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EE143 – Ali Javey
Section 4: Diffusion part 2
Jaeger Chapter 4
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EE143 – Ali Javey
Example : High Concentration Arsenic diffusion profile becomes “box-like”
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EE143 – Ali Javey
If doping conc < ni :
Use constant diffusivity solutions(profile is erfc or half-gaussian)
If doping conc > ni :
Solution requires numerical techniques
Summary of High-Concentration Diffusion
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EE143 – Ali Javey
Transient Enhanced Diffusion (TED)Dopant Implantation
Sisubstrate
Implantationinduced excesspoint defects
x
C(x)
no annealing
900oC, several sec (TED)Extremely rapid diffusion due to excess point defects
Implantation createslarge number of excess Siinterstitials and vacancies.(1000X than thermal process).After several seconds of annealing, the excess point defects recombine.
900oC, several minutes(After excess point defects recombine. slower diffusion)
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EE143 – Ali Javey
Diffusion: p-n Junction Formation
⎟⎟⎠
⎞⎜⎜⎝
⎛=
⎟⎟⎠
⎞⎜⎜⎝
⎛=
=
B
01-
B
0
NNerfc 2 :profileFunction Error
NNln 2 :ProfileGaussian
doping) type-nout cancels doping type-p e. (i. zero ision concentrat
impuritynet the wherepoint at the occursjunction n -P
DepthJunction calMetallurgi
Dtx
Dtx
x
x
j
j
j
j
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EE143 – Ali Javey
Sheet Resistance
Material of Squares ofNumber
Square]per [Ohms ResistanceSheet =
=⎟⎠⎞
⎜⎝⎛
=
⎟⎠⎞
⎜⎝⎛=⎟
⎠⎞
⎜⎝⎛⎟⎠⎞
⎜⎝⎛=
•=
WL
tR
WLR
WL
tR
tWA
S
S
ρ
ρ
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EE143 – Ali Javey
Resistivity vs. Doping
ρ =σ−1 = q μnn + μp p( )[ ]−1
n − type : ρ ≅ qμn ND − NA( )[ ]−1
p − type : ρ ≅ qμp NA − ND( )[ ]−1
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EE143 – Ali Javey
Explicit
No
(surface concentration) ,
xj(junction depth),
NB
RS
(sheet resistance),
p-type erfc n-type erfcp-type half-gaussiann-type half-gaussian
Irvin’s Curves
relationship between:
(background concentration),
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EE143 – Ali Javey
Approach1) The dopant profile can be uniquely determined if one knows the concentration values at two depth positions.
2) We will use the concentration values No at x=0 and NB at x=xj to determine the profile C(x). (i.e., we can determine the Dt value)
3) Once the profile C(x) is known, the sheet resistance RS can be integrated numerically from:
4) Irvin’s Curves are plots of No versus ( Rs•
xj ) for various NB .
( )∫ ⋅=
jxdxxNxq
Rs0
)(
1
μ
Allows us to calculate doping parameters if we know 3 out of 4 of the parameters on the previous page
Motivation to generate the Irvin’s Curves
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EE143 – Ali Javey
Resistivity Measurement: Four-Point Probe
tMeasuremen ResistanceTerminalFour
/square][ 53.42ln
t>> sfor m]-[ 2ln
s>>for t m]-[ 2
Ω≅==
Ω=
Ω=
IV
IV
tR
IVtIVs
Sπρ
πρ
πρ
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EE143 – Ali Javey
Impurity Profiling: Spreading Resistance
• Region of Interest is Angle- Lapped
• Two-Point Probe Resistance Measurements vs. Depth
• Profile Extracted
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EE143 – Ali Javey
Impurity Profiling Secondary Ion Mass Spectroscopy (SIMS)