晶體生長模擬軟件FEMAG之浮區(qū)法

1、晶體生長模擬軟件晶體生長模擬軟件FEMAG之浮區(qū)法之浮區(qū)法 Roman Rolinsky2, Nathalie Van den Bogaert2, Michael Wnscher3, David Despas1, Arnaud de Potter2, Franois Dupret1,2 1 CESAME Research Center Universit catholique de Louvain, Belgium2 FEMAGSoft S.A., Belgium3 Leibniz Institute for Crystal Growth (IKZ), Berlin, Germany+ 32

2、10 22 64 FEMAGSoft 2011Quasi-steady simulation of the growth of a 100 mm silicon crystal(1mm/min pull rate)Global temperature field (left),melt flow (right),and alternating magnetic field (bottom)IntroductionFEMAGSoft 2011Quasi-steady thermal equilibrium adapted heater power to get the prescribed cr

3、ystal diameter heat source on the solidification and melting fronts in proportion to the pull rateInverse dynamic adapted heater power to grow the prescribed crystal shape effect of pull rate and solid-liquid interface deformation on the solidification heat Direct dynamic calculated crystal shape pr

4、escribed heater power history effect of pull rate and solid-liquid interface deformation on the solidification heatTime dependentQuasi-steadyQuasi-dynamic frozen geometry (except the solid-liquid interfaces) adapted heater power to get the prescribed crystal diameter effect of pull rate and solid-li

5、quid interface deformation on the solidification heat Different simulation techniquesIntroduction (contd)FEMAGSoft 2011Inverse dynamic often more reliable than quasi-steady model highly attractive to predict crystal qualityQuasi-steady frequently used cheap, but not always valid does not allow cryst

6、al quality predictionDirect dynamic simulation of the system response to perturbations of the input parametersQuasi-dynamic may capture the detailed system dynamics at various stages very useful for controller designDifferent simulation techniques (contd)Introduction (contd)FEMAGSoft 2011Inverse mod

7、eling 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 in the present work, the open melting

8、 front (OMF) is imposed and the melting front is either imposed or calculated (as an isotherm)Introduction (contd)1. Introduction2. Global simulation tool3. Simulation examples4. DiscussionFEMAGSoft 2011Outline of the Presentation1. Introduction2. Global simulation tool3. Simulation examples4. Discu

9、ssionFEMAGSoft 2011Outline of the PresentationTypical FEMAG-FZ global unstructured mesh for heat transfer and induction heatingFEMAGSoft 20112. A global simulation toolInduction Heating in FZ semi-conductor growth FEMAGSoft 2011JsourceJeddyJ current densityJsource imposed by external source Jeddy in

10、duced by time-dependent magnetic fieldinductorsusceptor2. A global simulation tool (contd)Slottedinductor Top view Section S-SOuter boundaryInner boundarynseq qSSJsourceN : number of slits2. A global simulation tool (contd)FEMAGSoft 20112. A global simulation tool (contd)FEMAGSoft 2011Induction Heat

11、ing in FZ semi-conductor growth B magnetic inductionm0 magnetic permeability of vacuums electric conductivityw angular frequency Skin depth :dBConductorDissipated power: Force density:1) Heat flux2) Normal stress3) Tangential stressAlternating magnetic field effects :InductorSusceptor2. A global sim

12、ulation tool (contd)FEMAG-FZ quasi-steady simulation of the growth of a 200 mm silicon crystalFEMAGSoft 2011(right) Temperature field and isolines of the norm of the magnetic flux function.(bottom) Stream function isolines in the meltModel validationFEMAGSoft 20112. A global simulation tool (contd)C

13、rystal radius: 51 mmFeed rotation rate: 15 RPMCrystal rotation rate: (a) 5 RPM, (b) 10 RPM, (c) 15 RPMMarangoni coefficient: 1.0 10-4 N/mK(a)(b)(c)Good correspondence between predicted and experimental resultsEffect of crystalrotation rateon the melt flowFEMAGSoft 2011With the courtesy of IKZ, Berli

14、n2. A global simulation tool (contd)Time-dependent simulationsFEMAGSoft 20112. A global simulation tool (contd)t0t1t2t3t4t5t6timet7Cone growthBody growthTail-end stageMesh re-generationMesh deformationMesh generationGeneral geometrical strategyFEMAGSoft 20112. A global simulation tool (contd)FEMAGSo

15、ft 2011FEMAG-FZ time-dependent simulation of the growth of a silicon crystalUse of an equivalent thermal conductivity2. A global simulation tool (contd)FEMAGSoft 2011Prediction of Crystal Defects2. A global simulation tool (contd)FEMAGSoft 2011Quasi-steady simulation of the growth of a 100 mm silico

16、n crystal(1mm/min pull rate)Global temperature field (left),melt flow (right),and alternating magnetic field (bottom)2. A global simulation tool (contd)FEMAGSoft 2011Predicted defect delta -(CI-CV) distribution by means of a quasi-steady simulation Growth of a 100 mm silicon crystal(1mm/min pull rat

17、e)2. A global simulation tool (contd)FEMAGSoft 2011Thermal stressesin the growing crystal2. A global simulation tool (contd)FEMAGSoft 2011von Mises invariant:global view and detailRatio of the von Mises invariant over the CRSS2. A global simulation tool (contd)1. Introduction2. Global simulation too

18、l3. Simulation examples4. DiscussionFEMAGSoft 2011Outline of the Presentation1. Introduction2. Global simulation tool3. Simulation examples4. DiscussionFEMAGSoft 2011Outline of the PresentationFEMAGSoft 20113. Simulation examples 1st exampleCalculation of point defects in a growing FZ crystalFEMAGSo

19、ft 20113. Simulation examples (contd)Rs = 5.1 cm,Rf = 4.7 cm,Ws = 10 rpm,Wf = -15 rpmvpul = 3.4 mm/minTemperature fieldFEMAGSoft 20113. Simulation examples (contd)Rs = 5.1 cm,Rf = 4.7 cm,Ws = 10 rpm,Wf = -15 rpmvpul = 3.4 mm/minStreamlinesFEMAGSoft 20113. Simulation examples (contd)Rs = 5.1 cm,Rf =

20、4.7 cm,Ws = 10 rpm,Wf = -15 rpmvpul = 3.4 mm/minDifference of interstitial and vacancy concentrations(CI - CV )FEMAGSoft 20113. Simulation examples (contd)Rs = 5.1 cm,Rf = 4.7 cm,Ws = 10 rpm,Wf = -15 rpmvpul = 3.4 mm/minDifference of interstitial and vacancy concentrations(CI - CV ) (detail)FEMAGSof

21、t 20113. Simulation examples (contd) Variation of the pulling rate (from 3.4 to 3. mm/min) and of the crystal rotation rate (from 10. to 13. rpm) showed to have almost no effect on the defect distribution.Effect of the process parametersFEMAGSoft 20113. Simulation examples 2nd exampleCalculation of

22、thermal stresses in a growing FZ crystal without convectionFEMAGSoft 20113. Simulation examples (contd)Effect of a heat shield: temperature fieldNo convection,Rs = 5.1 cm, Rf = 4.7 cm,vpul = 3.4 mm/min a) Without heat shieldb) With a heat shieldFEMAGSoft 20113. Simulation examples (contd)Effect of a

23、 heat shield: von Mises stress a) b)growth orientationFEMAGSoft 20113. Simulation examples (contd) a) b)growth orientationEffect of a heat shield: von Mises stress1. Introduction2. Global simulation tool3. Simulation examples4. DiscussionFEMAGSoft 2011Outline of the Presentation1. Introduction2. Glo

24、bal simulation tool3. Simulation examples4. DiscussionFEMAGSoft 2011Outline of the PresentationFEMAGSoft 20114. Discussion 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 rad