Convection Properties In The Floating Half-Zone And Convection Control Of Rotating Magnetic Fields Under Microgravity

Floating zone for growing crystal is a unique containerless method, which can avoid contamination induced by container, and is an important technique for growing more pure crystal. The floating zone method under microgravity can avoid the influence of gravity field, break the limitation of the size of crystal, and ultimately grow larger and higher-quality single crystal. Because buoyancy convection is reduced greatly under microgravity, thermo-capillary flow becomes the dominant convection in floating zone crystal growth, and the main factor influencing the crystal quality. Thus, it is of great significance to control surface tension for improving convection construction and temperature distribution, ultimately to gain the higher-quality crystal. For better understanding the convection properties, a half-zone liquid bridge, which is a typical simplified model and widely used for investigating thermo-capillary flow in a floating zone, is adopted in the present paper. Convection properties of the thermo-capillary flow in a floating half-zone and convection control under external rotating magnetic fields (RMF) under microgravity are researched by using the conventional finite volume method.Without magnetic field, thermo-capillary flow in the floating half-zone for semiconductor with lower Pr number(Pr=0.01) loses its stability twice, when increasing Ma number. The thermo-capillary flow firstly transits from an axisymmetric steady flow to a three-dimensional steady one, then to a quasi-periodic oscillatory convection. As preliminary work for the convection control through magnetic fields, the convection characteristics of the two instabilities without magnetic fields in the liquid are successfully analyzed in the paper at first.These two instabilities in floating zone can lead to macro- and micro-segregation in the crystal, which are bad for growing high-quality crystal. Thus, convection control becomes the key factor for improving the crystal quality. The fact that semiconductor melt is excellent electrical conductivity, makes it possible to consider external magnetic field as a potential method to control melt convection. Although the uniform transverse magnetic field can effectively suppress the axial convection induced by the unbalanced surface tension, it can destroy the axisymmetric environment in floating zone crystal growth. The uniform axial magnetic field mainly damps the radial convection of melt. In this condition, the thermo-capillary flow, which can not penetrate the liquid bridge, is limited near the free surface, and the convection in the central of liquid bridge is very weak. Therefore, the convection under the uniform axial magnetic field can lead to radial segregation in the crystal. Compared with the static magnetic field, RMF has the advantage of requiring much lower magnetic induction for controlling convection effectively, and requiring less energy consumption finally. Thus, RMF has become increasingly interesting for convection control in crystal growth. To investigate the effects of RMF on the melt convection, the following works are executed in the present paper: based on magnetohydrodynamics theory and literature, the mathematical model of RMF is derived for controlling convection, and the corresponding functional procedure modules are programmed and merged in the CFD package. By using the program packages, firstly, effects of the RMF infinite model and RMF finite?₁-?₂ model on the three-dimensional thermo-capillary flow are compared; and effects of the transverse static magnetic field (SMF) and RMF with the same amplitude on the liquid are also compared; then, convection control of the RMF on the two instabilities in the liquid are investigated; and influences of the Ma number and the amplitude of the RMF are also considered; finally, effects of the RMF with different pole-pairs (p=2 and p=3) are investigated, and the influences of nonuniform RMF of different pole-pairs with the same amplitude and rotating frequency on the three-dimensional thermo-capillary flow are also compared. The following conclusions can be found by using the method of direct simulation:1) Three-dimensional thermo-capillary flow in the RMF is investigated numerically, with a focus on the difference between the RMF infinite and finite?₁-?₂ models. Two functions of the transverse RMF, electromagnetic stirring in the azimuthal direction and convection suppression in the axial direction, are exhibited in both RMF models, which are beneficial to the axisymmetric distribution of the three-dimensional thermo-capillary flow. For the same RMF, however, obvious differences of convection structure and temperature distribution are observed between the two models. The over-simplified RMF infinite model leads to larger azimuthal velocity and smaller axial velocity. Because of a large deviation existing in the RMF infinite model, we suggest choosing the?₁-?₂ model to study convection control by RMF.2) By comparing the influences of transverse SMF and uniform RMF on thermo-capillary convection, we get the conclusions that the effects of transverse SMF of 7mT is very weak for convection control, while the RMF with the same magnetic strength can control the thermo-capillary convection effectively. Besides, the transverse SMF can destroy the axisymmetric distribution of thermocapillary flow, which is bad for the crystal quality. On the contrary, in the uniform RMF, the induced Lorentz force is very effective in controlling convection, which is beneficial for the three-dimensional melt convection returning to a steady axisymmetric flow. Compared with the transverse SMF, the RMF is a promising method for convection control in floating zone.3) The convection after the first and the second instability in the liquid are well controlled under the proper external uniform RMF. The three-dimensional steady flow and the three-dimensional periodic oscillatory flow after the two instabilities both return to be a two-dimensional axisymmetric steady one under microgravity.4) Ma number and the intensity of RMF are primary factors influencing the convection property of the three-dimensional liquid bridge under the uniform RMF. For an external uniform RMF, the convection in the liquid bridge will change from a two-dimensional axisymmetric steady flow to a periodic oscillatory one, with the increase of Ma number. Then, the oscillatory frequency decreases gradually with increasing Ma number. In the present paper, the critical Ma numbers are also computed for different RMF by the method of direct numerical simulation. The result indicates that if the applied RMF is not strong enough to control thermo-capillary convection effectively, the second instability in the liquid bridge will take place earlier. Similarly, for a Ma number, if the intensity of RMF is comparatively small, the Lorenz force induced by RMF can not control thermo-capillary convection effectively, and the second instability in the liquid bridge will also occur in advance. Further increasing the intensity of RMF, the three-dimensional thermo-capillary convection can be controlled ultimately, and the periodic oscillatory flow returns to a two-dimensional axisymmetric steady one.5) Effects of the stirring action in the azimuthal direction and the damping effect in the axial direction are also induced by the Lorentz force in the RMF with p=2 and p=3. The two effects are both beneficial to transform the three-dimensional steady flow to a two-dimensional axisymmetric steady one.6) For the two-dimensional axisymmetric cylindrical melt, the distinction of controlling effects of RMF with different pole-pairs is gradually obvious with the increase of magnetic strength. The radial and axial maximal velocity in the melt are smallest under the RMF with p=3.For the three-dimensional thermo-capillary flow, the RMF with different pole-pairs (p=1, 2, 3) are all beneficial to the axisymmetric characteristics in the floating liquid bridge, and to improve the crystal quality in the floating zone ultimately. However, by the quantitative comparison, we can conclude that with the same magnetic fields (70mT, 50Hz), the RMF with p=3 can better control the radial and axial velocity in the liquid, which is the most excellent technology for growing higher quality crystal.