1. Section 4: Diffusion part 2
Jaeger Chapter 4
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2. Example : High Concentration Arsenic diffusion profile becomes “box-like”
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3. Summary of High-Concentration Diffusion
If doping conc < ni:
Use constant diffusivity solutions
(profile is erfc or half-gaussian)
If doping conc > ni:
Solution requires numerical techniques
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4. Transient Enhanced Diffusion (TED)
Dopant Implantation
C(x)
no annealing
900oC, several minutes
(After excess point defects
recombine. slower diffusion) Si
substrate
Implantation
induced excess
point defects
Implantation creates
large number of excess Si
interstitials and vacancies.
(1000X than thermal process).
After several seconds of annealing, the excess point defects recombine. x
900oC, several sec (TED)
Extremely rapid diffusion due
to excess point defects
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5. Diffusion: p-n Junction Formation
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6. Sheet Resistance
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7. Resistivity vs. Doping
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8. Irvin’s Curves p-type erfc n-type erfc p-type half-gaussian
n-type half-gaussian
Explicit
relationship between: N
(surface concentration) , o x
(junction depth), j N
(background concentration), B R
(sheet resistance), S
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9. Motivation to generate the Irvin’s Curves
Allows us to calculate doping parameters if we know 3 out of 4 of the parameters on the previous page
Approach
1) 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.
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10. Resistivity Measurement: Four-Point Probe
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11. Impurity Profiling: Spreading Resistance
Region of Interest is Angle-Lapped
Two-Point Probe Resistance Measurements vs. Depth
Profile Extracted
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12. Impurity Profiling Secondary Ion Mass Spectroscopy (SIMS)
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