Numerical study of Czochralski growth of silicon in an axisymmetric magnetic field

Abstract

The amounts and distributions of oxygen, dopants and other contaminants in Czochralski grown silicon depend critically on motions in the melt during the crystal growth. The motions in the melt, induced mainly by temperature gradients and by crystal and crucible rotations, can be suppressed and the crystal quality can be improved by application of a magnetic field. The flow fields for a 75 mm diameter crystal growth in a steady, axisymmetric (axial or cusp) magnetic field were numerically obtained for crystal rotational rates from 0 to 30 rpm and for crucible counter-rotational rates from 0 to 15 rpm. For small axial magnetic fields ( ≤ 0.1 T), the meridional flow field depended significantly on the crucible rotational rate and for large axial magnetic fields it depended significantly on the crystal rotational rate. For cusp magnetic fields, the meridional flow field was dominated by thermocapillarity. The flow fields indicated that the oxygen incorporation into the crystal would be less for the growth in a cusp magnetic field than in an axial magnetic field.