Dopant Diffusion
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Transcript of 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 implantationIt 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 Ohm’s Law: J =
Where J = current density (A/cm2) = electric field strength (V/m)=resistivity (cm)
Thus
= /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 = /xj /square ≡ s
for uniform doping.
For variable doping: dxxnNxnqx jx
Bjs
)()(
11
0
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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
Fick’s 1st law: F = -D dC/dx
Fick’s 2nd law:
C/t = F/x = (Fin – Fout)/x
dC/dt = D d2C/dx2
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Diffusion in SiliconIn 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-KThis 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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DtxtC
Dtx
DtQtxC
4exp),0(
4exp
2),(
22
QdxtxC
andxfortasCxfortasC
),(
00000
Gaussian Solution in an Infinite Medium
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Gaussian Diffusion near a Surface
DtxtC
Dtx
DTQtxC
4exp),0(
4exp),(
22
DtQtC
),0(
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Error-Function solution in an Infinite Medium
00000
xfortatCCxfortatC
DtxerfCtxC
21
2),(
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Error-Function solution near a Surface
)(1)(
2),(
21),(
xerfxerfcwhere
DtxerfcCtxC
orDtxerfCtxC
s
s
This solution assumes the concentration C is at the solid solubility limit and is infinite
DtCDtxerfCQ s
s 2
21
0
The dose, Q, is calculated by summing the concentration:
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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 = D1t1+D1t2+…D1tn
If D is not constant, then time is increased by the ratio of D2/D1, or
(Dt)eff = D1t1+D1t2(D2/D1)+…D1tn(Dn/D1)
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