工业级晶体生长FEMAG数值模拟.ppt

* * * * * * * * * * * * * * FEMAGSoft ? 2009 Evolution equations of UmV and WmV (diffusion dominated process) 4. Prediction of crystal quality (cont’d) 4. Prediction of crystal quality (cont’d) FEMAGSoft ? 2011 This model (which is an extension of the lumped model of Voronkov and Kulkarni) provides an approximate distribution of the micro-voids (average radius and mean square root) at any point and time. Full coupling between point-defects, micro-voids and any kind of species (oxygen or dopants) is currently under investigation. 4. Prediction of crystal quality (cont’d) FEMAGSoft ? 2011 Simulation results 4. Prediction of crystal quality (cont’d) FEMAGSoft ? 2011 Quasi-steady simulation From left to right : - Global temperature field - Global finite element mesh for heat and mass transfer calculations (temperature field and velocity field in the melt and the gas) Rs = 7.5 cm, Rc = 22 cm, Ws = -15 rpm, Wc = 8 rpm, vpul = .97 mm/min 4. Prediction of crystal quality (cont’d) FEMAGSoft ? 2011 Quasi-steady simulation Rs = 7.5 cm, Rc = 22 cm, Ws = -15 rpm, Wc = 8 rpm, vpul = .97 mm/min From left to right : - Unrefined finite element mesh for point- and micro-defect calculations in the crystal (2 successive mesh refinements were applied) - Temperature field in the crystal 4. Prediction of crystal quality (cont’d) FEMAGSoft ? 2011 From left to right: predicted Vacancy super-saturation ratio CV / CVeq (log10 scale)- Vacancy concentration CV (m-3, log10 scale)- Interstitial super-saturation ratio CI / CIeq (log10 scale)- Interstitial concentration CI (m-3, log10 scale)- Nucleation rate KmV (m-3s-1, log10 scale) Time-dependent simulationof micro-void nucleation and growth (Voronkov-Kulkarni model) Rs = 7.6 cm, Rc = 21.85 cm, Ws = 11 rpm, Wc = -5 rpm, vpul = 1.1 mm/min 4. Prediction of crystal quality (cont’d) FEMAGSoft ? 2011 4. Prediction of crystal quality (cont’d) FEMAGSoft ? 2011 Critical micro-void size nV* (n. lattice sites, log10 sca