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Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 11
ELEC 7770ELEC 7770Advanced VLSI DesignAdvanced VLSI Design
Spring 2008Spring 2008VLSI Test PrinciplesVLSI Test Principles
Vishwani D. AgrawalVishwani D. AgrawalJames J. Danaher ProfessorJames J. Danaher Professor
ECE Department, Auburn UniversityECE Department, Auburn University
Auburn, AL 36849Auburn, AL 36849
[email protected]@eng.auburn.eduhttp://www.eng.auburn.edu/~vagrawal/COURSE/E7770_Spr08/course.htmlhttp://www.eng.auburn.edu/~vagrawal/COURSE/E7770_Spr08/course.html
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 22
ReferenceReference
M. L. Bushnell and V. D. Agrawal, M. L. Bushnell and V. D. Agrawal, Essentials of Essentials of Electronic Testing for Digital, Memory and Mixed-Signal Electronic Testing for Digital, Memory and Mixed-Signal VLSI CircuitsVLSI Circuits, Springer, 2000., Springer, 2000.
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 33
Testing and DiagnosisTesting and Diagnosis
TestingTesting Determine whether of not a device is faulty.Determine whether of not a device is faulty. Accomplished through input-output experiment.Accomplished through input-output experiment.
DiagnosisDiagnosis Given a device has failed, locate the fault that caused Given a device has failed, locate the fault that caused
failurefailure Accomplished by analysis of test data and by intrusive Accomplished by analysis of test data and by intrusive
experiments.experiments.
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 44
Principle of TestingPrinciple of Testing
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 55
Automatic Test Equipment (ATE)Automatic Test Equipment (ATE) Consists of:Consists of:
Powerful computerPowerful computer Powerful 32-bit Powerful 32-bit Digital Signal ProcessorDigital Signal Processor (DSP) (DSP)
for analog testingfor analog testing Test Program (written in high-level language) Test Program (written in high-level language)
running on the computerrunning on the computer Probe Head (actually touches the bare or Probe Head (actually touches the bare or
packaged chip to perform fault detection packaged chip to perform fault detection experiments)experiments)
Probe CardProbe Card or or Membrane ProbeMembrane Probe (contains (contains electronics to measure signals on chip pin or electronics to measure signals on chip pin or pad)pad)
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 66
ADVANTEST Model T6682 ATEADVANTEST Model T6682 ATE
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 77
LTX FUSION HF ATELTX FUSION HF ATE
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 88
Cost of Manufacturing Test (2000AD)Cost of Manufacturing Test (2000AD) ATE purchase price: analog instruments, 1,024 ATE purchase price: analog instruments, 1,024
digital pins (0.5-1.0GHz)digital pins (0.5-1.0GHz)= $1.2M + 1,024 x $3,000 = $4.272M= $1.2M + 1,024 x $3,000 = $4.272M
Running cost (five-year linear depreciation)Running cost (five-year linear depreciation)= = Depreciation + Maintenance + OperationDepreciation + Maintenance + Operation
= $0.854M + $0.085M + $0.5M= $0.854M + $0.085M + $0.5M
= $1.439M/year= $1.439M/year
Test cost (24 hour ATE operation)Test cost (24 hour ATE operation)= $1.439M/(365 x 24 x 3,600)= $1.439M/(365 x 24 x 3,600)
= 4.5 cents/second= 4.5 cents/second
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 99
A Modern VLSI DeviceA Modern VLSI DeviceSystem-on-a-chip (SOC)System-on-a-chip (SOC)
DSPcore
RAMROM
Interfacelogic
Mixed-signalCodec
Dataterminal
Transmissionmedium
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 1010
Testing as Filter ProcessTesting as Filter Process
All fabricatedchips
Good chips
Defective chips
Prob(good) = Y
Prob(bad) = 1 – Y
Prob(pass test) = high
Prob(fail test) = high
Prob(fail test) = low
Prob(pass test) =
low
Mostlygoodchips
Mostlybad
chips
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 1111
VLSI Chip YieldVLSI Chip YieldVLSI Chip YieldVLSI Chip Yield A manufacturing defect is a finite chip area with A manufacturing defect is a finite chip area with
electrically malfunctioning circuitry caused by electrically malfunctioning circuitry caused by errors in the fabrication process.errors in the fabrication process.
A chip with no manufacturing defect is called a A chip with no manufacturing defect is called a good chip.good chip.
Fraction (or percentage) of good chips produced in Fraction (or percentage) of good chips produced in a manufacturing process is called the yield. Yield a manufacturing process is called the yield. Yield is denoted by symbol is denoted by symbol YY..
Cost of a chip:Cost of a chip:
Cost of fabricating and testing a wafer
Yield × Number of chip sites on the wafer
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 1212
Clustered VLSI DefectsClustered VLSI DefectsClustered VLSI DefectsClustered VLSI Defects
WaferDefects
Faulty chips
Good chips
Unclustered defectsWafer yield = 12/22 = 0.55
Clustered defects (VLSI)Wafer yield = 17/22 = 0.77
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 1313
Yield ParametersYield ParametersYield ParametersYield Parameters Defect density (d ) = Average number of defects per unit
of chip area Chip area (A ) Clustering parameter () 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)
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 1414
Yield EquationYield EquationYield EquationYield 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 !
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 1515
Defect Level or Reject RatioDefect Level or Reject RatioDefect Level or Reject RatioDefect Level or Reject Ratio 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: 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-defects refers to 3.4 or lower dpm.
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 1616
Determination of Determination of DLDLDetermination of Determination of DLDL
From field return data: Chips failing in the field From field return data: Chips failing in the field are returned to the manufacturer. The number are returned to the manufacturer. The number of returned chips normalized to one million chips of returned chips normalized to one million chips shipped is the shipped is the DLDL..
From test data: Fault coverage of tests and chip From test data: Fault coverage of tests and chip fallout rate are analyzed. A modified yield model fallout rate are analyzed. A modified yield model is fitted to the fallout data to estimate the is fitted to the fallout data to estimate the DLDL..
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 1717
Modified Yield EquationModified Yield EquationModified Yield EquationModified Yield Equation Three parameters:Three parameters:
Fault density, Fault density, ff = average number of stuck-at faults = average number of stuck-at faults per unit chip areaper unit chip area
Fault clustering parameter, Fault clustering parameter, Stuck-at fault coverage, Stuck-at fault coverage, TT
The modified yield equation: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
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 1818
Defect LevelDefect LevelDefect LevelDefect Level Y (T ) – Y (1)DL (T ) =
Y (T )
( β + TAf ) β
= 1 –
( 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.
, Y (T ) = e –TAf and DL(T ) = 1 – Y (1)1 –T
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 1919
Example: SEMATECH ChipExample: SEMATECH ChipExample: SEMATECH ChipExample: SEMATECH Chip Bus interface controller ASIC fabricated and tested at Bus interface controller ASIC fabricated and tested at
IBM, Burlington, VermontIBM, Burlington, Vermont 116,000 equivalent (2-input NAND) gates116,000 equivalent (2-input NAND) gates 304-pin package, 249 I/O304-pin package, 249 I/O Clock: 40MHz, some parts 50MHzClock: 40MHz, some parts 50MHz 0.80.8 CMOS, 3.3V, 9.4mm x 8.8mm area CMOS, 3.3V, 9.4mm x 8.8mm area Full scan, 99.79% fault coverageFull scan, 99.79% fault coverage Advantest 3381 ATE, 18,466 chips tested at 2.5MHz Advantest 3381 ATE, 18,466 chips tested at 2.5MHz
test clocktest clock Data obtained courtesy of Phil Nigh (IBM)Data obtained courtesy of Phil Nigh (IBM)
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 2020
Test Coverage from Fault SimulatorTest Coverage from Fault SimulatorTest Coverage from Fault SimulatorTest Coverage from Fault Simulator
Stu
ck-a
t fa
ult
co
vera
ge
Vector number, V
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 2121
Measured Chip FalloutMeasured Chip FalloutMeasured Chip FalloutMeasured Chip Fallout
Vector number, V
Mea
sure
d c
hip
fal
lou
t
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 2222
Model FittingModel FittingModel FittingModel Fitting
Clustered faults:1 – (1+TAf/β)– β
Af = 2.1, β = 0.083
Measured chip fallout
Y (1) = 0.7623
Ch
ip f
allo
ut
and
co
mp
ute
d
1-Y
(T
)
Stuck-at fault coverage, T
Unclustered faults:1 – e– TAf
Af = 0.31, β = Y (1) = 0.7348
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 2323
Computed Defect LevelComputed Defect LevelComputed Defect LevelComputed Defect LevelD
efec
t le
vel
(dp
m)
Stuck-at fault coverage (%)
Clustered faults, β = 0.083
Unclustered faults, β =
(1 – 0.7623)×106
(1 – 0.7348)×106
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 2424
Fault ModelingFault Modeling
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 2525
Why Model Faults?Why Model Faults?
I/O function tests inadequate for manufacturing (functionality versus component and interconnect testing)
Real defects (often mechanical) too numerous and often not analyzable
A fault model identifies targets for testing A fault model makes analysis possible Effectiveness measurable by experiments
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 2626
Some Real Defects in ChipsSome Real Defects in Chips Processing defects
Missing contact windows Parasitic transistors Oxide breakdown . . .
Material defects Bulk defects (cracks, crystal imperfections) Surface impurities (ion migration) . . .
Time-dependent failures Dielectric breakdown Electromigration . . .
Packaging failures Contact degradation Seal leaks . . .
Ref.: M. J. Howes and D. V. Morgan, Reliability and Degradation - Semiconductor Devices and Circuits, Wiley, 1981.
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 2727
Observed PCB DefectsObserved PCB Defects
Defect classes
ShortsOpensMissing componentsWrong componentsReversed componentsBent leadsAnalog specificationsDigital logicPerformance (timing)
Occurrence frequency (%)
51 1 613 6 8 5 5 5
Ref.: J. Bateson, In-Circuit Testing, Van Nostrand Reinhold, 1985.
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 2828
Common Fault ModelsCommon Fault Models Single stuck-at faults Transistor open and short faults Memory faults PLA faults (stuck-at, cross-point, bridging) Functional faults (processors) Delay faults (transition, path) Analog faults For more details of fault models, see
M. L. Bushnell and V. D. Agrawal, Essentials of Electronic Testing for Digital, Memory and Mixed-Signal VLSI Circuits, Springer, 2000.
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 2929
Single Stuck-at FaultSingle Stuck-at Fault Three properties define a single stuck-at fault
Only one line is faulty The faulty line is permanently set to 0 or 1 The fault can be at an input or output of a gate
Example: XOR circuit has 12 fault sites ( ) and 24 single stuck-at faults
a
b
c
d
e
f
10
g h i 1
s-a-0j
k
z
0(1)1(0)
1
Test vector for h s-a-0 fault
Good circuit valueFaulty circuit value
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 3030
Fault EquivalenceFault Equivalence Number of fault sites in a Boolean gate circuit is
= #PI + #gates + # (fanout branches) Fault equivalence: Two faults f1 and f2 are equivalent
if all tests that detect f1 also detect f2. If faults f1 and f2 are equivalent then the
corresponding faulty functions are identical. Fault collapsing: All single faults of a logic circuit can
be divided into disjoint equivalence subsets, where all faults in a subset are mutually equivalent. A collapsed fault set contains one fault from each equivalence subset.
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 3131
Equivalence RulesEquivalence Rules
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0
sa1
sa0
sa1
sa0
sa0sa1
sa1
sa0
sa0
sa0sa1
sa1
sa1
AND
NAND
OR
NOR
WIRE
NOT
FANOUT
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 3232
Equivalence ExampleEquivalence Example
sa0 sa1sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
Faults in boldfaceremoved byequivalencecollapsing
20Collapse ratio = ── = 0.625 32
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 3333
Fault DominanceFault Dominance If all tests of some fault F1 detect another fault F2, then
F2 is said to dominate F1. Dominance fault collapsing: If fault F2 dominates F1,
then F2 is removed from the fault list. When dominance fault collapsing is used, it is sufficient
to consider only the input faults of Boolean gates. See the next example.
In a tree circuit (without fanouts) PI faults form a dominance collapsed fault set.
If two faults dominate each other then they are equivalent.
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 3434
Dominance ExampleDominance Example
s-a-1F1
s-a-1F2 001
110 010 000101 100
011
All tests of F2
Only test of F1s-a-1
s-a-1
s-a-1s-a-0
A dominance collapsed fault set
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 3535
Dominance ExampleDominance Example
sa0 sa1sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
Faults in orangeremoved byequivalencecollapsing
15Collapse ratio = ── = 0.47 32
Faults in green removed bydominancecollapsing
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 3636
CheckpointsCheckpoints Primary inputs and fanout branches of a
combinational circuit are called checkpoints. Checkpoint theorem: A test set that detects all
single (multiple) stuck-at faults on all checkpoints of a combinational circuit, also detects all single (multiple) stuck-at faults in that circuit.
Total fault sites = 16
Checkpoints ( ) = 10
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 3737
Classes of Stuck-at FaultsClasses of Stuck-at Faults
Following classes of single stuck-at faults are identified by fault simulators:
Potentially-detectable fault – Test produces an unknown (X) state at primary output (PO); detection is probabilistic, usually with 50% probability.
Initialization fault – Fault prevents initialization of the faulty circuit; can be detected as a potentially-detectable fault.
Hyperactive fault – Fault induces much internal signal activity without reaching PO.
Redundant fault – No test exists for the fault. Untestable fault – Test generator is unable to find a test.
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 3838
Multiple Stuck-at FaultsMultiple Stuck-at Faults A multiple stuck-at fault means that any set of
lines is stuck-at some combination of (0,1) values.
The total number of single and multiple stuck-at faults in a circuit with k single fault sites is 3k-1.
A single fault test can fail to detect the target fault if another fault is also present, however, such masking of one fault by another is rare.
Statistically, single fault tests cover a very large number of multiple faults.
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 3939
Transistor (Switch) FaultsTransistor (Switch) Faults
MOS transistor is considered an ideal switch and two types of faults are modeled:
Stuck-open – a single transistor is permanently stuck in the open state.
Stuck-short – a single transistor is permanently shorted irrespective of its gate voltage.
Detection of a stuck-open fault requires two vectors. Detection of a stuck-short fault requires the
measurement of quiescent current (IDDQ).
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 4040
Stuck-Open ExampleStuck-Open Example
Two-vector s-op testcan be constructed byordering two s-at testsA
B
VDD
C
pMOSFETs
nMOSFETs
Stuck-open
1
0
0
0
0 1(Z)
Good circuit states
Faulty circuit states
Vector 1: test for A s-a-0(Initialization vector)
Vector 2 (test for A s-a-1)
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 4141
Stuck-Short ExampleStuck-Short Example
A
B
VDD
C
pMOSFETs
nMOSFETs
Stuck-short
1
0
0 (X)
Good circuit state
Faulty circuit state
Test vector for A s-a-0
IDDQ path in
faulty circuit
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 4242
SummarySummary Fault models are analyzable approximations of defects
and are essential for a test methodology. For digital logic single stuck-at fault model offers best
advantage of tools and experience. Many other faults (bridging, stuck-open and multiple
stuck-at) are largely covered by stuck-at fault tests. Stuck-short and delay faults and technology-dependent
faults require special tests. Memory and analog circuits need other specialized fault
models and tests.
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 4343
Review ExerciseReview Exercise What are three most common types of blocks a modern
SOC is likely to have – analog circuit, digital logic, fluidics, memory, MEMS, optics, RF?
The cost of a chip is $1.00 when its yield is 50%. What will be its cost if you could increased the yield to 80%.
What is the total number of single stuck-at faults, counting both stuck-at-0 and stuck-at-1, in the following circuit?
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 4444
AnswersAnswers What are three most common types of blocks a modern
SOC is likely to have – analog circuit, digital logic, fluidics, memory, MEMS, optics, RF.
The cost of a chip is US$1.00 when its yield is 50%. What will be its cost if you increased the yield to 80%.
Assume a wafer has n chips, then
wafer costChip cost = ──────── = $1.00
0.5 × n
Wafer cost = 0.5n × $1.00 = 50n cents
For yield = 0.8, chip cost = wafer cost / (0.8n) = 50n / (0.8n) = 62.5 cents
Spring 08, Mar 13Spring 08, Mar 13 ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 4545
Answers ContinuedAnswers Continued What is the total number of single stuck-at faults, counting
both stuck-at-0 and stuck-at-1, in the following circuit?
Counting two faults on each line,
Total number of faults = 2 × (#PI + #gates + #fanout branches)
= 2 × (2 + 2 + 2) = 12
s-a-0 s-a-1
s-a-0 s-a-1 s-a-0 s-a-1s-a-0 s-a-1
s-a-0 s-a-1
s-a-0 s-a-1