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Analysis of the Effect of Cusp‐Shaped Magnetic Fields on Heat, Mass, and Oxygen Transfer Using a Coupled 2D/3D Global Model

The recent development of power devices requires silicon wafers in the radial direction as well as in the depth direction in a low oxygen concentration. Magnetic fields such as transverse or cusp‐shaped magnetic fields are then applied to the silicon melt to reduce the oxygen concentration in the crystal, especially those 300 mm in diameter or larger. Several studies reported calculated results of reduced oxygen concentration in the melt with cusp‐shaped magnetic fields. However, few studies have reported on the 3D transfer processes of oxygen in the melt. This paper reports on the transfer mechanism of oxygen in silicon melts with 300‐mm‐diameter crystals under cusp‐shaped magnetic fields during the growth of silicon crystals via the Czochralski method. Using in‐house software with a coupled 2D/3D global model, this study examines the effects of the flow fields in the melt on heat, mass, and oxygen transfer as a function of the relative position between the zero‐Gauss plane and the melt.