Convective phenomena in large melts including magnetic fields

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

“…Refs. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] and the references therein. The major advantage of time-dependent versus static magnetic fields lies in the fact that considerably lower magnetic flux densities are required to induce a Lorentz force of the same order in the melt.…”

Numerical optimization of the interface shape at the VGF growth of semiconductor crystals in a traveling magnetic field

“…On the other side it demonstrates the strength and efficiency of the combined HMM very obviously. The actual value of F b within the present melt column can be estimated according the relation F b ¼ rbgDT [14] and becomes only about 25 N m À3 (r -density of the Ge melt ¼ 5.5 Â 10 3 kg m À3 [15], b -thermal volumetric expansion coefficient ¼ 1 Â 10 À4 K À1 [16], g -gravitational acceleration ¼ 9.81 m s À2 , DT -maximal radial temperature difference E4 K). Hence, in reality a much lower power of about 3 kW must be supplied to the given HMM to induce a counter-acting force density of identical value.…”

Travelling magnetic fields applied to bulk crystal growth from the melt: The step from basic research to industrial scale

“…To demonstrate the higher damping efficiency of TMF compared to SMF under realistic growth conditions, the considerations of Muiznieks et al [45] for a standard silicon Czochralski system are cited (see also [52], at VGF growth of 2 in. InP crystals under TMF with B of 4.5 mT (f ¼ 50 Hz) the downwardoriented Lorentz force led to a decreased flow velocity and interface flattening.…”

“…Table 1 compiles characteristic flow parameters, which predominate the melt convection in crystal growth systems. Their force densities were recently estimated by Muiznieks et al [45] for silicon melts in standard Czochralski pullers. Maximal force densities are generated by the buoyancyand rotation-driven flows of 142 and 150 N m À3 , respectively.…”