Shape and stability of Menisci in czochralski growth and comparison with analytical approximations

Abstract

The shape and stability of menisci occurring during Czochralski growth have been studied by means of numerical methods for the case of the free surface. The existence of minimal growth angles is shown, beyond which the growing crystal will separate from the melt. The dependence of the interface height on the growth angle for different crystal diameters is tabulated. The maximum stable height and the corresponding growth angle are calculated as a function of crystal diameter. Our results are compared with known analytical approximations. Limitations of the applications caused by a finite crucible radius or low g values are pointed out.