Czochralski crystal growth in an axial magnetic field: effects of Joule heating

The feasibility of using magnetohydrodynamic effects to improve the quality of silicon crystals obtained by Czochralski growth from the melt has been demonstrated by several experimenters. An earlier publication pointed out that certain approximations widely used in liquid metal MHD make it relatively easy to incorporate magnetomotive effects into numerical models for Czochralski flow. Specifically, the low value of the magnetic Reynolds number gives rise to two useful simplifications: the induced magnetic field is negligible, and the electric field is irrotational. These lead to the result that the magnetic part of the calculation is diagnostic rather than prognostic. The earlier paper simulated the effect of a strong axial field applied to the melt, under the assumption that Joule heating is negligible. The validity of that assumption is confirmed here: except under extremely high fields, Joule heating represents only a miniscule part of the energy budget in magnetic Czochralski growth. Its effect upon the melt circulation can be ignored. © 1983.