Hydromagnetic flows and effects on Czochralski silicon crystals

Abstract

The most important method of producing single crystals in large quantities is Czochralski growth. Fluid motion within the melt affects the transport of heat and solutes to the growth interface, and has therefore been the subject of much study. Some Czochralski melts, such as silicon, are excellent conductors of electricity, so that the flow can be modified hydromagnetically. Flow under the influence of an axial magnetic field has received the most attention because the configuration remains rotationally symmetric. In the case of a uniform field, the theory has been extensively developed, using both asymptotic and numerical methods. The advantage of quiescent flow is offset by an unfavorable radial distribution of solutes in the finished crystal. Consequently, alternate configurations are being explored. A transverse field destroys the axial symmetry, but can sometimes be investigated by a combination of asymptotic and numerical methods. A non-uniform axial field is another possibility that may offer advantages. This can be investigated with minor modifications of the theory for uniform fields. © 1993.