Indo - German Winter Academy 06 Digha IIT KANPUR

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1 Indo - German Winter Academy 06 Digha IIT KANPUR

2 Crystal Growth Simulations Shubham Gupta Electrical Engg. Mentor: Mr. Santhanu Jana

3 Contents Crystal Growth: Need to Study. Various Growth Methods. Czochralski(Cz) Process : Details. Basic equations. Boundary Conditions. Internal processes and their interrelations. Simulation : An Insight.

4 Overview: Crystals It is the building block for Advanced & Pure Materials Research :To satiate needs of research and technology for high-quality, tailor-made crystals of all kinds. New materials are the lifeblood of solid state research and device technology.

5 Crystal Growth Controlled phase transformations from a disordered fluid phase. Initiated :Seed crystal for a proper crystallographic orientation and to avoid large super cooling of the fluid phase which could generate uncontrolled nucleation. How to Study : Experiments or Simulation?

6 Numerical Simulation Numerical Simulations aren't Hot Allows Research. Cuts test run costs Allows us a crystal with the optimal parameters. Quality requirements for semiconductor and optical crystals on the market: Fine Tuning needed.

7 Crystal Growth Processes Czochralski Growth Bridgman Growth Floating Zone Silicon Crystal

8 Czochralski Growth:Intro Most Popular Technique : Si,GaAs,InP etc Poly Extra Grade Silicon melted in Quartz Crucible Seed crystal to induce crystallization. Doping as per requirements. Seed pulled upwards with rotation Desired wafer diameter. Details upcoming!

9 Bridgman Growth Directional Solidification. Cheap Simple Low thermal gradient Useful for materials which can sustain less thermal stresses. Horizontal & Vertical

10 Bridgman Temperature distribution from simulation of the growth furnace.

11 Floating Zone Very pure Single Crystal Silicon wafers. It involves the passing of a molten zone through a polysilicon rod. No Crucible,so pure. Wafers not as large as Cz growth Low Oxygen content. Photovoltaic applications

12 Insight into Cz -Process

13 How it works!

14 Overview Seed crystal effects desired Crystallographic orientation SiO, CO generated owing to quartz crucible. Purging Argon for inert environment Rotation for better thermal axisymmetry and crystal uniformity. Ensure wafer quality: oxygen,carbon, defects.

15 Temperature Distribution

16 Important processes to be treated Information about: Interplay of convection. Heat and mass transfer. The solidifying interface. Defect reactions and dynamics. Rotation effects. Also to be considered are other forces.

17 Governing Equations Conservation of Mass Equation for Momentum & Energy transport. Conservation of Species (Oxygen)

18

19

20 Basics contd.. Momentum equation Source terms Gravitation force Magnetic force(lorentz Force : J X B) Using Charge Conservation These equations are solved simultaneously.

21 Modelling Turbulence. DNS (Direct Numerical Simulations): Accuracy & High computing Power Needed. RANS :(Reynolds Averaged Navier Stokes) Works on Approximations, Used for Starting guess. LES ( Large Eddy Simulation):Simulation of large eddies only, Midway of above two.

22 Interface & Boundary Conditions We need them for Velocity Temperature Oxygen Electric Potential Axi-symmetric Conditions

23 Interface & Boundary Conditions At Growth interface: Energy balance Mass balance

24 Marangoni Convection Surface Tension Gradient induces this convection. Temperature gradients at free surface. Increases flow velocity at interface. Influences rate of oxygen evaporation.

25 Normal Force Free balancesurface Tangential Force Balance Radiation We take Flat free surface.

26 Bound. Condns. for others. Appropriate models for Oxygen Evaporation Magnetic field conditions for crucible wall, Growth interface. Some Crucial Factors in Cz Growth.

27 Crystal - melt Interface Crystal melt interface shape : Quality Depends on factors: 1.Rotation of Crucible 2.Convection 3.Magnetic Field Interface

28 Oxygen Transport Interstitial Oxygen precipitates during growth. Phases involved are: Dissolution from crucible, transport in melt, evaporation at interface & incorporation in crystal. Effected by Crucible & Crystal rotation. Concentration decrease with Crystal Rotation.

29 Magnetic Field Vertical,Transverse & Radial magnetic Fields. Control melt flow and suppress fluctuations in velocity, temperature & concentration. Uniformity increases. Increase of magnetic field makes oxygen assimilation less.

30 Some Results Temperature at 60mm from Bottom of Crucible

31 Comparing Oxygen Conc. Without Rotation

32 Comparing Oxygen Conc. With Rotation

33 Conclusion Through simulation one can see interplay of transport processes. High Crystal Quality Demand. Proper combination of crystal/crucible rotation rates and applied magnetic fields The desired growth interface shapes, uniform and less oxygen levels in the grown crystal, and good mixing in the melt.

34 Thanks I wish to thank University of Erlangen-Nuremberg & IIT Kanpur for this opportunity, and all of you for your patient hearing.

35 Happy Christmas & Happy 2007 for all.

36 Doubts???? ALE Single.. Dopant Segregation

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