1. Sino-German Workshop on Electromagnetic Processing of Materials, 11.10 – 13.10.2004 Shanghai, PR China Magnetic Field Control of Heat and Mass Transport Processes in Industrial Growth of Silicon and III-V Semiconductors Crystals J.Dagner, P. Schwesig, D. Vizman, O. Gräbner, M.Hainke, J.Friedrich, G.Müller Outline: Time dependent magnetic fields applied to growth process of InP Stationary magnetic fields in large scale Czochralski facilities

2. Process: Vertical Gradient Freeze (VGF) growth of InP Task: Substrates with low dislocation density without additional dopands for lattice hardening Problem: Generation of dislocations during the relaxation of thermal stresses Possible Solution: Usage of time dependent magnetic fields to control convective heat transfer èChange the shape of the solid liquid interface in order to minimize the von Mises Stress èOptimization using numerical modeling Motivation Melt Crystal Crucible

3. Numerical modeling Furnace Setup : Existing VGF setup located at the Crystal Growth Laboratory in Erlangen (currently used for R&D activities for S-doped InP) Already optimized thermal field using numerical modeling Numerical Modeling: Global model of the complete setup for heat transfer with CrysVUn (conduction radiation and melt convection) Quasistationary calculations for different position of the phase boundary Investigated field types: Rotating magnetic fields (RMF) Traveling magnetic fields (TMF) Insulation Inert gas 9 Heating zones Crucible support Steel autoclave Boron-oxide Melt cover InP Crystal

4. Time dependent magnetic fields Traveling Magnetic Field [2]: Lorenz-force Time average Lorenz –force density for TMF: I 1 is the modified Bessel-function of first order; Time average Lorenz –force density for TMF: I 1 is the modified Bessel-function of first order; r z BrBr BzBz t t+  t [2] K. Mazuruk, Adv. Space Res. 29,4,541-548 (2002) Lorenz –force for RMF: p is the number of magnetic poles Lorenz –force for RMF: p is the number of magnetic poles  Lorenz-force r [3] B. Fischer et al., Proc. EPM 2000, 497-502 (2000)

5. RMF vs. TMF – transition to time dependent isothermal flow Critical Taylor number for transition to time dependent flow as function of the aspect ratio; Comparison with the literature: RMF: Volz et al.[4] compiled numerical data from different sources which is in good agreement with the results obtained by CrysVUn TMF: No literature known [4] Volz et al., Int. J. Heat Trans., 42, 1037-1045 (1999)  A stationary flow field at the beginning will be maintained till the end of the process Magnetic Taylor number for RMF/TMF:

6.  No significant influence on the bending of the interface and the resulting von Mises stress Process time Applying RMF to the standard growth process Bending (b) of the solid liquid interface for different process times. Max. von Mises stress at solid liquid interface for different process times. Melt Crystal concave convex b>0 b<0 Interface

7. Upward configuration Downward configuration Standard Process 1,2 MPa 2,0 mm 4,6 mm/s 2,1 MPa0,6 MPa Max. von Mises stress at the phase boundary 2,1 mm1,6 mm Bending of the solid liquid interface 9,6 mm/s5,3 mm/s Maximum velocity in the melt.  Only the down- ward configuration is useful Applying TMF to the standard growth process – influence of the orientation of the Lorentz-force Aspect ration: 0.5 Isotherms dT = 1k Streamlines

8. Function of the velocity in z direction has a minimum The bending of the solid liquid interface changes from concave to concave- convex shape (hat or W-shape) Applying TMF – Influence of the strength of the magnetic induction on the flow pattern Streamlines for different magnetic induction at a aspect ration of 0.9. Only half of the computational domain is show.

9. èMinimum of the von Mises stress at 5,5 mT, but the phase boundary has a W- shape. èTwo contradicting optimization criteria: a)Minimization of the bending of the phase boundary b)Minimization of von Mises stress at the phase boundary Applying TMF – Resulting von Mises stress at the solid liquid interface

10. Comparison of the results for RMF and TMF

11. Rotating magnetic fields (RMF): Only small influence on the bending of the phase boundary and the resulting von Mises stress(< 15%) Higher growth velocities have no advantages, in contrast to prior studies on GaAs (Hainke et al. Magnethydrodynamics 39:513-519 2003) Traveling magnetic fields (TMF): Reduction of the resulting von Mises stress while maintaining a flat phase boundary Further reduction is possible if a W-shape interface does not create additional problems in the growth process Major drawback for the practical application: The integration of an inductor for generating a TMF in a high pressure and high temperature vessel with corrosive atmosphere (Phosphor vapor) is complicated and expensive. (Schwesig et al. Journal of Crystal Growth 226:224-228 2004) Conclusions –Part I

12. transversalaxialcusp Czochralski growth of Si crystals Objectives for using magnetic fields: Stabilization of convection Reduction of temperature fluctuations Control of oxygen transport and interface shape Field strength: several mT up to several hundreds of mT

13. Optimization of the seeding phase by reducing diameter fluctuations Magnetic field withwithout Magnetic field with without Magnetic field with without Hirmke, Study Work 2001 Diameter Temperature 5K 1mm Time in sec

14. (in collaboration with Siltronic) Czochralski growth of Si crystals under the influence of steady magnetic fields Determination of the temperature distribution in the melt and at the crucible wall by using a special thermocouple set- up Gräbner, Proc. EMRS 2000 Measured temperature distribution at the wall (lines) compared with calculated values (point).

15.  x = -20rpm,  c = 2rpm  x = -20rpm,  c = 5rpm Experiment 2D - Simulation Axial Field 128mT  x = -20rpm,  c = 5rpm Cusp Field 40mT  x = -20rpm,  c = 5rpm Experiment 2D - Simulation Czochralski growth of Si crystals under the influence of steady magnetic fields Temperature distribution in a Si melt with 20kg under different process conditions – stationary numerical simulations with fixed shape of the melt pool; low Reynolds number k-  model (CFD-ACE); magnetic fields by FZHDM 1. [1] Mühlbauer et. al. J.o.Cryst.Growth 1999 pp 107

16. 3D view Crystal rotation:  x = -15rpm Crucible rotation:  c = 4rpm Side view 300mm Czochralski growth of Si crystals under the influence of steady magnetic fields Shape of solid/liquid interface under the influence of a horizontal magnetic field. Calculations (magnetic and flow field) with STHAMAS 3D. Free melt surface. The temperature is color-coded. Vizman, PAMIR 2002

17. Static magnetic fields: Widely used for large scale Czochralski process Measurement techniques for obtaining temperature values in the melt are available Comparing this measured data to values obtained by numerical simulations show a qualitative agreement Simulation of Czochralski process is still a matter of intense research Conclusions –Part II

18. Acknowledgement This work is financially supported by the German federal ministry of education and research and Humbolt foundation. The calculations with CFD-ACE were performed at SILTRONIC, Burghausen, Germany