Simulation of the Organization of Heteroepitaxial Monolayer Islands Under Anisotropic Conditions
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Simulation of the Organization of Heteroepitaxial Monolayer Islands Under Anisotropic Conditions Gajendra Pandey and Robert V. Kukta Department of Mechanical Engineering State University of New York at Stony Brook Stony Brook, NY 11794-2300 U.S.A. ABSTRACT This paper addresses the effect of anisotropy on the organization of epitaxial islands deposited on a substrate. Focus is on in-plane anisotropies in surface stress and lattice mismatch between the film and substrate materials. Starting from a configuration where island sizes and position are random, evolution towards equilibrium through mass transport via condensation/evaporation is simulated. The effect of the degree of anisotropy is investigated. An efficient numerical method is obtained by reducing a model of square monolayer islands of finite size to point defects that interact through their elastic fields. Models for both the kinetics and energetics of the system are obtained by this reduction. It is found that the point source model is accurate for island separations larger than about 3 times the width of an island. Under isotropic conditions islands tend to form into hexagonal arrays, and as there is no preferred orientation of these arrays, defects analogous to grain boundaries in a crystalline material tend to arise. With anisotropy islands tend to align in particular directions. This is found to enhance organization in cases of modest anisotropy and cause islands to form into zigzagged lines in cases of high anisotropy. INTRODUCTION Fabrication of regular quantum dot arrays by self-assembly of epitaxial islands has been investigated for over a decade with modest progress. Much of the research has focused on achieving regular two dimensional arrays with islands of uniform size [1-3]. Islands typically nucleate randomly on the substrate [4] and subsequently grow and evolve by mass transport between islands or within individual islands. As the system evolves, organization is driven by elastic interactions between islands [3, 5], which guides mass transport. For an isotropic system, islands repel each other. The repulsion is independent of orientation and tends to produce a hexagonal array of islands. However since there is no directional preference, hexagonal domains form across the substrate with random orientations and meet to form defects. Material anisotropies provide a directional preference, which if large enough can cause domains to form with the same orientation and thereby decrease defect formation and promote organization over large areas of the substrate. The effect of anisotropy on the organization of islands is discussed in this article. Interest is on sub-monolayer growth where islands are atomically flat raised terraces bounded by steps on the substrate surface. The system evolves by mass transport driven by elastic interactions between surface steps. Following Alerhand et al. [6] and Tersoff et al. [7, 8], the elastic field of a step is approximated by a line distribution of force applied on the surface of an elastic half space. The
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