Effects of the finite electrical conductivity of the crystal on hydromagnetic Czochralski flow

Abstract

There has recently been much interest in using hydromagnetic damping to reduce the turmoil of Czochralski silicon melts. Since molten silicon conducts electricity nearly as well as mercury, applied magnetic fields in the range of a few kilogauss have a pronounced effect on the melt motion. Digital simulations of magnetic Czochralski flow have taken the solid crystal to be a perfect electrical insulator. However, asymptotic considerations have shown this to be questionable: even though the electrical conductivity of solid silicon is only 3% that of the melt, current leakage into the crystal can significantly modify the melt flow. Numerical studies described here confirm quantitatively the predictions of the asymptotic theory. Accounting for crystal conductivity in the computational model leads to the expected major changes in the azimuthal motion. The meridional circulation and, concomitantly, the dopant transport are only slightly modified for the rotation rates considered.