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Toward multiscale modeling of thin-film growth processes using SLKMC

Published online by Cambridge University Press:  28 March 2018

Shree Ram Acharya  and
Talat S. Rahman
Shree Ram Acharya
Affiliation:
Department of Physics, University of Central Florida, Orlando, Florida 32816, USA
Talat S. Rahman*
Affiliation:
Department of Physics, University of Central Florida, Orlando, Florida 32816, USA; and Donostia International Physics Center, Donostia-San Sebastian 20018, Spain
*
a)Address all correspondence to this author. e-mail: [email protected]
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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.

Keywords

diffusionepitaxykinetics
Type
Articles
Information
Journal of Materials Research , Volume 33 , Issue 6 , 28 March 2018 , pp. 709 - 719
Copyright
Copyright © Materials Research Society 2018 

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References

REFERENCES

Brune, H., Romainczyk, C., Röder, H., and Kern, K.: Mechanism of the transition from fractal to dendritic growth of surface aggregates. Nature 369, 469 (1994).Google Scholar
Mulazzi, M., Stanescu, S., Fujii, J., Vobornik, I., Boeglin, C., Belkhou, R., Rossi, G., and Barbier, A.: Structural and electronic properties of thin Ni layers on Cu(111) as investigated by ARPES, STM and GIXD. Surf. Sci. 600, 3938 (2006).Google Scholar
Fischer, B., Brune, H., Barth, J.V., Fricke, A., and Kern, K.: Nucleation kinetics on inhomogeneous substrates: Al/Au(111). Phys. Rev. Lett. 82, 1732 (1999).Google Scholar
Meakin, P.: Formation of fractal clusters and networks by irreversible diffusion-limited aggregation. Phys. Rev. Lett. 51, 1119 (1983).Google Scholar
Liu, S., Bönig, L., and Metiu, H.: Effect of small-cluster mobility and dissociation on the island density in epitaxial growth. Phys. Rev. B 52, 2907 (1995).Google Scholar
Feng-Min, W., Qiao-Wen, L., and Zi-Qin, W.: Effect of small cluster diffusion during two-dimensional thin film growth on metal surface. Chin. Phys 9, 672 (2000).Google Scholar
Bowker, M. and Leibsle, F.: The importance of diffusion in surface reactions demonstrated with STM. Catal. Lett. 38, 123 (1996).Google Scholar
Malmejac, Y. and Frohberg, G.: Mass Transport by Diffusion, in Fluid Sciences and Materials Science in Space (Springer, 1987); p. 159.Google Scholar
Woo, C.: Theory of irradiation deformation in non-cubic metals: Effects of anisotropic diffusion. J. Nucl. Mater. 159, 237 (1988).Google Scholar
Wen, J-M., Evans, J.W., Bartelt, M., Burnett, J.W., and Thiel, P.A.: Coarsening mechanisms in a metal film: From cluster diffusion to vacancy ripening. Phys. Rev. Lett. 76, 652 (1996).CrossRefGoogle Scholar
Wang, S., Kürpick, U., and Ehrlich, G.: Surface diffusion of compact and other clusters: Ir x on Ir(111). Phys. Rev. Lett. 81, 4923 (1998).CrossRefGoogle Scholar
Schlößer, D.C., Morgenstern, K., Verheij, L.K., Rosenfeld, G., Besenbacher, F., and Comsa, G.: Kinetics of island diffusion on Cu(111) and Ag(111) studied with variable-temperature STM. Surf. Sci. 465, 19 (2000).Google Scholar
Kellogg, G.: Oscillatory behavior in the size dependence of cluster mobility on metal surfaces: Rh on Rh(100). Phys. Rev. Lett. 73, 1833 (1994).CrossRefGoogle ScholarPubMed
Zhang, Z. and Lagally, M.G.: Atomistic processes in the early stages of thin-film growth. Science 276, 377 (1997).Google Scholar
Wang, S. and Ehrlich, G.: Diffusion of large surface clusters: Direct observations on Ir(111). Phys. Rev. Lett. 79, 4234 (1997).Google Scholar
Signor, A., Wu, H.H., and Trinkle, D.R.: Misfit-dislocation-mediated heteroepitaxial island diffusion. Surf. Sci. 604, L67 (2010).Google Scholar
Alder, B.J. and Wainwright, T.: Studies in molecular dynamics. I. General method. J. Chem. Phys. 31, 459 (1959).CrossRefGoogle Scholar
Vineyard, G.H.: Frequency factors and isotope effects in solid state rate processes. J. Phys. Chem. Solid. 3, 121 (1957).Google Scholar
Voter, A.F. and Doll, J.D.: Dynamical corrections to transition state theory for multistate systems: Surface self-diffusion in the rare-event regime. J. Chem. Phys. 82, 80 (1985).Google Scholar
Bortz, A.B., Kalos, M.H., and Lebowitz, J.L.: A new algorithm for Monte Carlo simulation of Ising spin systems. J. Comput. Phys. 17, 10 (1975).Google Scholar
Voter, A.F.: Classically exact overlayer dynamics: Diffusion of rhodium clusters on Rh(100). Phys. Rev. B 34, 6819 (1986).Google Scholar
Henkelman, G. and Jónsson, H.: Long time scale kinetic Monte Carlo simulations without lattice approximation and predefined event table. J. Chem. Phys. 115, 9657 (2001).Google Scholar
Trushin, O., Karim, A., Kara, A., and Rahman, T.: Self-learning kinetic Monte Carlo method: Application to Cu(111). Phys. Rev. B 72 (2005).Google Scholar
Shah, S.I., Nandipati, G., Kara, A., and Rahman, T.S.: Extended pattern recognition scheme for self-learning kinetic Monte Carlo simulations. J. Phys.: Condens. Matter 24, 354004 (2012).Google Scholar
Karim, A., Al-Rawi, A., Kara, A., Rahman, T., Trushin, O., and Ala-Nissila, T.: Diffusion of small two-dimensional Cu islands on Cu(111) studied with a kinetic Monte Carlo method. Phys. Rev. B 73, (2006).CrossRefGoogle Scholar
Shah, S.I., Nandipati, G., Kara, A., and Rahman, T.S.: Self-diffusion of small Ni clusters on the Ni(111) surface: A self-learning kinetic Monte Carlo study. Phys. Rev. B 88, 035414 (2013).CrossRefGoogle Scholar
Shah, S.I., Nandipati, G., Karim, A., and Rahman, T.S.: 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
Acharya, S.R., Shah, S.I., and Rahman, T.S.: Diffusion of small Cu islands on the Ni(111) surface: A self-learning kinetic Monte Carlo study. Surf. Sci. 662, 42 (2017).Google Scholar
Kara, A., Trushin, O., Yildirim, H., and Rahman, T.S.: 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
Andersen, H.C.: Molecular dynamics simulations at constant pressure and/or temperature. J. Chem. Phys. 72, 2384 (1980).CrossRefGoogle Scholar
Hohenberg, P. and Kohn, W.: Inhomogeneous electron gas. Phys. Rev. 136, B864 (1964).Google Scholar
Kohn, W. and Sham, L.J.: Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, A1133 (1965).Google Scholar
Henkelman, G. and Jónsson, H.: Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points. J. Chem. Phys. 113, 9978 (2000).Google Scholar
Henkelman, G. and Jónsson, H.: A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives. J. Chem. Phys. 111, 7010 (1999).Google Scholar
Knorr, N., Brune, H., Epple, M., Hirstein, A., Schneider, M., and Kern, K.: Long-range adsorbate interactions mediated by a two-dimensional electron gas. Phys. Rev. B 65, 115420 (2002).Google Scholar
Müller, B., Nedelmann, L., Fischer, B., Brune, H., and Kern, K.: Initial stages of Cu epitaxy on Ni(100): Postnucleation and a well-defined transition in critical island size. Phys. Rev. B 54, 17858 (1996).CrossRefGoogle Scholar
Liu, C., Cohen, J., Adams, J., and Voter, A.: 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).Google Scholar
Rilling, W., Gilmore, C., Andreadis, T., and Sprague, J.: An embedded-atom-method study of diffusion of an Ag adatom on (111) Ag. Can. J. Phys. 68, 1035 (1990).Google Scholar
Foiles, S., Baskes, M., and Daw, M.: Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. Phys. Rev. B 33, 7983 (1986).Google Scholar
Daw, M.S. and Baskes, M.I.: Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals. Phys. Rev. B 29, 6443 (1984).Google Scholar
Elkoraychy, E., Sbiaai, K., Mazroui, M., Boughaleb, Y., and Ferrando, R.: Numerical study of hetero-adsorption and diffusion on (100) and (110) surfaces of Cu, Ag and Au. Surf. Sci. 635, 64 (2015).Google Scholar
Da Silva, E. and Antonelli, A.: Diffusion of Pd clusters on Pd(111) surfaces: A molecular dynamics study. Surf. Sci. 452, 239 (2000).Google Scholar
Liu, F., Hu, W., Deng, H., He, R., Yang, X., Luo, W., Lu, K., and Deng, L.: Dynamics diffusion behaviors of Pd small clusters on a Pd(111) surface. Modell. Simul. Mater. Sci. Eng. 18, 045010 (2010).Google Scholar
Papanicolaou, N. and Papaconstantopoulos, D.: Interatomic potential for Pd and molecular-dynamics simulation of diffusion in Pd/Pd(111) system. Thin Solid Films 428, 40 (2003).Google Scholar
Chang, C., Wei, C., and Chen, S.: Self-diffusion of small clusters on fcc metal (111) surfaces. Phys. Rev. Lett. 85, 1044 (2000).Google Scholar
Adams, J., Foiles, S., and Wolfer, W.: Self-diffusion and impurity diffusion of fee metals using the five-frequency model and the embedded atom method. J. Mater. Res. 4, 102 (1989).Google Scholar
Rosenfeld, G., Lipkin, N., Wulfhekel, W., Kliewer, J., Morgenstern, K., Poelsema, B., and Comsa, G.: New concepts for controlled homoepitaxy. Appl. Phys. A 61, 455 (1995).Google Scholar
Nandipati, G., Shim, Y., Amar, J.G., Karim, A., Kara, A., Rahman, T.S., and Trushin, O.: Parallel kinetic Monte Carlo simulations of Ag(111) island coarsening using a large database. J. Phys.: Condens. Matter 21, 084214 (2009).Google Scholar
Nandipati, G., Kara, A., Shah, S.I., and Rahman, T.S.: Island-size selectivity during 2D Ag island coarsening on Ag(111). J. Phys.: Condens. Matter 23, 262001 (2011).Google Scholar
Acharya, S.R. and Rahman, T.S.: (to be published).Google Scholar