FEMAG块晶体生长数值模拟-如何将直拉法模拟技术拓展到区熔法生长.ppt

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,FEMAG,Soft,2013,How to extend Cz modeling techniques to FZ growth?,Modeling of FZ growth,FEMAG,Soft,2013,Global temperature field(left),melt flow(right),and alternating magnetic field(bottom),Quasi-steady simulation of the Floating Zone(FZ)growth of a 100 mm silicon crystal,(1mm/min pull rate),Modeling of FZ growth(contd),Turbulent viscosity is low and the melt flow can be computed by means of a laminar model.,FEMAG,Soft,2013,Modeling of FZ growth(contd),Induction heating,FEMAG,Soft,2013,Modeling of FZ growth(contd),Induction Heating in,FZ semi-conductor growth,FEMAG,Soft,2013,J,source,J,eddy,J,current density,J,source,imposed by external source,J,eddy,induced by time-dependent magnetic field,inductor,susceptor,Modeling of FZ growth(contd),Slottedinductor,Top view Section,S-S,Outer boundary,Inner boundary,n,s,e,q,S,S,J,source,N:,number of slitsFEMAG,Soft,2013,Modeling of FZ growth(contd),Numerical results,Non-slotted inductor,Slotted inductor,z,r,susceptor,inductor,z,r,susceptor,inductor,FEMAG,Soft,2013,Modeling of FZ growth(contd),Real part of magnetic flux,FEMAG,Soft,2013,Imaginary part of magnetic flux,Modeling of FZ growth(contd),Difficulties,FEMAG,Soft,2013,melt-atmosphere interface shape(magnetic pressure),open melting front,(thin fluid film),tangential stress exerted onto the melt free surface:,-generally undesired resulting shear flow,-potentially useful effect to control the flow.,Induction Heating in,FZ semi-conductor growth,Modeling of FZ growth(contd),FEMAG,Soft,2013,Induction Heating in,FZ semi-conductor growth,B,magnetic induction,m,0,magnetic permeability of vacuum,s,electric conductivity,w,angular frequency,Skin depth:,d,B,Conductor,Dissipated power:Force density:,Heat flux,2)Normal stress,3)Tangential stress,Alternating magnetic field effects:,Inductor,Susceptor,Modeling of FZ growth(contd),Development of a,mathematical model,of the electromagnetic field distribution in planar and axisymmetric configurations,Hypothesis:,low value of the magnetic skin depth,FEMAG,Soft,2013,Model based on using:,-a matched asymptotic expansion technique to approximate the electromagnetic field inside the conductors,-a Finite Element numerical representation of the electromagnetic field outside the conductors.,Modeling of FZ growth(contd),Mean dissipated power:,Mean body force density:,Equivalent normal,heat flux,q,neq,:,Equivalent surfacestress,t,eq,:,s,s,t,eq,n,n,n,s,n,s,q,n,eq,FEMAG,Soft,2006,Equivalent magnetic stresses and heat flux,Modeling of FZ growth(contd),Flow and temperature calculations are performed with a 200 mm diameter crystal.,The melt viscosity is set to 5 times the actual silicon viscosity to obtain steady results.,Re,Polycrystal,=7460,Re,Crystal,=3730,Pe=261,Gr =2.7x10,7,Ma =6116,Floating Zone Silicon Growth,Simulation,FEMAG,Soft,2013,Modeling of FZ growth(contd),Temperature field and isolines of the norm of the magnetic flux function.,FEMAG-FZ quasi-steady,simulation of the growth,of a 200 mm silicon crystal,FEMAG,Soft,2013,Modeling of FZ growth(contd),With,equivalent magnetic tangential stress.,Without,equivalent magnetic tangential stress.,Temperature field(left)and Stokes stream function(right)in the melt,FEMAG,Soft,2013,6.Modeling of FZ growth(contd),FEMAG-FZ quasi-steady simulation of the growth of a 200 mm silicon crystal,FEMAG,Soft,2013,(right)Temperature field and isolines of the norm of the magnetic flux function.,(bottom)Stream function isolines in the melt,Modeling of FZ growth(contd),Model validation,FEMAG,Soft,2013,Modeling of FZ growth(contd),Crystal radius51 mm,Feed rotation rate:15 RPM,Crystal rotation rate:(a)5 RPM,(b)10 RPM,(c)15 RPM,Marangoni coefficient:1.0 10,-4,N/mK,(a),(b),(c),Good correspondence between predicted and experimental results,Effect of crystal,rotation rate,on the melt flow,(FZ growth),FEMAG,Soft,2013,With the courtesy of IKZ,Berlin,Modeling of FZ growth(contd),FEMAG,Soft,2013,Calculation of point defects in a growing FZ crystal,Modeling of FZ growth(contd),FEMAG,Soft,2013,Global temperature field(left),melt flow(right),and alternating magnetic field(bottom),Quasi-steady simulation of the Floating Zone(FZ)growth of a 100 mm silicon crystal,(1mm/min pull rate),Modeling of FZ growth(contd),FEMAG,Soft,2013,Growth of a 100 mm silicon crystal,(1mm/min pull rate),Predicted defect delta -(C,I,-C,V,)distribution by means of a,quasi-steady,simulation,Modeling of FZ growth(contd),FEMAG,Soft,2013,Second example,Modeling of FZ growth(contd),FEMAG,Soft,2013,R,s,=5.1 cm,R,f,=4.7 cm,W,s,=10 rpm,W,f,=-15 rpm,v,pul,=3.4 mm/min,Temperature field,Modeling of FZ growth(contd),FEMAG,Soft,2013,R,s,=5.1 cm,R,f,=4.7 cm,W,s,=10 rpm,W,f,=-15 rpm,v,pul,=3.4 mm/min,Streamlines,Modeling of FZ growth(contd),FEMAG,Soft,2013,R,s,=5.1 cm,R,f,=4.7 cm,W,s,=10 rpm,W,f,=-15 rpm,v,pul,=3.4 mm/min,Difference of interstitial and vacancy concentrations,(C,I,-C,V,),Modeling of FZ growth(contd),FEMAG,Soft,2013,R,s,=5.1 cm,R,f,=4.7 cm,W,s,=10 rpm,W,f,=-15 rpm,v,pul,=3.4 mm/min,Difference of interstitial and vacancy concentrations,(C,I,-C,V,),(detail),Modeling of FZ growth(contd),FEMAG,Soft,2013,von Mises invariant:,global view and detail,Ratio of the von Mises invariant over the CRSS,Modeling of FZ growth(contd),FEMAG,Soft,2013,Calculation of thermal stresses in a growing FZ crystal without convection,Modeling of FZ growth(contd),FEMAG,Soft,2013,Effect of a heat shield:temperature field,No convection,R,s,=5.1 cm,R,f,=4.7 cm,v,pul,=3.4 mm/min,a)Without heat shieldb)With a heat shield,Modeling of FZ growth(contd),FEMAG,Soft,2013,Effect of a heat shield:von Mises stress,a),b),growth orientation,Modeling of FZ growth(contd),FEMAG,Soft,2013,a),b),growth orientation,Effect of a heat shield:von Mises stress,Modeling of FZ growth(contd),Typical FEMAG-FZ global unstructured mesh for heat transfer and induction heating,FEMAG,Soft,2013,Modeling of FZ growth(contd),FEMAG,Soft,2013,FEMAG-FZ time-dependent simulation of the growth of a silicon crystal,Use of an equivalent thermal conductivity,Modeling of FZ growth(contd),Free interface constraining loci(secondary mesh)in FZ growth,FEMAG,Soft,2013,Modeling of FZ growth(contd),FEMAG,Soft,2013,Inverse modeling in FZ growth,much more difficult,problem than in Cz growth,can lead to,misleading interpretations,of the simulation results since completely inverse models result in the,calculation of the melt volume,and hence parametric studies are difficult to interpret,with classical simplified models,the,open melting front,(OMF)is imposed and the,melting front,is either imposed or calculatedas an isotherm),Modeling of FZ growth(contd),FEMAG,Soft,2013,Open Melting Front after extraction of the single crystal,Modeling of FZ growth(contd),FEMAG,Soft,2013,Main issue:modeling of the Open Melting Front(OMF),Physical problem:,the,flow of the molten silicon,along the OMF and the,angle at which the melt-gas interface detaches,from the OMF require accurate modeling in view of their direct impact on the radiation transfer to the OMF and on the melt-gas interface shape,Numerical problem:,the coupled solution of a problem with 4 interfaces(solidification front,melting front,melt-gas interface,and OMF)and 3 tri-junctions represents a difficult problem of computational geometry.,Modeling of FZ growth(contd),FEMAG,Soft,2013,Other key issues:,Species transport(dopant and impurities):,the,problem,is similar to species transport in Cz growth,but much more difficult since almost,no turbulent mixing,is present in FZ growth,Oscillations of the crystal and/or feed-rod rotation rates:,this technique is often used to better mix the melt and can be simulated by use of a,quasi-dynamic model,3D effects:,non-axisymmetric effects are generated(i)by the inductor shape and possibly(ii)by the use of non-aligned crystal and feed-rod rotation axes,Modeling of FZ growth(contd),FEMAG,Soft,2013,Investigation of ACRT technique,Modeling of FZ growth(contd),A first,quasi-steady,simulation is performed with fixed OMF and melt-gas interface,Feed rotation rate=-15 RPM,Seed rotation rate=10 RPM,Investigation of ACRT technique,FEMAG,Soft,2013,A subsequent,quasi-dynamic,simulation is performed with the resulting QS interfaces and temperature field fixed,Feed rotation rate=-15 to 15 RPM,Alternation period=30 s,Seed rotation rate=10 RPM,A last,quasi-steady,simulation is performed to calculate Boron concentration from the,averaged,QD,velocity field,.,Feed rotation rate=0 RPM,Seed rotation rate=10 RPM,Modeling of FZ growth(contd),FEMAG,Soft,2013,Quasi-steady simulation:,global temperature field,Quasi-steady simulation:,local temperature field,Modeling of FZ growth(contd),FEMAG,Soft,2013,Quasi-steady simulation:,global temperature field,Quasi-steady simulation:,local temperature field and meridional velocity vectors,Modeling of FZ growth(contd),FEMAG,Soft,2013,Quasi-dynamic simulations,Temperature field and meridional velocity,Modeling of FZ growth(contd),FEMAG,Soft,2013,Quasi-dynamic simulations,Azimuthal velocity,Modeling of FZ growth(contd),FEMAG,Soft,2013,Top right:,temperature field and meridional velocity,Bottom left:,azimuthal velocity,Quasi-dynamic simulations,Modeling of FZ growth(contd),FEMAG,Soft,2013,Definition of an average flow for species transport inverse simulation,Average flow:,quasi-dynamic results are further,time-averaged,in order to provide mean velocity,viscosity,and heat and species diffusivity fields,Inverse simulations:,time-averaged fields are used in quasi-steady or inverse dynamic simulations in order to predict,species transport,in the melt and incorporation into the crystal,Ultimate goal:,to predict the,resistivity distribution,in the crystal.,Modeling of FZ growth(contd),FEMAG,Soft,2013,Quasi-steady and quasi-dynamic“ACRT”simulation:,local temperature field and average meridional velocity vectors,Quasi-steady simulation:,local temperature field and meridional velocity vectors,The average flow is weaker than the quasi-steady flow,Modeling of FZ growth(contd),FEMAG,Soft,2013,Quasi-steady results,Radial velocity,Azimuthal velocity,Axial velocity,Average quasi-dynamic results,Modeling of FZ growth(contd),FEMAG,Soft,2013,Boron concentration prediction,Calculations from the initial quasi-steady simulation,Calculations from the averaged quasi-dynamic simulation,Modeling of FZ growth(contd),FEMAG,Soft,2013,Conclusion,Physics of the flow:,due to the very low molten silicon viscosity,the,feed-rod almost slips onto the melt surface,So alternating the feed-rod rotation sense only affects a,thin boundary layer,along the fusion interface and a,limited region,around the axis,Mixing efficiency:,with feed alternate rotations the,ACRT technique has,limited efficiency,to mix the silicon melt,Possible solutions:,selection of,improved parameters,or use of,non-aligned,crystal and feed-rod,rotation axes,in order to generate efficient 3D mixing.,Modeling of FZ growth(contd),