Hydrodynamical aspects of the floating zone silicon crystal growth process

• System of mathematical models was verified for 4 inch floating zone process.
• Experimental tendencies for current frequency lowering were obtained numerically.
• Resistivity of grown Si single crystal was compared to experimental data.
• Differences between axis-symmetric and nonsymmetric models are analyzed.

3D numerical modeling of dopant transport in the melt is carried out for the 100 mm floating zone silicon single crystal growth process. The axis-symmetric shape of the molten zone is calculated with the program FZone   considering the coil and the high frequency (HF) electromagnetic (EM) field in 3D. Time dependent melt flow, temperature and dopant concentration fields are modeled using a specialized solver based on the open source code library OpenFOAM®OpenFOAM®. The influence of the Marangoni coefficient in the boundary conditions on the melt velocity field is analyzed. The obtained shapes of the crystallization interface and resistivity profiles in the grown crystal are compared with experimental results. Differences between axis-symmetric and non-symmetric models are analyzed.