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Computational Science, Engineering & Technology Series
ISSN 17593158 CSETS: 20
TRENDS IN ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: M. Papadrakakis, B.H.V. Topping
Chapter 14
Continuum and AtomicScale Modeling of SelfPositioning Microstructures and Nanostructures G.P. Nikishkov and Y. Nishidate
The University of Aizu, AizuWakamatsu City, Fukushima, Japan G.P. Nikishkov, Y. Nishidate, "Continuum and AtomicScale Modeling of SelfPositioning Microstructures and Nanostructures", in M. Papadrakakis, B.H.V. Topping, (Editors), "Trends in Engineering Computational Technology", SaxeCoburg Publications, Stirlingshire, UK, Chapter 14, pp 271294, 2008. doi:10.4203/csets.20.14
Keywords: nanostructure, selfpositioning, finite element method, atomicscale.
Summary
Selfpositioning fabrication procedure can be effectively used for creation of threedimensional micro and nanostructures. Multilayer structures composed of materials with different lattice periods are formed by the molecular beam epitaxy method. The selfpositioning occurs during etching out the sacrificial material layer. For the straight etching front, the selfpositioning produces structures shaped as rolledup hinges and tubes. This article presents investigations of the selfpositioning phenomena by analytical techniques, finite element analysis and atomicscale modeling.
Closedform solutions for curvature radius estimation of selfpositioning 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. Closedform solution for curvature radius estimation of selfpositioning rolledup structures is derived for the case of plane strain [1] (wide strips with bending constraint in one direction). Generalized plane strain deformation of multilayer selfpositioning structures is also considered [2]. An algorithm of the finite element method for threedimensional 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 selfpositioning of nanostructures consisting of GaAs and In_{0.2}Ga_{0.8}As epitaxial layers. Anisotropic analysis of selfpositioning 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 atomicscale finite element method (AFEM) based on the Tersoff interatomic potential has been developed [5]. Solution procedure for problems with large displacements is organized as the NewtonRaphson iteration procedure. The developed AFEM code is applied to modeling of GaAs and InAs bilayer selfpositioning 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), atomicscale effects play a considerable role. References
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