Effect of magnetic fields in 400 mm Czochralski
Time-averaged temperature and velocity distribution in a vertical CS without MF and
at Ar flowrate of 5200 slh.
Time-averaged temperature and velocity distribution in a vertical CS at
cusp MF of 30 mT and Ar flowrate of 5200 slh.
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.
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.
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.
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.
Fig. 6. Computed
deflections of the crystallization front (a) and the respective distributions
of the V/G parameter along the melt/crystal interface (b).