FREE-SURFACE SHAPE AND AC ELECTRIC-CURRENT DISTRIBUTION FOR FLOAT ZONE SILICON GROWTH WITH A RADIO-FREQUENCY INDUCTION COIL

The float zone process involves a molten silicon zone between a melting polycrystalline feed rod above and a growing single crystal below. Frequently the feed rod is melted and the float zone is kept molten by the joulean heating from AC electric currents induced by a radio frequency induction coil around the float zone. The shape of the melt's free surface is determined by a balance of the hydrostatic pressure in the melt, the surface tension force and the inward electromagnetic body force due to the AC electric currents near the surface of the melt. For a given geometry of the induction coil, the distribution of AC electric currents depends on the free surface shape. Therefore the determination of the free surface shape and the determination of the distribution of the AC electric currents due to the induction coil are intrinsically coupled. This paper presents an iterative method to determine both the free surface shape and the AC electric current distribution. This treatment assumes that the zone's radial and axial dimensions are known. This method is illustrated with four cases combining two different induction coil shapes and two different AC voltages applied to the induction coil. © 1990.