On the Manipulation of Nanoscale Self-Assembly by Elastic Field
- PDF / 86,491 Bytes
- 6 Pages / 612 x 792 pts (letter) Page_size
- 32 Downloads / 185 Views
T9.3.1
On the Manipulation of Nanoscale Self-Assembly by Elastic Field Y.F. Gao Division of Engineering, Brown University, Providence, RI 02920, U.S.A. ABSTRACT Morphological and compositional self-assembly can be manipulated by the long-range elastic field. This paper gives a universal formulation that determines the dependence of energetically favored orientation of those self-assembled structures on the elastic interaction. Elasticity anisotropy can lead to symmetry breaking and herringbone structures. A layered substrate can tune the feature size by modulus mismatch, or tune the orientation if the layers have different orientation preference, or guide the self-assembly by embedded structures. A closed-form result is derived for elastically isotropic layers by using Dundurs parameters. The self-assembled structures can also be affected by a nonuniform residual stress field or external force field. Higher order (nonlinear) perturbation theory, coupling between morphology and composition, and other issues are also addressed in the discussion. INTRODUCTION Nanoscale self-assembled structures offer many opportunities in growing uniform nanostructures with long-range orders and regular sizes. Surface self-assembly is usually due to the competition of surface energy and a force field [1-6]. This paper discusses how to manipulate nanoscale self-assembly by engineering the long-range elastic field. We focus our attention to morphological and compositional self-assembly. Examples of such phenomena can be found in adsorbate-induced surface restructuring, quantum dot formation, binary epitaxial thin films, among many others. Morphological self-assembly Under certain conditions, the nominally flat surface of a stressed solid can be unstable, leading to morphological instability (see, for instance, [1] and references therein). The elastic energy of a stressed solid with a wavy surface is always smaller than that with a flat surface. Elastic interaction can be better accommodated for morphological modulations with large frequencies (short wavelengths), which, however, gives rise to large surface energy. The competition between elastic energy and surface energy selects a critical wavelength above which perturbations grow and below which they decay. The morphological change is effected either by materials diffusing on the surface or by directly exchanging materials with the environment (e.g., evaporation/condensation, chemical etching). The chemical potential field along the surface is χ = χ 0 + Ω(γκ + w) , where χ 0 is the chemical potential field of the stress-free flat solid, Ω is the atomic volume, γ is the interface energy density, κ is the curvature (positive if the surface is convex), and w is the strain energy density on the solid surface. The mechanical equilibrium is assumed to be always attained, but
T9.3.2
the system is not in chemical equilibrium. The morphological modulation gives rise to a nonuniform chemical potential field along the surface, which provides the driving force for diffusive mass transport or di
Data Loading...
