WIAS Preprint No. 1884, (2013)

Equilibrium shapes of poly-crystalline silicon nanodots


  • Korzec, Maciek D.
  • Roczen, Maurizio
  • Schade, Martin
  • Wagner, Barbara
  • Rech, Bernd

2010 Mathematics Subject Classification

  • 37D35 74E10 49Q10

2008 Physics and Astronomy Classification Scheme

  • 61.50.Ah


  • equilibrium shapes, anisotropic surface energy, adhesion energy, constrained optimization, Wulff construction, silicon nanodots, TEM


This 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 SiO$_2$ 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.

Appeared in

  • Journal of Applied Physics, 115 (2014) pp. 074304/1--074304/12.

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