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

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

“…2, and considering TMFs generated by different currents with different frequencies and phase shifts, similar to the measurements reported in Ref. [17].…”

“…Finding ways to reduce the required magnetic flux densities is a main goal of the project KRIST g MAG, see also Refs. [16][17][18]. As suggested in Ref.…”

Model experiments and numerical simulations for directional solidification of multicrystalline silicon in a traveling magnetic field

“…[16]); the corresponding inductor current follows from the F L0 scaling mentioned above and is in both target cases 56% from the reference value. For the industrial scale, the scaled Lorentz force becomes rather weak, resulting also in relatively small flow velocities of 1 cm/s.…”

“…The additional influence of a TMF in large silicon melts is considered by Dropka et al [13]. Several studies are devoted to the effect of a TMF in small furnaces utilizing cylindrically shaped crucibles for growing various materials [14][15][16][17]40]. Grants et al carried out a general flow analysis for a wide range of parameters considering an idealized TMF for low frequencies with the skin effect neglected, but also only for cylindrical melts [18][19][20].…”

Influence of travelling magnetic fields on S–L interface shapes of materials with different electrical conductivities

“…Particularly, the application of a KRIST g MAG s internal heater-magnet module (HMM) for coupled generation of heat and TMF can significantly intensify the melt convection by generated Lorentz forces [4,5]. In the KRIST g MAG s project it was also shown that TMF can be successfully used in vertical gradient freeze (VGF) growth of Ge crystals to smooth the crystal-melt interface [6,7]. By the optimization of magnetic parameters as phase shift, amplitude and frequency of the AC part of the supplied HMM power, the interface morphology can be modified from an unfavorable concave one to a more promising slightly convex curvature.…”