Formation of the spiral morphology of high melting point crystals pulled from the crucible

This paper presents a description and a model for the transition from cylindrical to spiral growth during Czochralski crystal pulling of high melting point materials. This transition comprises a number of symmetry breakings of the rotational symmetry of the crystal where the first one is ascribed to flaring growth. Flaring growth occurs when the crystal-melt interface has gained a supercritical concave shape. The concave shape arises in case of high melting point semitransparent oxides mainly when the axial radiative heat transport through the crystal becomes insufficient - e.g. when exceeding a certain grown length - and it arises for silicon crystals when the growth speed was chosen too large. The spiral growth starts with the growth of the crystal axis off the rotational axis. This is followed by two more symmetry breakings deforming the melt meniscus-crystal area. The azimuthal growth of the deformed meniscus, together with its axial growth by pulling, results in the spiral morphology. The transition from cylindrical to spiral growth discussed here is a genuine growth-instability - one which is not induced by external disturbances - and it is limiting the cylindrical growth in a fundamental way.