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![Crystal Growth StepsCrystal Growth Steps
Induce Supersaturation
– Sub cooled melt
– S=exp[T∫∆Hf/(RT2
)dT]
Nucleation
Growth at different rates on each
Crystal Face
Results in crystal with a particular
Crystal Habit or shape](https://image.slidesharecdn.com/lecture8-180117083333/75/Lecture8-0-silicon-crystal-growth-15-2048.jpg)
![NucleationNucleation
Free Energy
– GTOT=∆Gv V + γA
Critical Size
– R*=2βAγVm/(3βvRgT lnS)
Nucleation Rate
J=(2D/d5
)exp[- ∆G(R*)/(RgT)]
D=diffusion coefficient
d= molecular diameter](https://image.slidesharecdn.com/lecture8-180117083333/75/Lecture8-0-silicon-crystal-growth-16-2048.jpg)
![Mass Transfer to Rotating CrystalMass Transfer to Rotating Crystal
Local BL-MT Flux
J[mole/(cm2
s)] = 0.62 D2/3
(Co-Ceq) ν-1/6
ω1/2
J[mole/(cm2
s)] = 0.62 D2/3
Ceq(S-1) ν-1/6
ω1/2
– 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](https://image.slidesharecdn.com/lecture8-180117083333/75/Lecture8-0-silicon-crystal-growth-23-2048.jpg)
![Heat Transfer to Rotating CrystalHeat Transfer to Rotating Crystal
Local BL-HT Flux
J[mole/(cm2
s)] = h(Teq-T)/∆Hf
J[mole/(cm2
s)]
• = 0.62 k α-1/3
ν-1/6
ω1/2
(Teq-T)/∆Hf
– 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](https://image.slidesharecdn.com/lecture8-180117083333/75/Lecture8-0-silicon-crystal-growth-24-2048.jpg)
Uploaded bysudeep kumar
Lecture8.0 silicon crystal growth
This document discusses the process of silicon crystal growth. Key points include: 1) Silicon is zone refined to achieve high purity, then pieces are used to grow large mono-crystals via the Czochralski method. 2) The Czochralski method involves pulling a crystal from a melt using a seed crystal. Factors like temperature, impurity concentration, and pull rate impact the crystal growth process. 3) Crystal growth occurs through processes like boundary layer diffusion and surface/edge diffusion. The growth rate is determined by limiting steps like these diffusion processes or surface nucleation. 4) The crystal habit, or shape, depends on factors like the equilibrium crystal shape, kinetic growth
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Lecture8.0 silicon crystal growth
- 1. Lecture 8.0Lecture 8.0 SiliconCrystal Growth
- 2. Silicon Mfg. -oldSilicon 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 RefiningZone Refining 0=x-Ut,k=CS/CL Co=solute concentration in melt or of solid on first pass Co=0∫x+L Cs(x)dx - o∫x-L kCL(x)dx
- 4. Si-Fe Phase DiagramSi-FePhase Diagram
- 5. Si-O Phase DiagramSi-OPhase Diagram
- 6.
- 7. Silicon Mfg. -newSilicon Mfg. - new Produce ultra pure Silicon cylinder Use pieces to fill crystallization apparatus Grow Mono-Crystal of large size
- 8. Add Dopants toAddDopants to Silicon GrownSilicon Grown Melt is maintained with a given impurity concentration Melting Point is decreased Solid produced has a given impurity concentation
- 9. Ultra-pure Silicon ProductionUltra-pureSilicon Production Si + 3HClSiHCl3 +H2 – fluidized bed reactor at 500 to 700K – Condense chlorosilane, SiHCl3 Distillation of liquid SiHCl3 SiHCl3+H2Si + 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)Boule12” (30 cm) Boule
- 11.
- 12. Czochralski Crystal GrowthCzochralskiCrystal Growth ApparatusApparatus 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 SystemCzochralskiGrowing System
- 14. 12” (30 cm)Boule12” (30 cm) Boule
- 15. Crystal Growth StepsCrystalGrowth Steps Induce Supersaturation – Sub cooled melt – S=exp[T∫∆Hf/(RT2 )dT] Nucleation Growth at different rates on each Crystal Face Results in crystal with a particular Crystal Habit or shape
- 16. NucleationNucleation Free Energy –GTOT=∆Gv V + γA Critical Size – R*=2βAγVm/(3βvRgT lnS) Nucleation Rate J=(2D/d5 )exp[- ∆G(R*)/(RgT)] D=diffusion coefficient d= molecular diameter
- 17. Surface NucleationSurface Nucleation Surface energy, γ, is replaced by γ cos θ, where θ is the contact angle between phases Geometric factors changed Units #/(cm2 sec) Surface Nucleation – Limits growth of flat crystal surfaces
- 18. Crystal GrowthCrystal Growth Boundary Layer Diffusion Surface Diffusion Edge Diffusion Kink Site Adsorption Loss of Coordination shell at each step
- 19. Crystal Growth RateCrystalGrowth Rate Limiting StepsLimiting Steps Boundary Layer Diffusion Surface Diffusion Surface Nucleation – Mono – Poly Screw Disslocation Edge Diffusion Kink Site Adsorption Loss of Coordination shell
- 20. Screw Surface GrowthScrewSurface Growth
- 21.
- 23. Mass Transfer toRotating CrystalMass Transfer to Rotating Crystal Local BL-MT Flux J[mole/(cm2 s)] = 0.62 D2/3 (Co-Ceq) ν-1/6 ω1/2 J[mole/(cm2 s)] = 0.62 D2/3 Ceq(S-1) ν-1/6 ω1/2 – 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 toRotating CrystalHeat Transfer to Rotating Crystal Local BL-HT Flux J[mole/(cm2 s)] = h(Teq-T)/∆Hf J[mole/(cm2 s)] • = 0.62 k α-1/3 ν-1/6 ω1/2 (Teq-T)/∆Hf – 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 HabitCrystal Habit EquilibriumShape – h1/γ1=h2/γ2=h3/γ3 Kinetic Shape – h1=G1(S)*t – h2=G2 (S)* t – h3=G3 (S)* t
- 26. Crystal FacesCrystal Faces Flat Face Stepped Face Kinked Face Diffusion Distances to Kink sites are shorter on K &S Faces
- 27.
- 28. Wafers Cut fromBoule & PolishedWafers Cut from Boule & Polished