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Higher Order Regularization of Anisotropic Geometric Evolution Equations in Three Dimensions

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Understanding the dynamics of crystalline surfaces on a nanometer scale is one of the key issues for several semiconductor applications. We consider the thermal faceting of such surfaces resulting from strong anisotropies and generalize recently proposed geometric evolution laws based on curvature dependent free energy densities. Mathematical arguments on the regularity of the solution in 3D lead us to new evolution laws which are based on free energy functions including not only the curvature but also its derivative.
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Keywords: ANISOTROPIC GEOMETRIC EVOLUTION LAWS; HIGHER ORDER EQUATIONS; THERMAL FACETING

Document Type: Research Article

Publication date: August 1, 2006

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  • Journal of Computational and Theoretical Nanoscience is an international peer-reviewed journal with a wide-ranging coverage, consolidates research activities in all aspects of computational and theoretical nanoscience into a single reference source. This journal offers scientists and engineers peer-reviewed research papers in all aspects of computational and theoretical nanoscience and nanotechnology in chemistry, physics, materials science, engineering and biology to publish original full papers and timely state-of-the-art reviews and short communications encompassing the fundamental and applied research.
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