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Section 4: Diffusion part 2

Jaeger Chapter 4

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Example : High Concentration Arsenic diffusion profile becomes “box-like”

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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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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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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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Sheet Resistance

Material of Squares ofNumber

Square]per [Ohms ResistanceSheet =

=⎟⎠⎞

⎜⎝⎛

=

⎟⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛=

•=

WL

tR

WLR

WL

tR

tWA

S

S

ρ

ρ

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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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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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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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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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Impurity Profiling: Spreading Resistance

• Region of Interest is Angle- Lapped

• Two-Point Probe Resistance Measurements vs. Depth

• Profile Extracted

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Impurity Profiling Secondary Ion Mass Spectroscopy (SIMS)