Instability of Coupled Thermo-Solute Capillary Convection in the Floating Zones and Its Active Control by Magnetic Field

Author:Zou Yong

Supervisor:huang hu lin


Degree Year:2018





The floating zone crystal growth is a complex heat and mass transport process,which contains various heat transfer and flow modes such as solid heat conduction,melt convection,solid-liquid phase transition and so on.It has been widely used in the growth of high precision silicon,superalloy and other semiconductor materials because of its free from crucible contamination.Under microgravity,the buoyancy convection caused by gravity almost disappears.The capillary convection in the melt caused by the surface tension gradient becomes one of the main factors that affect the quality of floating zone crystals.In order to improve the quality of monocrystalline materials growth in floating zone method,it is particularly important to investigate the characteristics of capillary convection in floating zone for its instability control.In this thesis,a numerical study is carried out of capillary convection in melting zone.Under zero gravity,the characteristics of pure solute capillary convection and pure thermocapillary convection,and the instability of coupled thermo-solute capillary convection are investigated respectively.The behavior of capillary convection in the melt is simulated under different types of magnetic field.The main research contents and the major results obtained are as follows.Firstly,in a static magnetic field,the appearance and evaluation of thermocapillary convection instability are numerically investigated in the half-zone liquid bridges with length of 5 mm.With increasing Marangoni numbers,the thermocapillary convection undergoes two-dimensional axisymmetric flow and three-dimensional steady flow,then transforms into 3-D single frequency periodic oscillation flow,and then to multi frequency oscillatory flow,finally evolves into a periodic oscillatory flow in turn for melting Si.The harmonic frequencies and the fundamental frequency satisfy the frequency doubling relationship of fn=nf1 when the melt convection is in the multi-frequency oscillation mode.On the other hand,when the aspect ratio changes,the convection in the liquid bridge will also exhibit various flow characteristic.Keeping Ma number at a constant value of 100,the thermocapillary convection shows a three-dimension stable model with As=0.5,while the flow field and temperature field transformed from stable state to a periodic oscillation mode at As=1.When As=1.25,the velocity of the monitoring point presents a small amplitude oscillation mode with a high oscillation frequency.Meanwhile the temperature oscillation disappears under the same condition of Ma=100.For three-dimensional steady flow,the circumferential wave number m remains the value of 2,which does not show the correlation with the aspect ratio As.When the As increases,the three critical Ma numbers corresponding to the different aspect ratios chosen in the work are 21,19 and 18 respectively.The horizontal magnetic field is more effective than the axial magnetic field to suppress the convective instability under the same magnetic field intensity.However,the suppressing effect of horizontal magnetic field is directional on the hydrothermal waves,which makes the convection in the melt present three dimensional distribution characteristics.Secondly,in a rotating magnetic field,numerical simulations are performed to study the coupled thermo-solute convection in the SixGe1-x system of the half-zone liquid bridge.The results show a two-dimensional axisymmetric model of the pure solute capillary convection.The temperature field is mainly determined by thermal diffusion while the concentration field is dominated by convection together with the solute diffusion.The coupled thermo-solute capillary convection is a three-dimensional periodic and rotating oscillatory flow,yet the pure thermocapillary convection presents three-dimensional steady non-axisymmetric flow in the absence of the solute capillary convection.It can be inferred that the instability of convection will increase when the two kinds of capillary convection are coupled.The circumferential wave number m of the coupled capillary convection shows a strong dependence on the aspect ratio As with the expression as m×As∈[2,2.2].Violent oscillation with a large amplitude will emerge in the coupled capillary convection as the thermal to solutal Marangoni number ratio equals to 1.5,namely MaT:MaC=3:2.When the rotating magnetic field is applied,the circumferential velocity of the melt increases with radius.Both the concentration field and the flow field in the melt generate a two-dimensional axisymmetric distribution.Thirdly,considering the impurity segregation effect,the characteristics of thermocapillary convection in the melt are studied at different radiation heating temperatures under the effects of rotating magnetic fields(RMF)in a floating-zone growth process of doped Si crystals under zero gravity.The influence of magnetic field intensity and frequency are analyzed on flow field and impurity concentration field.Under the rotating magnetic field with strength fixed at B0=1 mT and angular frequency increasing,the axial velocity of the monitoring point decreases from 0.89 cm/s without magnetic field to 0.59 cm/s under the angular frequency ofω=500π.The convection in the melt is unsatisfiedly suppressed,which causes the circumferential wave number to change to-and-fro between 2 and 3.The Lorentz force induced by the applied RMF under 1 mT withω=500πis not sufficient to effectively control the thermocapillary flow.In this case,the thermocapillary flow presents a rotating oscillatory three-dimensional convection with an oscillatory frequency decreasing with increasing radiation temperature and varying linearly with Ma number.The temperature field in the melt has a 2-D steady axisymmetric distribution,which is mainly determined by the diffusion effect when the Ma number is relatively low.However,at the relatively high Ma number,the temperature of the melt is influenced by flow and exhibits periodic oscillation with the same frequency of melt convection.By fixing RMF frequency at 50 Hz and increasing the magnetic field intensity,the flow in melt turns into a quasi-2-D rotating axisymmetric flow from a 3-D periodic oscillatory flow.Accordingly,the thermocapillary convection presents a mirror-symmetry structure at the middle plane.Both the temperature and velocity fluctuations in the melt with Ma=21.8,32.9,43.7are effectively suppressed by applying RMF under 2mT,3mT and 5mT respectively.Meanwhile,the concentration field in the melt zone shows two-dimensional axial symmetrical distributions.The concentration contours become closer and flatter near the mid-cross section of the floating zone.The impurity transport in this region becomes diffusion dominant under the effect of RMF.The axial inhibition effect and circumferential stirring action on melt flow caused by rotating magnetic field both contribute to the stability of melt flow,the homogeneity of concentration distribution and temperature distribution,which is conducive to the growth of high quality crystals.Finally,considering the solid-liquid phase change in crystal growth,the characteristics of heat and mass transfer,fluid flow and the site and shape of the melt/solid interfaces in molten zone with different operating conditions are solved numerically by finite-volume method for a full floating-zone model.Both axial and cusp magnetic fields of different strength are applied to suppress the thermocapillary convection in the melt during silicon crystal growth.The thermocapillary convection intensities increase with the temperature difference.The reverse flow vortex cell develops to the free surface in the high temperature region while the thermocapillary convection vortex moves to the low temperature zone.Therefore the relative positions of the thermocapillary convection vortex and the reverse flow vortex in the melt change from the left and right structures to the upper and lower structures.With the increase of the surface tension gradient,the thermocapillary convection vortex moves toward the intersection of the free surface and the solid/liquid interface.Meanwhile the whole narrowed capillary convection vortex results in the occupation of the melt bulk by the reverse flow vortex cells.The temperature distribution in the melt also changes as the height of the melting zone decreases.The thermocapillary convection vortex and reverse flow vortex in the melt change from the upper and lower structures to the left and right structures with the decrease of the melting zone height.With the increase of the pulling speed,the reverse flow vortex cell near the melt/polycrystalline interface and the thermocapillary convection vortex near the melt/single crystal interface have a tendency to merge into a large convective vortex cell.The cusp magnetic field,which can help suppress melt flow in both axial and radial direction,has better performance compared to axial magnetic field on inhibiting the flow instability.The site and shape of the melt/solid interfaces is analyzed as well under different magnetic field strength.The melt/solid interfaces under axial magnetic field coincide with that without axial magnetic fields.The melt/solid interfaces are convex toward single crystal at the edge of the free surface when the axial magnetic fields are relatively weaker,while in the cusp magnetic fields the melt/solid interfaces become very smooth.The mechanism of melting and crystallization of crystals is explored,and a new criterion for melting and crystallization is presented.It is the critical state of crystallization or melting when the interionic separation at the phase change interface in binding system equals the interionic separation corresponding to the inflection point in the potential energy curve.