Three-dimensional simulation of heat flow, segregation, and zone shape in floating-zone silicon growth under axial and transversal magnetic fields

Three-dimensional simulation is carried out to illustrate the effects of magnetic fields on the heat flow, dopant segregation, and the zone shape in a small-scale floating-zone silicon growth. With an axial magnetic field, a steady growth can be found. However, with the increasing magnetic field strength, there is a steady solution with a four-fold symmetry before reaching an axisymmetric state. With a transversal field, although the molten zone is asymmetric, the minimum field strength required for a steady growth is found much lower than the axial one. The calculated results show a simple two-fold symmetry with respect to the magnetic direction. Although the convection on the plane parallel to the transversal field can be significantly suppressed, the flow on the perpendicular plane is not weakened at all due to the buildup of electric potential. This leads to a non-uniform zone and an elliptic crystal shape. Besides, due to the significant dopant mixing on the perpendicular plane, for the same field strength, the radial segregation in the transversal field is found smaller than that in the axial field.