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### Lecture 9.0

Silicon Oxidation/Diffusion/Implantation

Silicon Oxidation

- Reactor
- Furnace at T=850C
- Pure Oxygen
- Si + O2 SiO2

- Kinetics
- BL-Mass Transfer
- J=Kg(CA-0)

- SS-Diffusion
- J=DO-SiO2 (dC/dx)

- Heat Transfer
- BL, q=h(T1-T)
- Solid, q=kSiO2(dT/dx)

- J=q/Hrxn

- BL-Mass Transfer

Grxn<0, Spontaneous

Kinetics

- Thickness
- Linear Rate
- Reaction Control
- First Order

- BL-MT Control
- BL-HT Control

- Reaction Control
- Parabolic Rate
- Product diffusion Control
- Product heat transfer Control

- Linear Rate
- J =(dx/dt) SiO2/MW SiO2

Thickness Experiments

- Parabolic Rate
- Derive it!
- dx2/dt=2K
- K=Ko exp(-Ea/RgT)
- x=o @ t=0
- x= at t=

- Very common!!
- Slow Solid State Diffusion
- Slow Heat Conduction

Field Oxide

- Thick oxide
- Oxygen
- Steam

- High Temperature Reaction

Diffusion

- Deposition of B or P on surface
- Heat and Hold for period of time
- Solid State Diffusion
- dC/dt=D d2C/dx2
- C=Co at x=0
- C=0 at x=

- C=Co(1-erf[x/(4Dt)])

- Etch excess B or P from surface

Diffusion Coefficient

- Self Diffusion
- D*=Doexp(-Ea/RgT)

- Diffusion of A in B
- Depends on A and matrix B

- DAB =(D*A XB + D*B XA) (d ln [aA]/d ln [XA])
- d ln [aA]/d ln [XA] = 1+ (d ln [A]/d ln [XA])
- d ln [aA]/d ln [XA] ~ 1 for ideal solutions
- And
- DAB =(D*A XB + D*B XA) = (D*A (1-XA) + D*B XA)
- Note Concentration dependence!!
- DAB ~D*A when XA ~0 , the dilute solution limit
- Good for dopants

Implantation

- Energy Loss
- Stopping of Ion
- Nuclear cross section, Sn(E)
- Electronic cross section, Se(E)
- ρT = atomic density of target (#/cc)

Average Range

- Integration of Energy Loss equation

Implantation

- Create Ions in Vacuum
- Accelerate in Electric Field

Implantation

- Impinge onto Silicon Surface
- Knock out Si ion(s)
- Charge Balance

- Travel deep into Silicon

Implant Depth

Depth Increases with Energy

Implantation Straggle

Increases with Energy

Implantation Concentration Profile

- Probability Based
- N(x)=Nmax exp[(x-xave)2/2x2]
- Nmax=(Ndose/[(2) x])~(0.4 Ndose/ x)
- Ndose=Qdose/e
- Qdose= current applied/cm2
- σx = standard deviation of projected range

Implantation Through Slit

- Slit opening = a
- N(x) =projected range formula
- ΔR = transverse straggle

Mask Thickness

- To effectively prevent ions penetrating in thick zone
- Relatively thick Oxide Protection layer
- Patterned
- Thinning (etching) of Oxide Protection layer over implantation zone
- Remove oxide layer with impurities inside

Mask Thickness

- Transmission through mask
- T=1/2 erfc[(x-xave)/2 x]

- To stop 99.99% of implanted materials, T=10-4
- Solve for x, the thickness to stop 99.99% of ions.

SiO2 Mask Thickness

Si3N4 Mask Thickness

Implant Depth

Depth Increases with Energy

Diffusion of Implanted Dopants

- Diffusion Furnace or Laser
- Heat Treatment
- Solid State Diffusion
- dC/dt = CT d/dz(DAB dXA /dz)
- C=Co(z) = CT XA(z) at z=0
- C=0 at z=

- DAB =(D*A XB + D*B XA) (d ln [aA]/d ln [XA])
- Interdiffusion or mutual diffusion coefficient