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

1. Lecture 8.0Lecture 8.0
Silicon Crystal 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-Fe Phase Diagram

5. Si-O Phase DiagramSi-O Phase Diagram

6. Crystal GrowthCrystal Growth

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 toAdd Dopants 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-pure Silicon Production
 Si + 3HClSiHCl3 +H2
– fluidized bed reactor at 500 to 700K
– Condense chlorosilane, SiHCl3
 Distillation of liquid SiHCl3
 SiHCl3+H2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) Boule12” (30 cm) Boule

11. Crystal GrowthCrystal Growth

12. Czochralski Crystal GrowthCzochralski Crystal 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 SystemCzochralski Growing System

14. 12” (30 cm) Boule12” (30 cm) Boule

15. 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

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 RateCrystal Growth 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 GrowthScrew Surface Growth

21. FluxesFluxes
Boundary
Layer
Surface
Edge

23. 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

24. 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

25. Crystal HabitCrystal Habit
Equilibrium Shape
– 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. Crystal HabitCrystal Habit

28. Wafers Cut from Boule & PolishedWafers Cut from Boule & Polished