Preprint 21-2013

Equilibrium shapes of poly-crystalline silicon nanodots

Author(s) : Maciek Korzec , Barbara Wagner , Maurizio Roczen , Martin Schade , Bernd Rech

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 21-2013

MSC 2000

74G15 Numerical approximation of solutions

74G65 Energy minimization

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 SiO$_2$ 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.

Keywords : equilibrium shapes, anisotropic surface energy, adhesive energy, constrained optimization, Wulff construction, silicon nanodots, TEM