Dopant Diffusion

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Dopant Diffusion

• Topics
• Doping methods
• Resistivity and Resistivity/square
• Dopant Diffusion Calculations
• -Gaussian solutions
• -Error function solutions

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As devices shrink, controlling diffusion profiles
with processing and annealing is critical in
acquiring features down to 10-20 nm
Schematic of a MOS device cross section, showing
various resistances. Xj is the junction depth in
the table above
As devices shrink, controlling the depth of the
gate channel becomes critical
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Deposition Methods

• Chemical Vapor Deposition
• Evaporation
• -Physical Vapor Deposition
• -Sputtering
• Ion Beam Implantation

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Vapor Deposition Chemical (CVD)
In Chemical Vapor Deposition (CVD) a reactive
gas is passed over the substrate to be coated,
inside of a heated, environmentally controlled
reaction chamber. In this case (right) CH4 gas
is introduced to create a diamond-like coating
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Vapor Deposition Physical (PVD)
Physical Vapor Deposition (PVD) may be from
evaporation or sputtering. Sometimes a plasma is
used to create high energy species that collide
with target (right)
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Sputtering
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Ion beam implantation gives excellent control
over the predeposition dose and is the most
widely used doping method
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Ion beam implantation
It can cause surface damage in the form of
sputtering of surface atoms, surface roughness
and changes in the crystal structure.
Though these defects can be removed by annealing,
annealing also results in a high degree of dopant
diffusion.
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Resistivity and Sheet Resistance
From Ohms Law rJ e Where J current density
(A/cm2)e electric field strength
(V/m)rresistivity (W-cm) Thus r e/J
In semiconductors, the doped regions have higher
conductivity than the sheet as a whole. We are
interested in the depth of the junction, xj. The
resistance we measure is that of a square of any
dimension with depth xj, or R r/xj W/square
rs for uniform doping.
For variable doping
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Solid solubility
Sometimes dopants cluster around vacancies and
other point defects, as above, becoming
electrically neutral. As a result, effective
level of doping may be lower than equilibrium
values in the adjacent figure
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Diffusion Models
Ficks 1st law F -D dC/dx
Ficks 2nd law DC/Dt DF/Dx (Fin
Fout)/Dx dC/dt D d2C/dx2
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Diffusion in Silicon
In general, diffusivity is given by D
Doexp(-Ea/kT) Where Ea activation energy 3.5
4.5 eV/atom k 8.61x10-5 eV/atom-K
This applies to intrinsic conditions. Dopant
levels (ND, NA) need to be less than the
intrinsic carrier density, ni as shown in the
graph
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Gaussian Solution in an Infinite Medium
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Gaussian Diffusion near a Surface
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Error-Function solution in an Infinite Medium
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Error-Function solution near a Surface
The dose, Q, is calculated by summing the
concentration
This solution assumes the concentration C is at
the solid solubility limit and is infinite
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Effect of successive diffusion steps

• If diffusion occurs at constant temperature,
  where the diffusivity is constant, then the
  effective thermal budget, Dt is
• (Dt)eff D1t1D1t2D1tn
• If D is not constant, then time is increased by
  the ratio of D2/D1, or
• (Dt)eff D1t1D1t2(D2/D1)D1tn(Dn/D1)

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