International Scientific Colloquium Modelling for Electromagnetic Processing Hannover, March 24-26, 2003 Numerical 2D Modelling of Turbulent Melt Flow in CZ System with AC Magnetic Fields A. Krauze, A. Muižnieks, A. Mühlbauer, Th. Wetzel, L. Gorbunov, A. Pedchenko Abstract The paper presents investigations of features of turbulent melt flow in axially symmetric CZ silicon crystal growth system with various AC magnetic fields (travelling, alternating) by 2D mathematical modelling. The electromagnetic system is calculated by self-developed program and the calculations of melt motion are carried out with the user modified hydrodynamic program package CFD-ACE 5.4. Extremely fine grids and a modified low Re k- ε turbulence model are used for HD calculations. The features of the flow and temperature field structure are investigated and the influence of AC field strength and crucible and crystal rotation is shown. The comparison between calculation results and temperature measurements in the corresponding laboratory model with low temperature InGaSn eutectics has shown good agreement. Introduction Czochralski silicon (up to 300mm) crystal growth systems become large due to microelectronics demands. Fast and stable growth, along with increasing requirements on crystal quality, are difficult to reach by conventional means. Therefore, new additional influence possibilities on melt movement are needed. One such a possibility is the use of AC magnetic fields. Models with AC magnetic fields were calculated previously, examples could be found in [1-2]. However, a more detailed analysis of melt flow features and a careful comparison with experiment are needed, especially because of turbulence. This paper presents a 2D model system based on a self-developed program for EM calculations and the program package CFD-ACE 5.4 with modified low Re k-ε turbulence model for HD calculations. Comparisons of results of numerical calculations and measurement data for averaged temperatures and temperature fluctuations are done. 1. Experimental CZ system model An experimental model of CZ system was build by ELMATEC Ltd, Latvia (L. Gorbunov, Y. Gelfgat and A. Pedchenko). Instead of silicon, InGaSn eutectics was used in this model. The scheme of experimental model can be seen in Fig. 1. It consists of 20 crucible and a crystal model, both can rotate. A cooling system was implemented on the free surface to emulate radiation losses. Special heaters were used to heat the crucible. Temperature and temperature fluctuation distributions were measured and used in comparison with calculation results. 219
2. Numerical model Alternating current magnetic field generates eddy currents in the melt. These currents interacting with magnetic field create EM force distribution that affects melt flow. EM and force fields were calculated with self-developed program package. An example of magnetic field distribution (isolines of real part of vector potential) for Travelling up field with phase shift 60º can be seen in Fig. 1. Various magnetic fields were calculated travelling up, travelling down, alternating and others. The Program package CFD-ACE 5.4 with modified low Re k-ε turbulence model was used for HD calculations. EM force fields were used as momentum sources in HD equations. Calculation series with each magnetic field were carried out changing EM field intensity. Also series with different crucible and crystal rotation rates without magnetic field were done. Fig. 1. Vector potential isoli-nes in case of Travelling up magnetic field; phase shift 60º. Fig. 2. Radial temperature distribution 5 mm below the free surface in case of Travelling up magnetic field; phase shift 60º. Fig. 3. Dependence of radial temperature drop 5 mm below the free surface on inductor current for Travel-ling up magnetic field, phase shift 60º. Fig. 4. Dependence of radial temperature drop 5 mm below the free surface on inductor current for Alternating magnetic field. 220
3. Calculation results and comparison with experimental data Here, the results of calculations performed for cases with rotating crystal (15 rpm) and crucible (-5 rpm) are presented. Various field distributions for the cases without magnetic field (reference case, Fig. 5), with travelling up field, phase shift 60º (Fig. 6) and with alternating magnetic field (Fig. 7, here only the middle coil of TMF inductor is working) are shown. Radial temperature distributions and radial temperature drop 5 mm below the free surface can also be seen in Fig. 2-4 for some cases. Fig. 5. Case without magnetic field. Crucible rotation rate 5 rpm, crystal rotation rate 15 rpm. Distributions in meridional plane. 221
Only net values of heat flow for cooling on the free surface and crystal and for heating on crucible wall were known from experiment. Thus, several heat flow density distributions were examined in order to obtain one that fits the experimental radial temperature distribution 5 mm below the free surface in reference case. Fig. 2 presents corresponding radial temperature distributions for cases with and without travelling up field. Despite some discrepancies, both calculations and measurements show lowering of temperature near the crucible wall, if the field strength is increased (see also temperature drop 5 mm below the free surface in Fig. 3). Although alternating field causes different velocity distribution in the melt, radial temperature drop have similar dependence on magnetic field strength, see Fig. 4 and Fig. 7. Fig. 6. Case with Travelling up field, phase shift 60º, I = 1667 Aw. Crucible rotation rate 5 rpm, crystal rotation rate 15 rpm. Distributions in meridional plane. 222
From a qualitative analysis for fields distributions in Fig. 5-7 follows that in the case without magnetic field (see Fig. 5), azimuthal flow near the wall suppresses meridional vortices but under the crystal an intensive vortex appears. The temperature distribution is affected by this, and experimental data confirm this distribution. Travelling magnetic field up creates a vortex flow in meridional plane near the wall, see Fig. 6. Although it is very intense, the vortex flow under the crystal also exists, like in the case without magnetic field. So temperature distribution under the crystal is similar in these cases, the difference appears near the wall. Intensive vortex flow near the wall increases convection and turbulent viscosity, so temperature gradients and temperature itself decrease near the wall. There is also a good agreement with experimental data. Fig. 7. Case with Alternating field, I = 3000 Aw. Crucible rotation rate 5 rpm, crystal rotation rate 15 rpm. Distributions in meridional plane. 223
Alternating field causes similar impact in temperature distribution, see Fig. 7. It causes a jet flow near the wall, and that creates two separate vortices there. So temperature distribution is similar to the case with travelling up field vortices near wall increase turbulent heat conductivity and convection, and temperature gradients near the wall decrease. The agreement between calculated and measured temperature fields is good. Temperature pulsations show generally good agreement for all considered cases, but some discrepancies in the zone under the crystal can be found. Conclusions Calculations with both travelling and alternating magnetic fields show a good agreement with measurements. The reason for this is the fact that the corresponding EM force distributions do not depend on velocity distribution in the melt and cause very intense and well defined flow in the melt. In other cases, with rotation only, agreement with measurements was usually worse, because the buoyancy forces itself are dependent on temperature field which is influenced by velocity field. References [1] Wetzel, Th., Muiznieks, A., Mühlbauer, A., Gelfgat, Y., Gorbunov, L., Virbulis, J., Tomzig, E., Ammon, W.v.: Numerical model of turbulent CZ melt flow in the presence of AC and CUSP magnetic fields and its verification in a laboratory facility. Journal of Crystal Growth, Vol. 230, 2001, pp. 81-91. [2] Virbulis, J., Wetzel, Th., Muiznieks, A., Hanna, B., Dornberger, E., Tomzig, E., Mühlbauer, A., Ammon, W.v.: Numerical investigation of silicon melt flow in large diameter CZ-crystal growth under the influence of steady and dynamic magnetic fields. Journal of Crystal Growth, Vol. 230, 2001, pp. 92-99. Authors MSc.-Phys. Krauze, Armands Prof. Dr.-Phys. Muižnieks, Andris Faculty of Physics and Mathematics Faculty of Physics and Mathematics University of Latvia University of Latvia Zellu str. 8 Zellu str. 8 LV-1002 Riga, Latvia LV-1002 Riga, Latvia Institute for Electrothermal Processes Institute for Electrothermal Processes University of Hannover University of Hannover Wilhelm-Busch-Str. 4 Wilhelm-Busch-Str. 4 D-30167 Hannover, Germany D-30167 Hannover, Germany E-mail: krauze@ewh.uni-hannover.de E-mail: muizniek@ewh.uni-hannover.de Prof. Dr-Ing. Dr. h.c. Mühlbauer, Alfred Dr.-Ing. Wetzel, Thomas Institute for Electrothermal Processes Wacker Siltronic AG University of Hannover Central Research and Development, Wilhelm-Busch-Str. 4 B-RD-CM D-30167 Hannover, Germany D-84479 Burghausen, Germany E-mail: mbr@ewh.uni-hannover.de E-mail: thomas.wetzel@wacker.com Dr. Phys. Gorbunov, Leonid MSc.-Phys. Phys. Pedchenko, Aleksandr Institute of Physics Institute of Physics University of Latvia University of Latvia Miera str. 32 Miera str. 32 LV-1169 Salaspils-1, Latvia LV-1169 Salaspils-1, Latvia E-mail: leonid@sal.lv E-mail: al@sal.lv 224