Abstract.
A hybrid scheme is developed to describe vicinal surface growth during epitaxy on two different time and length scales. For this purpose this algorithm combines two modules based on a continuum and an atomistic approach. The continuum module is realized by a phase-field-model which traces back to the Burton–Cabrera–Frank theory, the atomistic module is based on the anisotropic Ising model which is mapped onto a lattice-gas model. The latter provides thermal density fluctuations resulting in adatom clustering. With increasing temperature the probability for island nucleation on the terraces decreases according to 1-p where p is an Arrhenius-type activation probability which prevents clusters from becoming islands. Within this framework it is possible to find the transition from a rough surface at low temperatures to an evenly stepped surface at high temperatures where slight step meandering is observed. Furthermore two competing mechanisms of step bunching are investigated within this scale bridging algorithm: alternating anisotropic diffusion and different Ehrlich–Schwoebel barriers at the step edges. It is shown that a simulation of step bunching displaying the full variety of phenomena observed in experiments can only be achieved by the consideration of different time and length scales.
Similar content being viewed by others
References
P. Tejedor, P. Šmilauer, B.A. Joyce, Surf. Sci. 424, L309 (1999)
P. Tejedor, M.L. Crespillo, B.A. Joyce, Mater. Sci. Eng. C 26, 852 (2006)
B.Z. Nosho, B.R. Bennett, E.H. Aifer, M. Goldenberg, J. Cryst. Growth 236, 155 (2002)
D.D. Vvedensky, S. Clarke, K.J. Hugill, M.R. Wilby, T. Kawamura, J. Cryst. Growth 99, 54 (1990)
V.I. Trofimov, H.S. Park, Thin Solid Films 428, 170 (2003)
Y. Horikoshi, Handbook of Crystal Growth, Vol. 3, edited by D.T.J. Hurle (Elsevier Science B.V., Amsterdam, 1994), p. 691
G. Ehrlich, F.G. Hudda, J. Chem. Phys. 44, 1039 (1966)
R.L. Schwoebel, E.J. Shipsey, J. Appl. Phys. 37, 3682 (1966)
J. Mysliveček, C. Schelling, F. Schäffler, G. Springholz, P. Šmilauer, J. Krug, B. Voigtländer, Surf. Sci. 520, 193 (2002)
J. Mysliveček, C. Schelling, F. Schäffler, G. Springholz, P. Šmilauer, J. Krug, B. Voigtländer, Mat. Res. Soc. Symp. Proc. 749 (2003)
S. Clarke, M.R. Wilby, D.D. Vvedensky, Surf. Sci. 255, 91 (1991)
B. Voigtländer, T. Weber, P. Šmilauer, D.E. Wolf, Phys. Rev. Lett. 81, 2164 (1997)
W.K. Burton, N. Cabrera, F.C. Frank, Philos. Trans. R. Soc. London. Ser. A 243, 299 (1951)
G.S. Bales, A. Zangwill, Phys. Rev. B 41, 5500 (1990)
H. Emmerich, Phys. Rev. B 65, 233406 (2002)
H. Emmerich, Ch. Eck, Cont. Mech. Thermodyn. 17, 373 (2006)
T.P. Schulze, P. Smereka, E. Weinan, J. Comput. Phys. 189, 197 (2003)
T.P. Schulze, J. Cryst. Growth 263, 605 (2004)
G. Russo, L.M. Sander, P. Smereka, Phys. Rev. B 69, 121406(R) (2004)
M.H. Radke de Cuba, H. Emmerich, S. Gemming, Physica D (submitted)
M.H. Radke de Cuba, H. Emmerich, S. Gemming, Z. Anorg. Allg. Chem. 632, 2144 (2006)
H. Emmerich, The Diffuse Interface Approach in Material Science: Thermodynamic Concepts and Applications of Phase-Field Models, Lect. Notes Phys. 73 (Springer, Berlin, 2003)
H. Emmerich, Cont. Mech. Thermodyn. 15, 197 (2003)
T. Ihle, H. Müller-Krumbhaar, Phys. Rev. Lett. 70, 3083 (1993)
F. Liu, H. Metiu, Phys. Rev. E 49, 2601 (1994)
A. Karma, M. Plapp, Phys. Rev. Lett. 81, 4444 (1998)
E. Ising, Z. Phys. 31, 253 (1925)
Ch. Loppacher, U. Zerweck, L.M. Eng, S. Gemming, G. Seifert, C. Olbrich, K. Morawetz, M. Schreiber, Nanotechnology 17, 1568 (2006)
C. Olbrich, Bachelor Thesis, TU Chemnitz, 2004
N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, E. Teller, J. Chem. Phys. 21, 1087 (1953)
E. Stoll, K. Binder, T. Schneider, Phys. Rev. B 8, 3266 (1973)
J. Hoshen, R. Kopelman, Phys. Rev. B 14, 3438 (1976)
R.-F. Xiao, J.I.D. Alexander, F. Rosenberger, Phys. Rev. A 39, 6397 (1989)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Radke de Cuba, M., Emmerich, H. & Gemming, S. Finding polymorphic structures during vicinal surface growth. Eur. Phys. J. Spec. Top. 149, 43–56 (2007). https://doi.org/10.1140/epjst/e2007-00243-3
Issue Date:
DOI: https://doi.org/10.1140/epjst/e2007-00243-3