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- ItemEquilibrium shapes of poly-crystalline silicon nanodots(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Korzec, Maciek D.; Roczen, Maurizio; Schade, Martin; Wagner, Barbara; Rech, BerndThis study is concerned with the topography of nanostructures consisting of arrays of poly-crystalline nanodots. Guided by transmission electron microscopy (TEM) measurements of crystalline Si (c-Si) nanodots that evolved from a dewetting process of an amorphous Si (a-Si) layer from a SiO2 coated substrate, we investigate appropriate formulations for the surface energy density and transitions of energy density states at grain boundaries. We introduce a new numerical minimization formulation that allows to account for adhesion energy from an underlying substrate. We demonstrate our approach first for the free standing 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. We then use our method to predict the morphologies of poly-crystalline silicon nanodots.
- ItemOn a higher order convective Cahn-Hilliard type equation(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Korzec, Maciek Dominik; Rybka, PiotrA convective Cahn-Hilliard type equation of sixth order that describes the faceting of a growing surface is considered with periodic boundary conditions. By using a Galerkin approach the existence of weak solutions to this sixth order partial differential equation is established in $L^2(0,T; dot H^3_per)$. Furthermore stronger regularity results have been derived and these are used to prove uniqueness of the solutions. Additionally a numerical study shows that solutions behave similarly as for the better known convective Cahn-Hilliard equation. The transition from coarsening to roughening is analyzed, indicating that the characteristic length scale decreases logarithmically with increasing deposition rate