Numerical simulation of Czochralski crystal growth under the influence of a traveling magnetic field generated by an internal heater-magnet module (HMM)

Numerical studies of flow patterns during Czochralski growth of square-shaped Si crystals

“…Such a Lorentz force distribution causes a convection roll at the crucible moving downwards at the side walls and upwards in the region of the crystal. The inversion of the convection roll by a TMF was demonstrated by Klein et al in numerical simulations [8].…”

The sensitivity of a travelling magnetic field driven flow to axial alignment

“…1. Detailed information on the fluid flow in subcritical as well as in supercritical regimes may be found in [6,8,10,12,13,15,16].…”

“…Recently, TMFs in crystal growth gained popularity in the framework of the KRISTM AG project [11,12]. The target of this project is the development of an internal heater-magnet module for coupled generation of temperature and a TMF to be fitted into industrial Czochralski pullers and vertical gradient freeze equipments.…”

“…This heater-magnet module is described in [11] (quote): ''It replaces the conventional meander heater by a coil consisting of a spiral-or staircase-shaped current path, which is subdivided, in segments by contact points for the phase-shifted power supply.'' The authors of [12] call the inclusion of three-dimensional effects stemming from the particular bus-bar arrangement of the TMF 2.5D simulation. They compare the simple case of ignoring the bus-bars and holes with two other models taking these, in parts, into account, which models are again axisymmetric.…”

Applicability of LES turbulence modeling for CZ silicon crystal growth systems with traveling magnetic field

“…[1][2][3][4][5]. The main goal of using TMF is to get an additional process control ''button'' over melt motion, temperature gradients in the melt, and the shape of the crystallization interface and to ensure process stability.…”