Physical model of the Czochralski crystal growth in a horizontal magnetic field

The horizontal magnetic field (HMF) may improve conditions in the melt during large silicon single crystal growth by the Czochralski technique. This observation is counter-intuitive as the HMF evidently breaks the rotational symmetry. A previous study has shown that the HMF is not able to
significantly delay the Rayleigh-Bénard instability in a rotating cylinder [1]. It has been observed [2] that an oscillating flow sets in soon after the linear onset. Can we expect a stabilizing effect of the HMF in the Czochralski growth? Why the symmetry breaking by the HMF is eventually not
so relevant? These are two central questions for our primarily experimental study using the room-temperature eutectic alloy GaInSn for dedicated model experiments, allowing an almost complete measurement of the velocity field inside the melt [3]. Besides, it is also meant as a benchmark for comparison with the numerical codes. To serve the latter purpose the boundary conditions should be preferably well defined. Having this in mind the temperature boundary conditions are defined as follows. An isothermal heating is applied at the bottom of a cylindrical cell filled with GaInSn
alloy. The side wall is thermally insulated. An optionally rotating isothermal cooler models the growing crystal. A water-cooled layer of an alkaline solution keeps the rest of the metal surface free from oxides and models the radiation heat loss. The maximum HMF strength is 0.3 T that
corresponds to a Hartmann number of about 1200. Velocity profiles are measured by ultrasound Doppler velocimetry. Temperatures are monitored in the vicinity of the triple point at the rim of the cooler, at the rim of the cell, inside of the cooler and of the heater. The Nusselt-Grashof number
dependency is obtained by controlling the total heat flux injected at the bottom and measuring the temperature difference between the bottom plate and the cooler. The critical cooler rotation rate is determined at which the rotation introduces a significant variation of the velocity field dominated by the HMF-aligned convection rolls.