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Main Title: Equilibrium shapes of poly-crystalline silicon nanodots
Author(s): Korzec, Maciek
Wagner, Barbara
Roczen, Maurizio
Schade, Martin
Rech, Bernd
Type: Research Paper
Abstract: This study is concerned with the topography of nanostructures consisting of arrays of poly-crystalline nanodots. Guided by transmission electron microscopy (TEM) measurements of c-Si nanodots that evolved from a "dewetting" process of an a-Si layer from a SiO2 coated substrate, we investigate appropriate surface energy density formulations to model these equilibrium geometries. We explore the influence of smooth transitions between the energy density states at grain boundaries on the associated surface morphology of the equilibrium poly-crystals. Furthermore, we introduce a new numerical minimization formulation that allows to account for adhesive energy from an underlying substrate. We demonstrate our approach first for the unbounded case, where the solutions can be compared to well-known Wulff constructions, before we treat the general case for interfacial energy settings that support partial 'wetting'. Eventually, we use the method to study two-dimensional shapes of poly-crystalline silicon nanodots.
Subject(s): equilibrium shapes
anisotropic surface energy
adhesive energy
constrained optimization
Wulff construction
silicon nanodots
Issue Date: 21-Aug-2013
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 74G15 Numerical approximation of solutions
74G65 Energy minimization
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2013, 21
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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