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The present paper gives an overview of the complex mathematical modelling of industrial Czochralski (CZ) and floating‐zone (FZ) processes for the growth of large silicon single crystals from melt. Extensive numerical investigations of turbulent Si‐melt flows in large diameter CZ crucibles, global thermal calculations in growth facilities and analysis of the influence of various electromagnetic fields on CZ process are presented. For FZ process, a complex system of coupled 2D and 3D mathematical models is presented to show the possibilities of modelling from the calculation of the molten zone shape till the resistivity distribution in the grown crystal. A special developed program code is presented that is used to calculate the temperature field in the crystal including radiation exchange with reflectors, stress field due to thermal expansion and shape of the dislocated zone in the case of dislocation generation. Besides the macroscopic modelling of crystal growth processes, the crystallisation model on the atomistic level in the mean field approximation is also presented.

The paper describes numerical simulation tools for electromagnetic (EM), hydrodynamic, temperature and concentration fields in industrial Czochralski (CZ) and floating zone (FZ) single silicon crystal growth facilities under the influence of several alternating current (AC) and static DC magnetic fields. Such fields are expected to provide additional means to influence the melt behaviour, especially in the industrial growth of large diameter (200–300 mm) silicon crystals. The simulation tools are based on axisymmetric 2D models for (1) AC and DC magnetic fields in the whole crystal growth facility and (2) hydrodynamics, temperature and mass transport in the melt under the influence of the EM fields. The simulation tools are verified by comparison to temperature and velocity measurements in a laboratory CZ set‐up with eutectics InGaSn model melt and to resistivity measurements in grown silicon crystals.