C. Andersen: Molecular dynamics simulations at constant pressure and/or temperature. J. Chem. Phys. 72, 2384 (1980).

    CAS  Article  Google Scholar 

  31. 31.

    P. Hohenberg and W. Kohn: Inhomogeneous electron gas. Phys. Rev. 136, B864 (1964).

    Article  Google Scholar 

  32. 32.

    W. Kohn and L.J. Sham: Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, A1133 (1965).

    Article  Google Scholar 

  33. 33.

    G. Henkelman and H. Jónsson: Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points. J. Chem. Phys. 113, 9978 (2000).

    CAS  Article  Google Scholar 

  34. 34.

    G. Henkelman and H. Jónsson: A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives. J. Chem. Phys. 111, 7010 (1999).

    CAS  Article  Google Scholar 

  35. 35.

    N. Knorr, H. Brune, M. Epple, A. Hirstein, M. Schneider, and K. Kern: Long-range adsorbate interactions mediated by a two-dimensional electron gas. Phys. Rev. B 65, 115420 (2002).

    Article  CAS  Google Scholar 

  36. 36.

    B. Müller, L. Nedelmann, B. Fischer, H. Brune, and K. Kern: Initial stages of Cu epitaxy on Ni(100): Postnucleation and a well-defined transition in critical island size. Phys. Rev. B 54, 17858 (1996).

    Article  Google Scholar 

  37. 37.

    C. Liu, J. Cohen, J. Adams, and A. Voter: EAM study of surface self-diffusion of single adatoms of fcc metals Ni, Cu, Al, Ag, Au, Pd, and Pt. Surf. Sci. 253, 334 (1991).

    CAS  Article  Google Scholar 

  38. 38.

    W. Rilling, C. Gilmore, T. Andreadis, and J. Sprague: An embedded-atom-method study of diffusion of an Ag adatom on (111) Ag. Can. J. Phys. 68, 1035 (1990).

    CAS  Article  Google Scholar 

  39. 39.

    S. Foiles, M. Baskes, and M. Daw: Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. Phys. Rev. B 33, 7983 (1986).

    CAS  Article  Google Scholar 

  40. 40.

    M.S. Daw and M.I. Baskes: Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals. Phys. Rev. B 29, 6443 (1984).

    CAS  Article  Google Scholar 

  41. 41.

    E. Elkoraychy, K. Sbiaai, M. Mazroui, Y. Boughaleb, and R. Ferrando: Numerical study of hetero-adsorption and diffusion on (100) and (110) surfaces of Cu, Ag and Au. Surf. Sci. 635, 64 (2015).

    CAS  Article  Google Scholar 

  42. 42.

    E. Da Silva and A. Antonelli: Diffusion of Pd clusters on Pd(111) surfaces: A molecular dynamics study. Surf. Sci. 452, 239 (2000).

    Article  Google Scholar 

  43. 43.

    F. Liu, W. Hu, H. Deng, R. He, X. Yang, W. Luo, K. Lu, and L. Deng: Dynamics diffusion behaviors of Pd small clusters on a Pd(111) surface. Modell. Simul. Mater. Sci. Eng. 18, 045010 (2010).

    Article  CAS  Google Scholar 

  44. 44.

    N. Papanicolaou and D. Papaconstantopoulos: Interatomic potential for Pd and molecular-dynamics simulation of diffusion in Pd/Pd(111) system. Thin Solid Films 428, 40 (2003).

    CAS  Article  Google Scholar 

  45. 45.

    C. Chang, C. Wei, and S. Chen: Self-diffusion of small clusters on fcc metal (111) surfaces. Phys. Rev. Lett. 85, 1044 (2000).

    CAS  Article  Google Scholar 

  46. 46.

    J. Adams, S. Foiles, and W. Wolfer: Self-diffusion and impurity diffusion of fee metals using the five-frequency model and the embedded atom method. J. Mater. Res. 4, 102 (1989).

    CAS  Article  Google Scholar 

  47. 47.

    G. Rosenfeld, N. Lipkin, W. Wulfhekel, J. Kliewer, K. Morgenstern, B. Poelsema, and G. Comsa: New concepts for controlled homoepitaxy. Appl. Phys. A 61, 455 (1995).

    Article  Google Scholar 

  48. 48.

    G. Nandipati, Y. Shim, J.G. Amar, A. Karim, A. Kara, T.S. Rahman, and O. Trushin: Parallel kinetic Monte Carlo simulations of Ag(111) island coarsening using a large database. J. Phys.: Condens. Matter 21, 084214 (2009).

    Google Scholar 

  49. 49.

    G. Nandipati, A. Kara, S.I. Shah, and T.S. Rahman: Island-size selectivity during 2D Ag island coarsening on Ag(111). J. Phys.: Condens. Matter 23, 262001 (2011).

    Google Scholar 

  50. 50.

    S.R. Acharya and T.S. Rahman: (to be published).

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ACKNOWLEDGMENTS

We would like to acknowledge the computational resources provided by the STOKES facility at the University of Central Florida. We are pleased to acknowledge partial support from NSF grants: CHE-1310327, under which the project was started and MMN-1710306, under which the project was completed.

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Correspondence to Talat S. Rahman.

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Acharya, S.R., Rahman, T.S. Toward multiscale modeling of thin-film growth processes using SLKMC. Journal of Materials Research 33, 709–719 (2018). https://doi.org/10.1557/jmr.2018.44

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