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

Model Experiments for Flow Phenomena in Crystal Growth

“…• With Pr ≪ 1, suitable to model semiconductor melts: for example, Hg (melting point at -39°C), GaInSn (10.5°C), Ga (29.8°C), BiPbCdSn (Wood's metal) (72°C) • With Pr ≫ 1, suitable to model oxide or fluoride melts: for example, silicone oils, NaNO 3 (307°C) TC, potential probes [17,18] CZ Si 300 (800) BiPbCdSn 1·10 5 1·10 10 TC, potential probes [19] CZ Si 70 (178) GaInSn AC, DC 2·10 3 2·10 8 TC, UDV [20,21] FZ (high Pr) 6 NaNO 3 etc. + 2·10 1 2·10 3 TC, PIV [22,23] FZ Intermet 50 GaInSn AC 8·10 3 0 U D V [24] VGF (low Pr) 60 Ga, GaInSn AC, DC 9·10 2 6·10 6 TS, UDV [25,26] VGF GaAs, Ge 73 GaInSn AC, DC 7·10 2 5·10 6 TC, UDV [27,28] DS Si 100 Ga, GaInSn + AC 3·10 3 1·10 7 TC, UDV [29,30] DS Si 220 Ga + AC 3·10 4 1·10 8 TC, UDV [31,32] DS Si 420 BiPbCdSn AC 6·10 3 4·10 9 TC, UDV [33] Note that simple isothermal flows depend only on the Reynolds number, so that even water may be suitable to model a semiconductor melt.…”

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

“…It can be concluded that for the present system calculations without explicit turbulence models lead to a reasonable agreement with experiments. It is important to mention that in the literature very often turbulence models are employed for similar systems with a TMF, such as the k-omega-SST model [13,26] or various LES models [36].…”

“…First evaluation of the velocity oscillation spectra showed that the usual Fast Fourier Transform is not sufficient to filter out the noise and make reliable comparisons between numerical and experimental results. Instead, special algorithms as described, e.g., by Krauze et al [36] are required for a detailed analysis of velocity time profiles. This has not yet been done.…”

Numerical investigation of magnetic field effect on pressure in cylindrical and hemispherical silicon CZ crystal growth

“…The use of external magnetic fields is ubiquitous in the metals and semiconductor industries to control the melts behavior during solidification and ensuring improved process performances with better quality products 1–9. A direct current magnetic field is used to reduce nondesired turbulent flows and fluctuations associated with melt convection during solidification to help eliminating solidification defects and striations.…”

“…Inhomogeneties are thus reduced and the crystal quality is improved. The effect of magnetic field on temperature and flow fields has been considered by many researchers 1–11, while the pressure which is a key parameter in the growth process in natural, thermocapillary and forced convection modes 12 has not been studied under the influence of a magnetic field to our best knowledge. In addition, the silicon Czochralski crystal growth in spherical crucible is found to be of better advantages relatively to the cylindrical system when the magnetic field is not applied 12–16.…”