Eur. Phys. J. B (2012) 85: 117
https://doi.org/10.1140/epjb/e2012-20790-2

Regular Article

Equilibration of a cone: KMC simulation results

¹ Department of Physics, Faculty of Arts and Sciences, Cukurova University, 01330 Adana, Turkey
² Department of Science and Mathematics Education in Secondary Schools, Faculty of Education, Cumhuriyet University, 58140 Sivas, Turkey

^a e-mail: metoz@cu.edu.tr

Received: 26 September 2011
Received in final form: 12 February 2012
Published online: 9 April 2012

Abstract

We study the equilibration of an initial surface of conic shape that consists of concentric circular monolayers by Kinetic Monte Carlo (KMC) method. The kinetic processes of attachment and/or detachment of particles to/from steps, diffusion of particles on the surface, along a step or cluster edges are considered. The difference between an up hill and down hill motion of a particle at a step are taken into account through the Ehrlich-Schwoebel (ES) barrier. The height of the cone evolves as h(0) − h(t) ~ t^1/α where h(0) is the initial height of the surface and α is approximately 2. The ES barrier slows down the equilibration of the surface but the time dependence remains as given above. The exponent α depends neither on ES barrier nor on the temperature. The equilibration is found also to be independent of energy barrier to the motion of particles along the step edges. The number of particles in each layer except the top two circular layers is found to decrease as t^0.57.