Effective Distribution Coefficient of Silicon Dopants During Magnetic Czochralski Growth

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Abstract
Silicon crystals have been grown under axial magnetic fields of up to 0.2 T. At 0.05 T the field starts to interact with the melt and dopant incorporation becomes erratic. As the field is increased to 0.2 T the interaction becomes more controlled and it is seen that the effective distribution coefficient (keff) moves towards unity. A theory based on the analysis by Burton, Prim & Slichter of the dependence of the effective distribution coefficient (keff) on growth and crystal rotation rates in Czochralski growth is extended to include the effect of an imposed steady axial magnetic field. The flow fields incorporated into the theory are based on the analysis of the hydromagnetic flow at a rotating disc due to Kakutani (J. Phys. Soc. Jpn (1962) 17, 1496). It is shown that keff approaches unity as the field increases.

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