Mass transport in a Czochralski crystal puller with an axial magnetic field: Melt mouton due to crystal growth and buoyancy

Abstract

The mass transport of dopants and impurities in a silicon melt is considered for a Czochralski crystal puller with a uniform axial magnetic field. For magnetic field strengths 1≤ B O ≤5 T, the dominant flow fields are those driven by buoyancy and the growth of the crystal (the pulling of the crystal and the raising of the crucible bottom). The mass transport is intrinsically unsteady, and the concentration of a crystallizing particle depends on the entire history of the particle. The buoyancy driven flow provides a mechanism for the recirculation of fluid particles. However, the character of the flow in the diffusion boundary layers and the convection dominated cores depends on the competition between the crystal growth and buoyancy driven velocities, which in turn depends on the magnetic field strength and depth.