FEMAG晶体生长模拟软件-如何将直拉法模拟技术拓展到区熔法生长.ppt

1、,FEMAG晶体生长模拟软件 -How to extend Cz modeling techniques to FZ growth?,Modeling of FZ growth,FEMAGSoft 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)

2、,Modeling of FZ growth (contd),Turbulent viscosity is low and the melt flow can be computed by means of a laminar model.,FEMAGSoft 2013,Modeling of FZ growth (contd),Induction heating,FEMAGSoft 2013,Modeling of FZ growth (contd),Induction Heating in FZ semi-conductor growth,FEMAGSoft 2013,J current

3、density Jsource imposed by external source Jeddy induced by time-dependent magnetic field,inductor,susceptor,Modeling of FZ growth (contd),Slottedinductor,Top view Section S-S,S,S,Jsource,N : number of slits,FEMAGSoft 2013,Modeling of FZ growth (contd),Numerical results,Non-slotted inductor,Slotted

4、inductor,z,r,susceptor,inductor,z,r,susceptor,inductor,FEMAGSoft 2013,Modeling of FZ growth (contd),Real part of magnetic flux,FEMAGSoft 2013,Imaginary part of magnetic flux,Modeling of FZ growth (contd),Difficulties,FEMAGSoft 2013,melt-atmosphere interface shape (magnetic pressure),open melting fro

5、nt (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),FEMAGSoft 2013,Induction Heating in FZ semi-conductor gro

6、wth,B magnetic induction m0 magnetic permeability of vacuum s electric conductivity w angular frequency,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 mathematica

7、l model of the electromagnetic field distribution in planar and axisymmetric configurations,Hypothesis: low value of the magnetic skin depth,FEMAGSoft 2013, Model based on using: - a matched asymptotic expansion technique to approximate the electromagnetic field inside the conductors - a Finite Elem

8、ent 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 qneq :,Equivalent surfacestress teq :,FEMAGSoft 2006,Equivalent magnetic stresses and heat flux,Modeling of FZ

9、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.,RePolycrystal = 7460 ReCrystal = 3730 Pe = 261 Gr = 2.7x107 Ma = 6116,Floating Zone Silicon Growth Simulation,FEM

10、AGSoft 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,FEMAGSoft 2013,Modeling of FZ growth (contd),With equivalent magnetic tangential stress.,Without equivalent m

11、agnetic tangential stress.,Temperature field (left) and Stokes stream function (right) in the melt,FEMAGSoft 2013,6. Modeling of FZ growth (contd),FEMAG-FZ quasi-steady simulation of the growth of a 200 mm silicon crystal,FEMAGSoft 2013,(right) Temperature field and isolines of the norm of the magne

12、tic flux function. (bottom) Stream function isolines in the melt,Modeling of FZ growth (contd),Model validation,FEMAGSoft 2013,Modeling of FZ growth (contd),Crystal radius: 51 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,

13、(a),(b),(c),Good correspondence between predicted and experimental results,Effect of crystal rotation rate on the melt flow (FZ growth),FEMAGSoft 2013,With the courtesy of IKZ, Berlin,Modeling of FZ growth (contd),FEMAGSoft 2013,Calculation of point defects in a growing FZ crystal,Modeling of FZ gro

14、wth (contd),FEMAGSoft 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),FEMAGSoft 2013,Growth of a 100 mm silicon crys

15、tal (1mm/min pull rate),Predicted defect delta -(CI-CV) distribution by means of a quasi-steady simulation,Modeling of FZ growth (contd),FEMAGSoft 2013,Second example,Modeling of FZ growth (contd),FEMAGSoft 2013,Rs = 5.1 cm, Rf = 4.7 cm, Ws = 10 rpm, Wf = -15 rpm vpul = 3.4 mm/min,Temperature field,

16、Modeling of FZ growth (contd),FEMAGSoft 2013,Rs = 5.1 cm, Rf = 4.7 cm, Ws = 10 rpm, Wf = -15 rpm vpul = 3.4 mm/min,Streamlines,Modeling of FZ growth (contd),FEMAGSoft 2013,Rs = 5.1 cm, Rf = 4.7 cm, Ws = 10 rpm, Wf = -15 rpm vpul = 3.4 mm/min,Difference of interstitial and vacancy concentrations (CI

17、- CV ),Modeling of FZ growth (contd),FEMAGSoft 2013,Rs = 5.1 cm, Rf = 4.7 cm, Ws = 10 rpm, Wf = -15 rpm vpul = 3.4 mm/min,Difference of interstitial and vacancy concentrations (CI - CV ) (detail),Modeling of FZ growth (contd),FEMAGSoft 2013,von Mises invariant: global view and detail,Ratio of the vo

18、n Mises invariant over the CRSS,Modeling of FZ growth (contd),FEMAGSoft 2013,Calculation of thermal stresses in a growing FZ crystal without convection,Modeling of FZ growth (contd),FEMAGSoft 2013,Effect of a heat shield: temperature field,No convection, Rs = 5.1 cm, Rf = 4.7 cm, vpul = 3.4 mm/min,a

19、) Without heat shieldb) With a heat shield,Modeling of FZ growth (contd),FEMAGSoft 2013,Effect of a heat shield: von Mises stress,a),b), growth orientation,Modeling of FZ growth (contd),FEMAGSoft 2013,a),b), growth orientation,Effect of a heat shield: von Mises stress,Modeling of FZ growth (contd),T

20、ypical FEMAG-FZ global unstructured mesh for heat transfer and induction heating,FEMAGSoft 2013,Modeling of FZ growth (contd),FEMAGSoft 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 co

21、nstraining loci (secondary mesh) in FZ growth,FEMAGSoft 2013,Modeling of FZ growth (contd),FEMAGSoft 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 calcula

22、tion 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 calculated (as an isotherm),Modeling of FZ growth (contd),FEMAGSoft 2013,Open Melting Front after extra

23、ction of the single crystal,Modeling of FZ growth (contd),FEMAGSoft 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

24、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 geometr

25、y.,Modeling of FZ growth (contd),FEMAGSoft 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

26、 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),F

27、EMAGSoft 2013,Investigation of ACRT technique,Modeling of FZ growth (contd),Investigation of ACRT technique,FEMAGSoft 2013,Modeling of FZ growth (contd),FEMAGSoft 2013,Quasi-steady simulation: global temperature field,Quasi-steady simulation: local temperature field,Modeling of FZ growth (contd),FEM

28、AGSoft 2013,Quasi-steady simulation: global temperature field,Quasi-steady simulation: local temperature field and meridional velocity vectors,Modeling of FZ growth (contd),FEMAGSoft 2013,Quasi-dynamic simulations,Temperature field and meridional velocity,Modeling of FZ growth (contd),FEMAGSoft 2013

29、,Quasi-dynamic simulations,Azimuthal velocity,Modeling of FZ growth (contd),FEMAGSoft 2013,Top right: temperature field and meridional velocity Bottom left: azimuthal velocity,Quasi-dynamic simulations,Modeling of FZ growth (contd),FEMAGSoft 2013,Definition of an average flow for species transport i

30、nverse 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 transpor

31、t in the melt and incorporation into the crystal,Ultimate goal: to predict the resistivity distribution in the crystal.,Modeling of FZ growth (contd),FEMAGSoft 2013,Quasi-steady and quasi-dynamic “ACRT” simulation: local temperature field and average meridional velocity vectors,Quasi-steady simulation: local temperature