Kinetic Monte Carlo simulation of nucleation on patterned substrates L. Nurminen, A. Kuronen, and K. Kaski Helsinki University of Technology, Laboratory of Computational Engineering, P.O. Box 9400, FIN-02015 HUT, Finland Received 9 June 2000; revised manuscript received 18 August 2000; published 29 December 2000 The effects of a patterned substrate on island nucleation are investigated using kinetic Monte Carlo simu- lations. Two different models are formulated by incorporating an inhomogeneous energy surface into the basic solid-on-solid model of epitaxial growth to describe surface diffusion and consequent island nucleation on a patterned substrate. These models are related to two examples of real systems in which preferential nucleation at specific sites is encountered. Growth on a patterned substrate produces quite uniformly sized islands, which are are found to order into regular arrays displaying the periodicity of the underlying substrate. Confinement due to the patterned substrate is observed to be strongly dependent on the growth conditions. We demonstrate that there exists an optimal set of growth conditions determined by the length scale of the substrate pattern. In addition, the influence of the patterned substrate on the process of Ostwald ripening is discussed. DOI: 10.1103/PhysRevB.63.035407 PACS numbers: 79.60.Jv, 81.15.Aa, 02.70.Rr I. INTRODUCTION Much of the recent interest in studies of metallic and semiconductor systems has focused on atomic scale struc- tures, due to their great potential for numerous technological applications. 1 For example, spontaneous self-organization of islands in heteroepitaxial thin-film growth has been utilized to manufacture semiconductor quantum dots. These three- dimensional structures, where electrons are confined to a na- nometer scale in all three dimensions, have interesting opti- cal properties. The fabrication of actual device structures is, however, problematic, since a large number of uniformly shaped and sized islands is required. In the case of heterostructures, different properties of component materials can offer a way to grow a spatially ordered arrangement of islands with an improved size uniformity. 2 For example, quantum dot superlattices, which consist of several layers of different materials obtained by alternating growth of, e.g., GaAs and InAs, yield a structure with strained layers of InAs islands embedded in GaAs. The fascinating feature of this structure is that the islands tend to nucleate directly on top of the buried islands. This leads to a narrow island size distribution. 3–5 The vertical correlation in island positions is explained by the effect of strain on the surface caused by the underlying buried islands. This strain changes the activation energies of the diffusion of adatoms deposited on the strained surface, and thereby affects the nucleation of islands in the topmost layer. In some heteroepitaxial systems strain due to lattice mis- match is relieved by the spontaneous formation of domains separated by a regular network of dislocations. 6 One example is a system of 2 ML of Ag deposited on Pt111, 7,8 where dislocations constitute effective repulsive barriers for the dif- fusing adatoms on the surface, confining the adatoms to the domains. Consequently, nucleation on top of the dislocation network produces ordered arrays of rather uniformly sized submonolayer islands, most of which are located in spaces between dislocations. In this work, we concentrate on the initial stages of growth, i.e., on the growth of two-dimensional islands that are formed in the submonolayer regime or platelets. The ob- jective is to examine mechanisms that lead to spatially or- dered nucleation and consequently to a narrow island size distribution. In this study we present two different models, motivated by the examples above. These are used to study qualitatively how the spatial variation in diffusion activation energy affects island nucleation. This paper is organized as follows. In Sec. II we give details about the model systems and the simulation setup. In Sec. III we discuss our results. Finally, in Sec. IV we give a summary and concluding remarks. II. SIMULATION MODEL A. Diffusion model In this study the kinetic Monte Carlo KMC 9,10 method is applied to investigate the time evolution of surface growth. The KMC method is based on a solid-on-solid 11 model of epitaxial growth, which assumes a simple cubic lattice struc- ture with neither vacancies nor overhangs. The basic pro- cesses included in the model are deposition of adatoms and subsequent surface diffusion. The process of desorption has been omitted from the model since it is negligible under usual growth conditions of molecular beam epitaxy, which is commonly used in growing atomic scale structures. Thus the fractional surface coverage is given by  =Ft , where F is the constant deposition rate of atoms in ML/s, and t is the physical time. The deposition of adatoms takes place onto an initially flat substrate. In the simulations a deposition site is first selected at random, and then a search is carried out within a square of fixed linear size of 2 R i +1, centered upon the selected site. The site with a maximum number of lateral nearest neighbors is chosen as the deposition site. The diffusion rate of a single adatom is defined as the probability of a diffusion jump per unit time, and it is given by the Arrhenius-type expression k  E , T  =k 0 exp -E / k B T  , 1 where E is the activation energy, T is the substrate tempera- ture, and k B is the Boltzmann constant. The prefactor k 0 corresponds to the frequency of atomic vibrations, and it is PHYSICAL REVIEW B, VOLUME 63, 035407 0163-1829/2000/633/0354077/$15.00 ©2000 The American Physical Society 63 035407-1 © 2001 American Physical Society. Reprinted with permission from Physical Review B 63, pages 035407 : 1-7. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the publisher.