Growing cylindrical silicon (100) crystals from a melt, four crystal ridges appear on the external surface of the crystal, see Fig. 1 showing the cone of a Float zone single-crystal. The appearance of the ridges can be traced back to the presence of {111} crystal planes at the crystal-melt interface. The most detailed theoretical description of the crystal ridge growth has been presented by V. V. Voronkov [1].  The description analyses the effect of undercooling, needed to sustain 2D nucleation growth, on the crystal growth angle. To analyze the ridge growth we have solved Herring’s equation describing the equilibrium orientation of crystal-melt, crystal-vapor and melt-vapor interfaces [2]. The equilibrium shape of silicon crystal was obtained from our molecular dynamics calculations. The equilibrium shape of crystal-vapor and melt-vapor interfaces was found in literature. The angular diagram showing equilibrium orientation of the crystal-melt and crystal-vapor interfaces as a function of the orientation of the free melt angle is used to calculate the shape of the crystal growth ridges and to predict the appearance of mirror like facets on the external surface of silicon crystals. The analytical solution of the Laplace equation for the perturbation of the melt surface in the presence of the crystal ridge together with the angular diagram was used to calculate the shape and the size of the crystal ridges for the Float zone crystal growth taking into account temperature gradients created in the melt by an inductor. Understanding of the crystal ridge growth,  leads to better understanding of the physical conditions at the triple phase line during the silicon crystal growth from a melt.

Acknowledgements

The present work is carried out at the University of Latvia and has been supported by the European Regional Development Fund, project contract No. 2011-0002-2DP-2.1.1.1.0-10-APIA-VIAA-085.

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1. Modelling of 3D features of molten zone in FZ silicon crystal growth
2. Hydrodynamical aspects of floating zone silicon crystal growth process