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TRENDS IN ENGINEERING COMPUTATIONAL TECHNOLOGY
Edited by: M. Papadrakakis, B.H.V. Topping
Continuum and Atomic-Scale Modeling of Self-Positioning Microstructures and Nanostructures
G.P. Nikishkov and Y. Nishidate
The University of Aizu, Aizu-Wakamatsu City, Fukushima, Japan
G.P. Nikishkov, Y. Nishidate, "Continuum and Atomic-Scale Modeling of Self-Positioning Microstructures and Nanostructures", in M. Papadrakakis, B.H.V. Topping, (Editors), "Trends in Engineering Computational Technology", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 14, pp 271-294, 2008. doi:10.4203/csets.20.14
Keywords: nanostructure, self-positioning, finite element method, atomic-scale.
Self-positioning fabrication procedure can be effectively used for creation of three-dimensional micro- and nanostructures. Multilayer structures composed of materials with different lattice periods are formed by the molecular beam epitaxy method. The self-positioning occurs during etching out the sacrificial material layer. For the straight etching front, the self-positioning produces structures shaped as rolled-up hinges and tubes. This article presents investigations of the self-positioning phenomena by analytical techniques, finite element analysis and atomic-scale modeling.
Closed-form solutions for curvature radius estimation of self-positioning hinge structures are obtained for cases of plane strain and generalized plane strain deformation, which are suitable for wide strips with bending constraint in one direction.
Closed-form solution for curvature radius estimation of self-positioning rolled-up structures is derived for the case of plane strain  (wide strips with bending constraint in one direction). Generalized plane strain deformation of multilayer self-positioning structures is also considered .
An algorithm of the finite element method for three-dimensional anisotropic problems with large displacements and rotations has been formulated [3,4]. The finite element method is used to study the effect of material anisotropy on the self-positioning of nanostructures consisting of GaAs and In0.2Ga0.8As epitaxial layers. Anisotropic analysis of self-positioning structures with different orientation of material axes demonstrates that dependency of the curvature radius on the material orientation angle is a periodic curve with the maximum curvature radius observed for orientation angle of 45 degrees. Nanohinges with different material orientation angles can exhibit curvature radii differing by 35%.
An algorithm of the atomic-scale finite element method (AFEM) based on the Tersoff interatomic potential has been developed . Solution procedure for problems with large displacements is organized as the Newton-Raphson iteration procedure. The developed AFEM code is applied to modeling of GaAs and InAs bi-layer self-positioning nanostructures. A problem series includes investigation of nanohinge curvature radius dependence on the structure thickness and the material orientation angle. The curvature radius converges to the continuum mechanics solution under plane strain conditions with increasing the structure thickness. For nanostructures of small thickness (less than 40 nm), atomic-scale effects play a considerable role.
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