Scale up aspects of directional solidification and Czochralski silicon growth processes in traveling magnetic fields

• Scale up of DS-Si and Cz-Si in TMF was studied numerically and experimentally.
• Scale up method based on similitude was proposed using silicon as a model substance.
• Method related all present driving forces using Gr, Ste, Re, S and F numbers.

We performed 3D simulations of directional solidification (DS) and Czochralski (Cz) silicon growth processes in traveling magnetic fields (TMFs) and verified them with the experimental data that were available. Particularly, we studied silicon DS growth in real G1, G2 and G5 size setups and Cz growth in 6″ and 24″ crucibles in furnaces provided with KRISTMAG® heater magnet modules (HMMs). TMFs were used for a solid/liquid interface shaping and for a melt stirring. Based on our simulation findings, we discussed scale up challenges and proposed a method for safe upscaling. The method related all present driving forces using dimensionless numbers: Grashof (Gr), Stephan (Ste), Reynolds (Re), Shielding (S) and magnetic forcing number (F).