Surface Science Letters Non-equilibrium effects in profile spreading on stepped surfaces M. Ma  s  ın a,b, * , I. Vattulainen a , T. Ala-Nissila a,c , Z. Chvoj b a Helsinki Institute of Physics and Laboratory of Physics, Helsinki University of Technology, P.O. Box 1100, FIN-02015 HUT Espoo, Finland b Institute of Physics, Academy of Sciences, Czech Republic, Na Slovance 2, 182 21 Praha 8, Czech Republic c Department of Physics, Brown University, Providence, RI 02912-1843, USA Received 10 October 2002; accepted for publication 30 January 2003 Abstract We study non-equilibrium effects in spreading and collective diffusion of adatoms on stepped surfaces through Monte Carlo simulations of a lattice-gas model. The spreading density profiles are analyzed by the Boltzmann–Matano method to determine the temporal behavior of the effective collective diffusion coefficients. We find that the presence of steps induces considerable non-equilibrium effects in diffusion. For spreading along the steps, we find that these de- viations can be explained by the slow approach of the different adparticle concentrations on terraces and at step edges towardsequilibrium.Forspreadingacrossthesteps,however,wefindnosuchdependence,indicatingthebreakdownof the linear response theory at early times. Ó 2003 Elsevier Science B.V. All rights reserved. Keywords: Surface diffusion; Models of non-equilibrium phenomena; Computer simulations 1. Introduction Diffusion of adatoms and molecules on surfaces plays a crucial role in a number of phenomena such as the growth of electronic devices for the semiconductor industry, the migration of amphi- philic molecules on solid surfaces for biotechno- logical purposes, and chemical reactions for the purification of exhaust gases. Over the last decade, considerable effort has therefore been invested to understand the principles that govern surface dif- fusion [1–9]. However, while the diffusion prop- erties of ideal systems in equilibrium are now relatively well understood, much less is known about the non-equilibrium behavior of non-ideal systems characterized by impurities, steps, or other defects that are an inherent component of solid surfaces under both atmospheric and ultra-high vacuum conditions [10]. Recently, the question of the role of non-equi- libriumconditionsfordiffusionhasbeenaddressed in a few theoretical model studies for clean and * Corresponding author. Address: Helsinki Institute of Physics and Laboratory of Physics, Helsinki University of Technology, P.O. Box 1100, FIN-02015 HUT Espoo, Finland. Tel.: +358-9-451-5810; fax: +358-9-451-3116. E-mail addresses: mms@fyslab.hut.fi (M. Mas ˇı ´n), vattulai@ csc.fi (I. Vattulainen), alanissi@csc.fi (T. Ala-Nissila), chvoj@ fzu.cz (Z. Chvoj). 0039-6028/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0039-6028(03)00268-1 Surface Science 529 (2003) L256–L262 www.elsevier.com/locate/susc