Maximum growth rates for melt-grown ribbon-shaped crystals

From heat-balance considerations at the growing interface and an assumption of predominantly radiative heat loss from the surface, an expression for the maximum growth rate of melt-grown ribbon-shaped crystals has been derived. For a given material and a large width-to-thickness ratio, the maximum growth rate varies as the square root of the ribbon thickness and is independent of its width. A comparison of the maximum cylindrical and ribbon growth rates is made for the silicon system. Some representative values at 7.5 cm diameter or width are 45 cm/h or 2000 cu cm per h for a cylindrical Czochralski-grown crystal and 625 cm/h or 95 cu cm per h for a 0.02-cm-thick ribbon.