Global Optimization of 2-Dimensional Nanoscale Structures: A Brief Review

This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. In the cluster structure community, global optimization methods are common tools for arriving at the atomic structure of molecular and atomic clusters. The large number of local minima of the potential energy surface (PES) of these clusters, and the fact that these local minima proliferate exponentially with the number of atoms in the cluster simply demands the use of fast stochastic methods to find the optimum atomic configuration. Therefore, most of the development work has come from (and mostly stayed within) the cluster structure community. Partly due to wide availability and landmark successes of scanning tunneling microscopy (STM) and other high resolution microscopy techniques, finding the structure of periodically reconstructed semiconductor surfaces was not posed as a problem of stochastic optimization until recently, when it was shown that high-index semiconductor surfaces can posses a rather large number of local minima with such low surface energies that the identification of the global minimum becomes problematic. We have therefore set out to develop global optimization methods for systems other than clusters, focusing on periodic systems in two dimensions (2-D) as such systems currently occupy a central place in the field of nanoscience. In this article, we review some of our recent theoretical work on finding the atomic structure of surfaces, with emphasis the global optimization methods. While focused mainly on atomic structure, our account will show examples of how these development efforts contributed to elucidating several physical problems, and we will attempt to make a case for widespread use of these methods for structural problems in one and two dimensions. 1. Introduction Silicon surfaces are the most intensely studied crystal surfaces since they constitute the foundation of the billion-dollar semiconductor industry. Traditionally, the low-index surfaces such as …