FEMAG块晶体生长数值模拟-如何将直拉法模拟技术拓展到区熔法生长.ppt

* * Typical FEMAG-FZ global unstructured mesh for heat transfer and induction heating FEMAGSoft ? 2013 Modeling of FZ growth (cont’d) FEMAGSoft ? 2013 FEMAG-FZ time-dependent simulation of the growth of a silicon crystal Use of an equivalent thermal conductivity Modeling of FZ growth (cont’d) Free interface constraining loci (secondary mesh) in FZ growth FEMAGSoft ? 2013 Modeling of FZ growth (cont’d) FEMAGSoft ? 2013 Inverse modeling in FZ growth much more difficult problem than in Cz growth can lead to misleading interpretations of the simulation results since completely inverse models result in the calculation of the melt volume and hence parametric studies are difficult to interpret with classical simplified models, the open melting front (OMF) is imposed and the melting front is either imposed or calculated (as an isotherm) Modeling of FZ growth (cont’d) FEMAGSoft ? 2013 Open Melting Front after extraction of the single crystal Modeling of FZ growth (cont’d) FEMAGSoft ? 2013 Main issue: modeling of the Open Melting Front (OMF) Physical problem: the flow of the molten silicon along the OMF and the angle at which the melt-gas interface detaches from the OMF require accurate modeling in view of their direct impact on the radiation transfer to the OMF and on the melt-gas interface shape Numerical problem: the coupled solution of a problem with 4 interfaces (solidification front, melting front, melt-gas interface, and OMF) and 3 tri-junctions represents a difficult problem of computational geometry. Modeling of FZ growth (cont’d) FEMAGSoft ? 2013 Other key issues: Species transport (dopant and impurities): the problem is similar to species transport in Cz growth, but much more difficult since almost no turbulent mixing is present in FZ growth Oscillations of the crystal and/or feed-rod rotation rates: this technique is often used to better mix the melt and can be simulated by use of a quasi-dynamic model 3D effects: non-axisymmetric effects are generated (i) by