Project description

Objective 01

Modelling of melt flow under the influence of a special type of electromagnetic field (EMF) in an isothermal configuration

Due to the electromagnetic skin effect, it is likely that the techniques based on the implementation of simple magnetic fields in directional solidification method, that were seen to be quite efficient in Czochralski growth will not allow an adequate control of heat and species transfer in large crucibles, especially in the center of the mould.

The main idea of the present project is to obtain a melt stirring in a directional solidification rectangular configuration using a special type of an electromagnetic field. The mould is placed in a vertical magnetic field and an electrical DC current passes the melt through two or more small diameter electrodes attached to the melt surface. The effects of the electrode on the thermal and velocity field at the free surface were ignored due to the small size of the electrode. Because of the Lorentz force, generated by the VMF and the radial components of the electrical current, the melt will spontaneously rotate. With such an approach a better mixing can occur in the middle of the mould.

Time-dependent computations will be carried out with the software STHAMAS3D, which was developed at the Crystal Growth Laboratory in Erlangen, under the coordination of Prof. Dr. D. Vizman and already validated by experiments for the Czochralski and Bridgman processes. The discretization procedure of STHAMAS3D is based on the finite volume method. 3D model will be further developed in order to take in consideration one or more electrodes. In order to obtain a realistic solution starting from an arbitrary initial solution at least 800 sec real time should be computed with a time step of 0.1 sec. Therefore, a huge computational power is needed to perform a parametric study under these constraints. Therefore, STHAMAS3D will be developed in order to run on one of the most powerful supercomputer in Romania (IBM Blue Gene, 13Tflops), installed one month ago at West University of Timisoara.

Objective 02

Experimental study of melt flow under the influence of a special type of electromagnetic field (EMF) in a model experiment

One of the main issue in the development of numerical models is the validation procedure. Therefore it is of high importance for the model validation in the view of applications at industrial scale facilities to build up a model experiment in order to obtain relevant data to be compared with the numerical results. We propose to build up an experimental setup to study the melt flow under the influence of EMF. This model experiment will consists of the next parts:

  1. A coil with an iron core ready to produce a vertical magnetic field of max. 200mT. Our first intention is to obtain the stirring effect at lower intensities of the magnetic fields (tens of mT). Magnetic field will be measured with a Hall Magnetometer.

  2. A crucible with a rectangular cross section of max 10x10x10 cm made of Plexiglas will be filled with a GaInSn melt. The mould will be placed in a gap in iron core in order to be under the influence of a vertical magnetic field (VMF).

  3. Two or more electrodes made by graphite will be placed in contact with the free surface of the melt. A continuous electrical current will pass through these electrodes. The electrodes will be connected to a DC electrical source. Because of the Lorentz force, generated by the VMF and the radial components of the electrical current, the melt will spontaneously rotate.

  4. An ultrasound Doppler velocimetry (UDV) will be used for measuring the fluid velocity in the mould. UDV method is based on the pulse-echo technique and delivers instantaneous profiles of the local velocity along the ultrasonic beam and can be applied to obtain experimental data from a bulk in opaque liquids. The UDV sensors will be mounted at the outer wall of the mould within a vertical (or horizontal) line in order to measure the velocities in a horizontal or vertical section.

Using this experimental setup the flow structure in the mould can be investigated for different values of magnetic field, current intensities, number of the electrodes and their position. The flow structure in the bottom part of the mould is of particular interest because in real multicrystalline silicon growth facility the solid-liquid interface is at the bottom of the melt. The measured melt flow velocities can be compared with the numerical results obtained in Objective 1.

Objective 03

Modelling of melt flow and impurities distribution under the influence of EMF in an industrial scale directional solidification furnace for multicrystalline silicon growth

After experimental verification, presented EMF numerical model could be transferred to industrial scale furnace and numerical simulations will be performed for an industrial scale directional solidification for multicrystalline silicon in order to understand the physical phenomena and to give information for the design of the experimental configuration. The computational domain used for the local 3D-simulations with STHAMAS3D is restricted to the silicon melt and solid domains. The melt flow is described by the three-dimensional time-dependent equations of mass, momentum, and heat conservation taking into account the Boussinesq approximation for an incompressible Newtonian fluid. The heat transfer in the solid is assumed to take place by conduction. At the solid-liquid interface the latent heat generation is considered for the given crystallization velocity. In order to determine the position and shape of the solid-liquid interface, a phase tracking procedure was used, i.e. after each time step the grid is deformed in such way that the boundary between melt and solid fits to the melting temperature. The temperatures along the lateral vertical side walls and at the bottom are considered to be fixed and characteristic for real experimental configurations. First, the influence of the EMF on the fluid flow and on the interface shape will be studied. Secondly, in order to show the potential of EMF configuration to control C and N contamination in the melt, the diffusion equation in the melt will be solved together with momentum and heat equation. Temperature dependent C and N concentration at the crucible boundary will be considered. Another very important issue for directional solidification of silicon ingots is the formation of SiC-and Si3N4-precipitates in the melt and in the crystal. In order to demonstrate the influence of EMF on these precipitates distribution in the melt, a model of formation of particles[24] will be implemented in STHAMAS3D and numerical simulations will be performed for different field parameters.

It is expected that these simulations will show the potential of the EMF stirring to control the melt flow and impurity distribution in the directional solidification of silicon ingots and will provide valuable information for the design of an EMF experimental set up at industrial scale.