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### Lecture 8.0

Silicon Crystal Growth

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

Zone Refining

0=x-Ut, k=CS/CL

Co=solute concentration in melt or of solid on first pass

Co=0x+L Cs(x)dx - ox-L kCL(x)dx

Silicon Mfg. - new

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

Melt is maintained with a given impurity concentration

Melting Point is decreased

Solid produced has a given impurity concentation

Add Dopants to Silicon GrownUltra-pure Silicon 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

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!

Crystal Growth Steps

- Induce Supersaturation
- Sub cooled melt
- S=exp[THf/(RT2)dT]

- Nucleation
- Growth at different rates on each Crystal Face
- Results in crystal with a particular Crystal Habit or shape

Nucleation

- Free Energy
- GTOT=GvV + A

- Critical Size
- R*=2AVm/(3vRgT lnS)

- Nucleation Rate
- J=(2D/d5)exp[-G(R*)/(RgT)]
- D=diffusion coefficient
- d= molecular diameter

Surface Nucleation

- Surface energy, , is replaced by cos , where is the contact angle between phases
- Geometric factors changed
- Units #/(cm2sec)
- Surface Nucleation
- Limits growth of flat crystal surfaces

Crystal Growth

- Boundary Layer Diffusion
- Surface Diffusion
- Edge Diffusion
- Kink Site Adsorption
- Loss of Coordination shell at each step

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

Fluxes

- Boundary Layer
- Surface
- Edge

Mass Transfer to Rotating Crystal

- Local BL-MT Flux
- J[mole/(cm2s)] = 0.62 D2/3(Co-Ceq) n-1/6w1/2
- J[mole/(cm2s)] = 0.62 D2/3 Ceq(S-1) n-1/6w1/2
- 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

Heat Transfer to Rotating Crystal Crystal Growth Rate due to BL-HT as Rate Determining Step

- Local BL-HT Flux
- J[mole/(cm2s)] = h(Teq-T)/Hf
- J[mole/(cm2s)]
- = 0.62 k -1/3 n-1/6w1/2 (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 Habit

- Equilibrium Shape
- h1/1=h2/2=h3/3

- Kinetic Shape
- h1=G1(S)*t
- h2=G2 (S)* t
- h3=G3 (S)* t

Crystal Faces

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

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