Equilibrium Analysis of Lattice-Mismatched Nanowire Heterostructures
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Equilibrium Analysis of Lattice-Mismatched Nanowire Heterostructures E. Ertekin1, P.A. Greaney1, T. D. Sands2, and D. C. Chrzan1 1 Department of Materials Science and Engineering University of California, Berkeley, California and Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 2 School of Materials Engineering School of Electrical & Computer Engineering and the Birck Nanotechnology Center Purdue University ABSTRACT The quality of lattice-mismatched semiconductor heterojunctions is often limited by the presence of misfit dislocations. Nanowire geometries offer the promise of creating highly mismatched, yet dislocation free heterojunctions. A simple model, based upon the critical thickness model of Matthews and Blakeslee for misfit dislocation formation in planar heterostructures, illustrates that there exists a critical nanowire radius for which a coherent heterostructured nanowire system is unstable with respect to the formation of misfit dislocations. The model indicates that within the nanowire geometry, it should be possible to create perfect heterojunctions with large lattice-mismatch. INTRODUCTION The recent demonstration of coherent, lattice-mismatched nanowire semiconductor heterostructures [1,2] by the Vapor-Liquid-Solid (VLS) synthesis mechanism [3,4] represent the first foray into a new realm of heterojunction functionality and performance. These longitudinally heterostructured nanowires enable band gap engineering in one-dimensional structures, with potential applications towards unique quantum dot geometries, p-n and bipolar junctions, and nanowire superlattices (for example, see [5-8]). The design of such devices will be accelerated substantially if design engineers can use a simple model to predict circumstances under which misfit dislocations will form at the interface. One-dimensional heterostructures differ from their planar counterparts via their elastic boundary conditions: while a thin film is constrained laterally during growth, a nanowire can relieve strain energy via elastic relaxation. Matthews and Blakeslee [9,10] investigated the lattice-mismatch phenomenon in heteroepitaxial systems, and developed an equilibrium critical thickness model for planar systems based on strain energy and misfit dislocation energy considerations. The goal of this study is to develop a simple model by extending the MatthewsBlakeslee model to one-dimensional systems. A schematic illustration of the heterostructured nanowire system is shown in Fig. 1. The system is oriented along the z-axis and comprises an infinitely thick nanowire overlayer and nanowire substrate.
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Figure 1. Schematic illustration of latticemismatched heterostructured nanowire system comprising an infinitely thick nanowire substrate and an infinitely thick nanowire overlayer. The misfit dislocation configuration in the plane of intersection is denoted as well by the dislocation lines in at the heterostructure interface. COHERENCY LIMITS IN LATTICE-MISMATCHED NANOWIRES: MODEL The equilibriu
