An Interactive Desktop Computer Program for Simulating Nanometer Scale Surface Pattern Formation
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1177-Z09-19
AN INTERACTIVE DESKTOP COMPUTER PROGRAM FOR SIMULATING NANOMETER SCALE SURFACE PATTERN FORMATION
Michael Wang Albuquerque Academy High School, Albuquerque, New Mexico 87109, USA
ABSTRACT Nanometer-scale patterns may form as one or more chemical components deposit on a solid substrate. This self-assembly process can be described by a set of nonlinear integral-differential diffusion equations accounting for two opposing factors: phase separation to minimizing Gibb’s free energy in individual surface phases and reduction in phase boundaries to minimize surface energy created by phase separation. I here present a desktop computer program that allows us to interactively simulate self-assembly of nanometer-scale surface patterns. In particular, this program provides a convenient tool for studying the effects of temperature variations and preexisting patterns on the selfassembly process. Computer simulations show that an increase in temperature may enlarge pattern sizes and can eventually lead to the disappearance of the patterns.
INTRODUCTION The self-assembly of surface patterns on a solid substrate has recently attracted much attention because this process can potentially allow massive production of nanometer-scale arrays [1]. This self-patterning phenomenon has been observed in many chemical systems. For example, it has been shown that vapor deposition of lead onto a clean Cu (111) surface can lead to the formation of a complex set of nanometer-scale surface patterns, changing from circular islands to stripes and then to circular holes as the coverage of lead increases [2]. Similarly, cobalt deposited on a Mo(110) surface forms two-dimensional islands, whose structure and morphology strongly depend on the nature of the interface [3]. The islands are hexagonal on the clean surface and rectangular on a sulfur-covered surface [3]. Our ability to control or manipulate these nanostructures depends, to a large extent, on our mechanistic understanding of this self-assembly process. Phase Field models have recently been proposed to explain two-dimensional surface pattern formation. Among those, the models developed by Lu and his colleagues [4-7] are particular interesting. In those models, the self-assembly process is described by a set of nonlinear integral-differential diffusion equations accounting for two opposing factors: phase separation to minimizing Gibb’s free energy in individual surface phases and reduction in phase boundaries to minimize surface energy created by phase separation [4]. Those models explicitly couple the concentration of a surface chemical component with the surface stress induced by chemical concentration gradients. It has
been shown that such models are able to simulate complex surface pattern formations in binary and ternary systems [4-7]. In this paper, I present a desktop computer program that allows us to interactively simulate self-assembly of nanometer-scale surface patterns. This program is based on the models developed by Lu and his colleagues [4-7] but with inclusion of t
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