Fig. 1. Time-averaged temperature and velocity distribution in a vertical CS without MF and at Ar flowrate of 5200 slh.

Fig. 2. Time-averaged temperature and velocity distribution in a vertical CS at cusp MF of 30 mT and Ar flowrate of 5200 slh.

Effect of magnetic fields in 400 mm Czochralski Silicon growth

Increase in the crystal diameter necessitates the control over the turbulent natural convection in large volumes, which is often achieved via magnetic fields (MF). Application of MFs changes heat transfer and convection patterns in the melt. Flow laminarization at high MFs results in higher temperature gradients, which, along with vanishing turbulent mixing, increase dramatically the effect of Marangoni stress tension on the melt free surface. The effect of the gas shear stress on the melt surface velocity also radically increases and may even govern the global melt flow dynamics.

A parametric study performed using 3D unsteady simulations showed that Ar flow along with MF is of crucial importance for finding the optimal growth conditions and that certain essential effects can not be reproduced in computations unless Ar flow is taken into consideration.

Computations show that under the considered operating conditions downward melt motion takes place under the crystallization front when no magnetic field is applied, Figure 1. When cusp MF of low intensity is applied, thermal pulsations in the melt are largely suppressed, while mixing of the melt under the crystallization front remains vigorous, Figure 2.

Fig. 3. Time-averaged temperature and velocity distributions in a vertical CSs and at the melt free surface at horizontal MF of 30 mT and Ar flowrate of 5200 slh.

At the horizontal MF of 30 mT there is only a small difference between CSs positioned along and orthogonal to the magnetic induction vector, see Figure 3. The melt over the whole free surface, in this case, is rotating due to the crucible rotation and the temperature distribution is quite symmetric.

Fig. 4. Time-averaged temperature and velocity distributions in a vertical CSs and at the melt free surface at horizontal MF of 300 mT and Ar flowrate of 5200 slh.

As the MF increases up to 300 mT, it becomes obvious that strong horizontal MFs nearly completely suppress flow in a CS positioned along the induction vector, leaving high velocity flows in the melt CSs positioned orthogonal to the magnetic induction vector, Figure 4. One can also substantially asymmetric temperature distribution at the melt surface and an upward flow of the melt in the area located under the crystal. This upward motion results from combined action of MFs and Ar flow and, therefore, can not be reproduced when Ar flow is low or ignored in computations, see Figure 5.

Fig. 5. Time-averaged temperature and velocity distributions in a vertical CSs and at the melt free surface at horizontal MF of 300 mT and Ar flowrate of 500 slh.

Adequate account of the Ar flow is crucial for modelling of large diameter Silicon growth by Czochralski method as it allows one to reproduce and study regimes with upward flow motion under the crystal that appear to be close to optimal in terms of the crystallization front deflection and distribution of the V/G parameter, see Figure 6.

(a)	(b)
Fig. 6. Computed deflections of the crystallization front (a) and the respective distributions of the V/G parameter along the melt/crystal interface (b).