Transcript (Fall`07), Effectiveness Measures for VLSI Testing

Effectiveness Measures for VLSI Testing:
Defective Parts per Million, Defect
Coverage and Fault Coverage
Vishwani D. Agrawal
James J. Danaher Professor
Department of Electrical and Computer Engineering
Auburn University, Auburn, AL 36849
http://www.eng.auburn.edu/~vagrawal
[email protected]
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VLSI Chip Yield
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A manufacturing defect is a finite chip area with
electrically malfunctioning circuitry caused by
errors in the fabrication process.
A chip with no manufacturing defect is called a
good chip.
Fraction (or percentage) of good chips produced
in a manufacturing process is called the yield.
Yield is denoted by symbol Y.
Cost of a chip:
Cost of fabricating and testing a wafer

Yield × Number of chip sites on the wafer
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Clustered VLSI Defects
Good chips
Faulty chips
Defects
Wafer
Unclustered defects
Wafer yield = 12/22 = 0.55
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Clustered defects (VLSI)
Wafer yield = 17/22 = 0.77
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Yield Parameters
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Defect density (d ) = Average number of defects
per unit of chip area
Chip area (A )
Clustering parameter (a)
Negative binomial distribution of defects,
p (x ) = Prob(number of defects on a chip = x )
Γ (α +x )
(Ad / α) x
=  . 
x ! Γ (α)
(1+Ad / α) α+x
where Γ is the gamma function
α = 0, p (x ) is a delta function (max. clustering)
α =  , p (x ) is Poisson distr. (no clustering, William/Brown)
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Yield Equation
Y = Prob( zero defect on a chip ) = p (0)
Y = ( 1 + Ad / α ) – α
Example: Ad = 1.0, α = 0.5, Y = 0.58
Unclustered defects: α = , Y = e
– Ad
Example: Ad = 1.0, α = , Y = 0.37
too pessimistic !
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Defect Level or Reject Ratio
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Defect level (DL) is the ratio of faulty chips
among the chips that pass tests.
DL is measured as defective parts per million
(dpm, or simply ppm).
DL is a measure of the effectiveness of tests.
DL is a quantitative measure of the
manufactured product quality:
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For commercial VLSI chips a DL higher than 500
dpm is considered unacceptable.
Chip manufacturers strive for much lower defect
levels. Below 100 dpm means high quality.
Zero-defect refers to 3.4 dpm or below.
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Determination of DL
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From field return data: Chips failing in the
field are returned to the manufacturer.
The number of returned chips normalized
to one million chips shipped is the DL.
From test data: Fault coverage of tests
and chip fallout rate are analyzed. A
modified yield model is fitted to the fallout
data to estimate the DL.
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Modified Yield Equation
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Three parameters:
density, f = average number of
stuck-at faults per unit chip area
 Fault clustering parameter, b
 Stuck-at fault coverage, T
 Fault
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The modified yield equation:
Y (T ) = (1 + TAf / β) – β
Assuming that tests with 100% fault coverage
(T =1.0) remove all faulty chips,
Y = Y (1) = (1 + Af / β) – β
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Defect Level
Y (T ) - Y (1)
DL (T ) = 
Y (T )
( β + TAf )
=1–
β

( β + Af )
β
Where T is the fault coverage of tests, Af is the average number of
faults on the chip of area A, β is the fault clustering parameter. Af
and β are determined by test data analysis.
b =  , Y (T ) = e –TAf
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and DL(T ) = 1 – Y (1)1 –T
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Example: SEMATECH Chip
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Bus interface controller ASIC fabricated and
tested at IBM, Burlington, Vermont
116,000 equivalent (2-input NAND) gates
304-pin package, 249 I/O
Clock: 40MHz, some parts 50MHz
0.8m CMOS, 3.3V, 9.4mm x 8.8mm area
Full scan, 99.79% fault coverage
Advantest 3381 ATE, 18,466 chips tested at
2.5MHz test clock
Data obtained courtesy of Phil Nigh (IBM)
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Stuck-at fault coverage
Test Coverage from Fault Simulator
Vector number, V
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Measured chip fallout
Measured Chip Fallout
Vector number, V
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Chip fallout and computed 1-Y (T )
Model Fitting
Clustered faults:
1 – (1+TAf/β)– β
Af = 2.1, β = 0.083
Unclustered faults:
1 – e– TAf
Af = 0.31, β = 
Y (1) = 0.7348
Y (1) = 0.7623
Measured chip fallout
Stuck-at fault coverage, T
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Computed Defect Level
Defect level (dpm)
(1 – 0.7348)×106
(1 – 0.7623)×106
Unclustered
faults, β = 
Clustered
faults, β = 0.083
Stuck-at fault coverage (%)
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Reexamine Assumption
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Assumption: 100% fault coverage leads to
zero defect level.
Reality: 100% defect coverage leads to
zero defect level.
Must examine the two coverages.
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Fault vs. Defect Coverage
Fault coverage, T(V )
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Coverage = % of stuck-at
faults detected by vectors.
Faults are countable.
Alternative definition:
T (V ) = Prob (detection by
V vectors | a fault is
present)
All faults assumed equally
probable on a faulty chip.
Determined theoretically.
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Defect coverage, D(V )
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Coverage = % of real defects
detected by vectors.
Many types, large numbers.
Alternative definition:
D (V ) = Prob (detection by
V vectors | a defect is
present)
Each defect may have a
different probability of
occurrence.
Determined experimentally.
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Defect Coverage
D (V ) = Prob (detection by V vectors | chip is defective)
Prob (failure by V vectors)
= 
1 – Y (1)
1 – Y (d )
= 
1 – Y (1)
Measured yield, Y (d ), and estimated true yield, Y (1),
can provide a statistical estimate for defect coverage.
Source of inaccuracy: true yield, Y(1), is not known.
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Defect and Fault Coverages
Defect coverage D(V )
from test data
Coverage
Y(1) = 0.7623
Fault coverage T(V )
from fault simulator
Vector number (V )
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Defect coverage, D
Defect vs. Fault Coverage
Fault coverage, T
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Conclusion
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Defect coverage can be determined from the measured test
data.
Assumption:
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Either, tests are capable of activating the defect (Q: Can a delay
defect be detected by slow-speed stuck-at fault tests?)
Or, the real defect is clustered with faults detectable by the
tests.
The above assumption, “DL = 0 at f = 100%,” may be
justified since fault coverage appears to be more pessimistic
than defect coverage.
Defect coverage D (V ) is a transformation of test data:
 Vector 0 → coverage 0%
 Vector  → coverage 100%
Unclustered fault assumption adds pessimism.
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Future Directions
Defect density, d, should not be confused with defect
coverage, D (V ):
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Analyze test data for yield, defect coverage and defect
level without involving modeled faults.
Chip fallout fraction
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d = number of defects per unit area
D (V ) = percentage of all possible defects detected by V vectors
Experiment
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Vectors, V
Fraction of chips
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Y
0
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Prob(defect occurrence)
1.0
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Directions . . .
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Diagnosis: Defects do not conform to any
single fault model.
Question: Which is better?
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100% coverage for one fault model, or
some coverage for multiple fault models
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Directions . . .
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Generate tests for defect coverage and
diagnosis.
Question: which is better?
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100% stuck-at fault coverage, or
100% diagnostic coverage of stuck-at faults,
or
N-detect tests (longer tests), or
Any of the above + random vectors.
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References
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The clustered fault model used for Sematech data is described in
the book: M. L. Bushnell and V. D. Agrawal, Essentials of Electronic
Testing for Digital, Memory and Mixed-Signal VLSI Circuits,
Springer, 2000, Chapter 3.
The unclustered defect model is from the paper: T. W. Williams and
N. C. Brown, “Defect Level as a Function of Fault Coverage,” IEEE
Trans. Computers, vol. C-30, no. 12, pp. 987-988, Dec. 1981.
The discussion on defect coverage is from a presentation: J. T. de
Sousa and V. D. Agrawal, “An Experimental Study of Tester Yield
and Defect Coverage,” IEEE International Test Synthesis Workshop,
Santa Barbara, California, March 2001.
A direct analysis of defect level without involving the stuck-at fault
coverage is given in the paper: S. C. Seth and V. D. Agrawal, “On
the Probability of Fault Occurrence,” Defect and Fault Tolerance in
VLSI Systems, I. Koren, editor, Plenum Publishing Corp., 1989, pp.
47-52.
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