1. Lecture 8.0 Silicon Crystal Growth

2. Silicon Mfg. - old Produce Silicon metal bar Zone Refining – n times –To get purity Cut off impure end Use pieces to fill crystallization apparatus Grow Mono-Crystal of large size

3. Zone Refining 0=x-Ut, k=C S /C L C o =solute concentration in melt or of solid on first pass C o = 0  x+L C s (x)dx - o  x-L kC L (x)dx

4. Si-Fe Phase Diagram

5. Si-O Phase Diagram

6. Crystal Growth

7. Silicon Mfg. - new Produce ultra pure Silicon cylinder Use pieces to fill crystallization apparatus Grow Mono-Crystal of large size

8. Add Dopants to Silicon Grown Melt is maintained with a given impurity concentration Melting Point is decreased Solid produced has a given impurity concentation

9. Ultra-pure Silicon Production Si + 3HCl  SiHCl 3 +H 2 –fluidized bed reactor at 500 to 700K –Condense chlorosilane, SiHCl 3 Distillation of liquid SiHCl 3 SiHCl 3 +H 2  Si + 3HCl at 1400K Si vapor Deposits on Si mandrel in a purged fed batch reactor heated to 700K Results Large diameter Si with impurities at 10 ppt or 14-9’s pure

10. 12” (30 cm) Boule

11. Crystal Growth

12. Czochralski Crystal Growth Apparatus Figure 4. Today's Czochralski growth furnace, or crystal puller, is a far more sophisticated apparatus than that built by Gordon Teal nearly 50 years ago. It is however fundamentally identical. A crystal is pulled from a feedstock of molten material by slowly withdrawing it from the melt. Czochralski pullers often possess provisions for adding to the melt during a single pull so that crystals larger than what can be obtained in a single charge of the crucible may be produced. Today crystals of a 12-inch diameter are possible, and the industry will spend billions to adopt this new size in the coming years. This figure was taken directly from the Mitsubishi Semiconductor –website: http://www.egg.orjp/MSIL/ english/index-e.html!

13. Czochralski Growing System

14. 12” (30 cm) Boule

15. Crystal Growth Steps Induce Supersaturation –Sub cooled melt –S=exp[ T  H f /(RT 2 )dT] Nucleation Growth at different rates on each Crystal Face Results in crystal with a particular Crystal Habit or shape

16. Nucleation Free Energy –G TOT =  G v V +  A Critical Size –R*=2  A  V m /(3  v R g T lnS) Nucleation Rate J=(2D/d 5 )exp[-  G(R*)/( R g T )] D=diffusion coefficient d= molecular diameter

17. Surface Nucleation Surface energy, , is replaced by  cos , where  is the contact angle between phases Geometric factors changed Units #/(cm 2 sec) Surface Nucleation –Limits growth of flat crystal surfaces

18. Crystal Growth Boundary Layer Diffusion Surface Diffusion Edge Diffusion Kink Site Adsorption Loss of Coordination shell at each step

19. Crystal Growth Rate Limiting Steps Boundary Layer Diffusion Surface Diffusion Surface Nucleation –Mono –Poly Screw Disslocation Edge Diffusion Kink Site Adsorption Loss of Coordination shell

20. Screw Surface Growth

21. Fluxes Boundary Layer Surface Edge

23. Mass Transfer to Rotating Crystal Local BL-MT Flux J [mole/(cm 2 s)] = 0.62 D 2/3 (C o -C eq ) -1/6   J [mole/(cm 2 s)] = 0.62 D 2/3 C eq (S-1) -1/6   –Franklin, T.C. Nodimele, R., Adenniyi, W.K. and Hunt, D., J. Electrochemical Soc. 135,1944-47(1988). –Uniform, not a function of radius!! Crystal Growth Rate due to BL-MT as Rate Determining Step

24. Heat Transfer to Rotating Crystal Local BL-HT Flux J [mole/(cm 2 s)] = h(T eq -T)/  H f J [mole/(cm 2 s)] = 0.62 k  -1/3 -1/6   (T eq -T)/  H f –Franklin, T.C. Nodimele, R., Adenniyi, W.K. and Hunt, D., J. Electrochemical Soc. 135,1944-47(1988). –Uniform, not a function of radius!! Crystal Growth Rate due to BL-HT as Rate Determining Step

25. Crystal Habit Equilibrium Shape –h 1 /  1 =h 2 /  2 =h 3 /  3 Kinetic Shape –h 1 =G 1 (S)*t –h 2 =G 2 (S)* t –h 3 =G 3 (S)* t

26. Crystal Faces Flat Face Stepped Face Kinked Face Diffusion Distances to Kink sites are shorter on K &S Faces

27. Crystal Habit

28. Wafers Cut from Boule & Polished