Thermocapillary convection during floating-zone silicon growth with a uniform or non-uniform magnetic field

Numerical solutions are presented for the thermocapillary convection during the floating-zone growth of silicon crystals with a steady, externally applied magnetic field. Three floating-zone shapes are treated: the ''barrel shape'' corresponding to growth in microgravity, the ''bottle shape'' corresponding to terrestrial growth without an induction coil, and a ''necked shape'' corresponding to growth with a radio-frequency induction coil. The magnetic field is either uniform and axial, or it is non-uniform and axisymmetric. Two non-uniform fields are considered. The results for the bottle shape with a uniform magnetic field help explain recent experimental results presented by Croll et al. [J. Crystal Growth 137 (1994) 95]. The results for the non-uniform fields show how the radial dopant non-uniformities in these experimental results can be avoided. The results for the barrel shape and for both uniform and non-uniform magnetic fields point to the benefits of combining microgravity and a magnetic field.