A magnetic field can be applied in the CZ system in order to damp the oscillations in the melt. The process is called magnetic Czochralski crystal growth (MCZ). The applied field creates an electric current distribution and an induced magnetic field in the electrically conducting melt. This produces a Lorentz force that influences the flow and reduces the amplitude of the melt fluctuations.

External magnetic fields in MCZ growth may be steady-state, time-harmonic or time-dependent, and axial, transverse, axisymmetric or three-dimensional. The following results are for a static axisymmetric cusp field.

The model for the MCZ process leads to the following two main steps: First, we solve the external static magnetic field from a given magnet configuration and current distribution. Thereafter, we solve the time-dependent magnetohydrodynamical (MHD) problem for the coupled velocity, pressure, temperature and induced magnetic fields in the silicon melt. The MHD problem consists of Navier-Stokes, heat and induction equations.

The melt flow is driven by the forced convection due to the rotations of the crucible and the crystal, by Grashof and Marangoni convections due to temperature differences in the melt and by the Lorentz force due to both external and induced magnetic fields.

The figure compares the temperature (on the left side) and velocity (on the right side) fields in the CZ (topmost plot) and MCZ growth with a cusp field (the strength increasing from top to bottom). The larger the applied field, the larger the stabilizing effect on the melt convection is.