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Fundamentals of Digital Test and DFT

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Fundamentals of Digital Test and DFT Vishwani D. Agrawal Rutgers University, Dept. of ECE New Jersey http://cm.bell-labs.com/cm/cs/who/va January 2003 – PowerPoint PPT presentation

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Title: Fundamentals of Digital Test and DFT


1
Fundamentals of Digital Test and DFT
  • Vishwani D. Agrawal
  • Rutgers University, Dept. of ECE
  • New Jersey
  • http//cm.bell-labs.com/cm/cs/who/va
  • January 2003

2
Course Outline
  • Basic concepts and definitions
  • Fault modeling
  • Fault simulation
  • ATPG
  • DFT and scan design
  • BIST
  • Boundary scan
  • IDDQ test

3
VLSI Realization Process
Customers need
Determine requirements
Write specifications
Design synthesis and Verification
Test development
Fabrication
Manufacturing test
Chips to customer
4
Definitions
  • Design synthesis Given an I/O function, develop
    a procedure to manufacture a device using known
    materials and processes.
  • Verification Predictive analysis to ensure that
    the synthesized design, when manufactured, will
    perform the given I/O function.
  • Test A manufacturing step that ensures that the
    physical device, manufactured from the
    synthesized design, has no manufacturing defect.

5
Realities of Tests
  • Based on analyzable fault models, which may not
    map onto real defects.
  • Incomplete coverage of modeled faults due to high
    complexity.
  • Some good chips are rejected. The fraction (or
    percentage) of such chips is called the yield
    loss.
  • Some bad chips pass tests. The fraction (or
    percentage) of bad chips among all passing chips
    is called the defect level.

6
Costs of Testing
  • Design for testability (DFT)
  • Chip area overhead and yield reduction
  • Performance overhead
  • Software processes of test
  • Test generation and fault simulation
  • Test programming and debugging
  • Manufacturing test
  • Automatic test equipment (ATE) capital cost
  • Test center operational cost

7
Cost of Manufacturing Testing in 2000AD
  • 0.5-1.0GHz, analog instruments,1,024 digital
    pins ATE purchase price
  • 1.2M 1,024 x 3,000 4.272M
  • Running cost (five-year linear depreciation)
  • Depreciation Maintenance Operation
  • 0.854M 0.085M 0.5M
  • 1.439M/year
  • Test cost (24 hour ATE operation)
  • 1.439M/(365 x 24 x 3,600)
  • 4.5 cents/second

8
Present and Future
1997--2001
2003--2006
Feature size (micron) 0.25 - 0.15 0.13 - 0.10
Transistors/sq. cm 4 - 10M 18 -
39M
Pin count 100 - 900 160 -
1475
Clock rate (MHz) 200 - 730 530 - 1100
Power (Watts) 1.2 - 61 2
- 96
SIA Roadmap, IEEE Spectrum, July 1999
9
Method of Testing
10
ADVANTEST Model T6682 ATE
11
LTX FUSION HF ATE
12
VLSI Chip Yield
  • 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 x Number of chip
sites on the wafer
13
Defect Level or Reject Ratio
  • Defect level (DL) is the ratio of faulty chips
    among the chips that pass tests.
  • DL is measured as parts per million (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
    greater than 500 ppm is considered unacceptable.

14
Example SEMATECH Chip
  • 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
  • 0.45m 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)

15
Computed DL
237,700 ppm (Y 76.23)
Defect level in ppm
Stuck-at fault coverage ()
16
Summary Introduction
  • VLSI Yield drops as chip area increases low
    yield means high cost
  • Fault coverage measures the test quality
  • Defect level (DL) or reject ratio is a measure of
    chip quality
  • DL can be determined by an analysis of test data
  • For high quality DL lt 500 ppm, fault coverage
    99

17
Fault Modeling
18
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

19
Some 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.
20
Observed PCB Defects
Occurrence frequency () 51 1 6 13 6 8
5 5 5
Defect classes Shorts Opens Missing
components Wrong components Reversed
components Bent leads Analog specifications Digita
l logic Performance (timing)
Ref. J. Bateson, In-Circuit Testing, Van
Nostrand Reinhold, 1985.
21
Common 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 examples, see Section 4.4 (p. 60-70) of
    the book.

22
Single 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

Faulty circuit value
Good circuit value
c
j
0(1)
s-a-0
d
a
1(0)
g
h
1
z
i
0
1
e
b
1
k
f
Test vector for h s-a-0 fault
23
Fault Equivalence
  • Number of fault sites in a Boolean gate circuit
    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
    circuits 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.

24
Equivalence Example
sa0 sa1
Faults in red removed by equivalence collapsing
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 sa1
20 Collapse ratio
----- 0.625 32
25
Summary Fault Models
  • 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.

26
Fault Simulation
27
Problem and Motivation
  • Fault simulation Problem Given
  • A circuit
  • A sequence of test vectors
  • A fault model
  • Determine
  • Fault coverage - fraction (or percentage) of
    modeled faults detected by test vectors
  • Set of undetected faults
  • Motivation
  • Determine test quality and in turn product
    quality
  • Find undetected fault targets to improve tests

28
Fault simulator in a VLSI Design Process
Verification input stimuli
Verified design netlist
Fault simulator
Test vectors
Modeled fault list
Test compactor
Remove tested faults
Delete vectors
Low
Fault coverage ?
Test generator
Add vectors
Adequate
Stop
29
Fault Simulation Scenario
  • Circuit model mixed-level
  • Mostly logic with some switch-level for
    high-impedance (Z) and bidirectional signals
  • High-level models (memory, etc.) with pin faults
  • Signal states logic
  • Two (0, 1) or three (0, 1, X) states for purely
    Boolean logic circuits
  • Four states (0, 1, X, Z) for sequential MOS
    circuits
  • Timing
  • Zero-delay for combinational and synchronous
    circuits
  • Mostly unit-delay for circuits with feedback

30
Fault Simulation Scenario (continued)
  • Faults
  • Mostly single stuck-at faults
  • Sometimes stuck-open, transition, and path-delay
    faults analog circuit fault simulators are not
    yet in common use
  • Equivalence fault collapsing of single stuck-at
    faults
  • Fault-dropping -- a fault once detected is
    dropped from consideration as more vectors are
    simulated fault-dropping may be suppressed for
    diagnosis
  • Fault sampling -- a random sample of faults is
    simulated when the circuit is large

31
Essence of Fault Sim.
Test vectors
Fault-free circuit
Comparator
f1 detected?
Circuit with fault f1
Comparator
f2 detected?
Circuit with fault f2
Comparator
fn detected?
Circuit with fault fn
  • Disadvantage Much repeated computation CPU time
    prohibitive for VLSI circuits
  • Alternative Simulate many faults together

32
Fault Sampling
  • A randomly selected subset (sample) of faults is
    simulated.
  • Measured coverage in the sample is used to
    estimate fault coverage in the entire circuit.
  • Advantage Saving in computing resources (CPU
    time and memory.)
  • Disadvantage Limited data on undetected faults.

33
Random Sampling Model
Detected fault
Undetected fault
All faults with a fixed but unknown coverage
Random picking
Np total number of faults (population
size) C fault coverage (unknown)
Ns sample size Ns ltlt Np
c sample coverage (a random variable)
34
Probability Density of Sample Coverage, c

(x--C )2
--
------------
1 2s 2 p (x )
Prob(x lt c lt x dx ) -------------- e
s (2
p) 1/2
C (1 - C) Variance, s 2
------------ Ns
Sampling error
s
s
p (x )
Mean C
x
1.0
C 3s
C -3s
x
C
Sample coverage
35
Sampling Error Bounds
C (1 - C ) x - C 3
-------------- 1/2 Ns
Solving the quadratic equation for C, we get
the 3-sigma (99.7 confidence) estimate
4.5 C 3s x ------- 1
0.44 Ns x (1 - x )1/2 Ns

Where Ns is sample size and x is the measured
fault coverage in the sample. Example A circuit
with 39,096 faults has an actual fault coverage
of 87.1. The measured coverage in a random
sample of 1,000 faults is 88.7. The
above formula gives an estimate of 88.7 3.
CPU time for sample simulation was about 10 of
that for all faults.

36
Summary Fault Sim.
  • Fault simulator is an essential tool for test
    development.
  • Concurrent fault simulation algorithm offers the
    best choice.
  • For restricted class of circuits (combinational
    and synchronous sequential with only Boolean
    primitives), differential algorithm can provide
    better speed and memory efficiency (Section
    5.5.6.)
  • For large circuits, the accuracy of random fault
    sampling only depends on the sample size (1,000
    to 2,000 faults) and not on the circuit size.
    The method has significant advantages in reducing
    CPU time and memory needs of the simulator.

37
Automatic Test-pattern Generation (ATPG)
38
Functional vs. Structural ATPG
39
Functional vs. Structural(Continued)
  • Functional ATPG generate complete set of tests
    for circuit input-output combinations
  • 129 inputs, 65 outputs
  • 2129 680,564,733,841,876,926,926,749,
  • 214,863,536,422,912 patterns
  • Using 1 GHz ATE, would take 2.15 x 1022 years
  • Structural test
  • No redundant adder hardware, 64 bit slices
  • Each with 27 faults (using fault equivalence)
  • At most 64 x 27 1728 faults (tests)
  • Takes 0.000001728 s on 1 GHz ATE
  • Designer gives small set of functional tests
    augment with structural tests to boost coverage
    to 98

40
Random-Pattern Generation
  • Flow chart for method
  • Use to get tests for 60-80 of faults, then
    switch to D-algorithm or other ATPG for rest

41
Path Sensitization Method Circuit Example
  • Fault Activation
  • Fault Propagation
  • Line Justification

42
Path Sensitization Method Circuit Example
  • Try path f h k L blocked at j, since there
    is no way to justify the 1 on i

1
D
D
D
D
1
0
D
1
1
43
Path Sensitization Method Circuit Example
  • Try simultaneous paths f h k L and
  • g i j k L blocked at k because
    D-frontier (chain of D or D) disappears

1
D
D
1
1
D
D
D
44
Path Sensitization Method Circuit Example
  • Final try path g i j k L test found!

0
0
D
D
1
D
D
D
1
1
45
Sequential Circuits
  • A sequential circuit has memory in addition to
    combinational logic.
  • Test for a fault in a sequential circuit is a
    sequence of vectors, which
  • Initializes the circuit to a known state
  • Activates the fault, and
  • Propagates the fault effect to a primary output
  • Methods of sequential circuit ATPG
  • Time-frame expansion methods
  • Simulation-based methods

46
Concept of Time-Frames
  • If the test sequence for a single stuck-at fault
    contains n vectors,
  • Replicate combinational logic block n times
  • Place fault in each block
  • Generate a test for the multiple stuck-at fault
    using combinational ATPG with 9-valued logic

Vector -n1
Vector 0
Vector -1
Fault
Unknown or given Init. state
Next state
State variables
Time- frame 0
Time- frame -1
Time- frame -n1
Comb. block
PO 0
PO -1
PO -n1
47
An Example of Seq. ATPG
FF1
B
A
FF2
s-a-1
48
Nine-Valued Logic (Muth)0,1, 1/0, 0/1, 1/X, 0/X,
X/0, X/1, X
A
0
A
X
s-a-1
s-a-1
X/1
0/1
0/X
X
0/X
FF1
FF1
0/1
X
X/1
FF2
FF2
B
X
B
0/1
Time-frame -1
Time-frame 0
49
Seq. ATPG Results
s1423
s5378 s35932 Total
faults 1,515
4,603 39,094 Detected faults
1,414 3,639
35,100 Fault coverage 93.3
79.1 89.8 Test
vectors 3,943
11,571 257 CPU time
1.3 hrs. 37.8 hrs.
10.2 hrs. HP J200 256MB
Ref. M. S. Hsiao, E. M. Rudnick and J. H. Patel,
Dynamic State Traversal for Sequential
Circuit Test Generation, ACM Trans. on
Design Automation of Electronic Systems (TODAES),
vol. 5, no. 3, July 2000.
50
Summary ATPG
  • Combinational ATPG is significantly more
    efficient than sequential ATPG.
  • Combinational ATPG tools are commercially
    available.
  • Design for testability is essential if the
    circuit is large (million or more gates) and high
    fault coverage (95) is required.

51
Design for Testability
52
Definition
  • Design for testability (DFT) refers to those
    design techniques that make test generation and
    test application cost-effective.
  • DFT methods for digital circuits
  • Ad-hoc methods
  • Structured methods
  • Scan
  • Partial Scan
  • Built-in self-test (BIST)
  • Boundary scan
  • DFT method for mixed-signal circuits
  • Analog test bus

53
Ad-Hoc DFT Methods
  • Good design practices learnt through experience
    are used as guidelines
  • Avoid asynchronous (unclocked) feedback.
  • Make flip-flops initializable.
  • Avoid redundant gates. Avoid large fanin gates.
  • Provide test control for difficult-to-control
    signals.
  • Avoid gated clocks.
  • . . .
  • Consider ATE requirements (tristates, etc.)
  • Design reviews conducted by experts or design
    auditing tools.
  • Disadvantages of ad-hoc DFT methods
  • Experts and tools not always available.
  • Test generation is often manual with no guarantee
    of high fault coverage.
  • Design iterations may be necessary.

54
Scan Design
  • Circuit is designed using pre-specified design
    rules.
  • Test structure (hardware) is added to the
    verified design
  • Add a test control (TC) primary input.
  • Replace flip-flops by scan flip-flops (SFF) and
    connect to form one or more shift registers in
    the test mode.
  • Make input/output of each scan shift register
    controllable/observable from PI/PO.
  • Use combinational ATPG to obtain tests for all
    testable faults in the combinational logic.
  • Add shift register tests and convert ATPG tests
    into scan sequences for use in manufacturing
    test.

55
Scan Design Rules
  • Use only clocked D-type of flip-flops for all
    state variables.
  • At least one PI pin must be available for test
    more pins, if available, can be used.
  • All clocks must be controlled from PIs.
  • Clocks must not feed data inputs of flip-flops.

56
Scan Flip-Flop (SFF)
Master latch
Slave latch
D
TC
Q
Logic overhead
MUX
Q
SD
CK
D flip-flop
Master open
Slave open
CK
t
Normal mode, D selected
Scan mode, SD selected
TC
t
57
Level-Sensitive Scan-Design Flip-Flop (LSSD-SFF)
Master latch
Slave latch
D
Q
MCK
Q
D flip-flop
SCK
SD
MCK
Normal mode
Logic overhead
TCK
MCK
TCK
Scan mode
TCK
SCK
t
58
Adding Scan Structure
PI
PO
SFF
SCANOUT
Combinational logic
SFF
SFF
TC or TCK
Not shown CK or MCK/SCK feed all SFFs.
SCANIN
59
Comb. Test Vectors
I2
I1
O1
O2
PI
PO
Combinational logic
SCANIN TC
SCANOUT
N2
N1
S2
S1
Next state
Present state
60
Testing Scan Register
  • Scan register must be tested prior to application
    of scan test sequences.
  • A shift sequence 00110011 . . . of length nsff4
    in scan mode (TC0) produces 00, 01, 11 and 10
    transitions in all flip-flops and observes the
    result at SCANOUT output.
  • Total scan test length
    (ncomb 2) nsff ncomb 4 clock periods.
  • Example 2,000 scan flip-flops, 500 comb.
    vectors, total scan test length 106 clocks.
  • Multiple scan registers reduce test length.

61
Scan Overheads
  • IO pins One pin necessary.
  • Area overhead
  • Gate overhead 4 nsff/(ng10nff) x 100, where
    ng comb. gates nff flip-flops Example ng
    100k gates, nff 2k flip-flops, overhead
    6.7.
  • More accurate estimate must consider scan wiring
    and layout area.
  • Performance overhead
  • Multiplexer delay added in combinational path
    approx. two gate-delays.
  • Flip-flop output loading due to one additional
    fanout approx. 5-6.

62
ATPG Example S5378
Original 2,781 179 0 0.0
4,603 35/49 70.0 70.9 5,533 s
414 414
Full-scan 2,781 0 179
15.66 4,603 214/228 99.1 100.0
5 s 585 105,662
Number of combinational gates Number of non-scan
flip-flops (10 gates each) Number of scan
flip-flops (14 gates each) Gate overhead Number
of faults PI/PO for ATPG Fault coverage Fault
efficiency CPU time on SUN Ultra II, 200MHz
processor Number of ATPG vectors Scan sequence
length
63
Summary Scan Design
  • Scan is the most popular DFT technique
  • Rule-based design
  • Automated DFT hardware insertion
  • Combinational ATPG
  • Advantages
  • Design automation
  • High fault coverage helpful in diagnosis
  • Hierarchical scan-testable modules are easily
    combined into large scan-testable systems
  • Moderate area (10) and speed (5) overheads
  • Disadvantages
  • Large test data volume and long test time
  • Basically a slow speed (DC) test

64
Built-In Self-Test(BIST)
65
BIST Process
  • Test controller Hardware that activates
    self-test simultaneously on all PCBs
  • Each board controller activates parallel chip
    BIST Diagnosis effective only if very high fault
    coverage

66
Example External XOR LFSR
  • Characteristic polynomial f (x) 1 x x3
  • (read taps from right to left)

67
Definitions
  • Aliasing Due to information loss, signatures of
    good and some bad machines match
  • Compaction Drastically reduce bits in
    original circuit response lose information
  • Compression Reduce bits in original circuit
    response no information loss fully invertible
    (can get back original response)
  • Signature analysis Compact good machine
    response into good machine signature. Actual
    signature generated during testing, and compared
    with good machine signature

68
Example Modular LFSR Response Compacter
  • LFSR seed value is 00000

69
Multiple-Input Signature Register (MISR)
  • Problem with ordinary LFSR response compacter
  • Too much hardware if one of these is put on each
    primary output (PO)
  • Solution MISR compacts all outputs into one
    LFSR
  • Works because LFSR is linear obeys
    superposition principle
  • Superimpose all responses in one LFSR
    final remainder is XOR sum of remainders of
    polynomial divisions of each PO by the
    characteristic polynomial

70
Modular MISR Example
71
Built-in Logic Block Observer (BILBO)
  • Combined functionality of D flip-flop, pattern
    generator, response compacter, scan chain
  • Reset all FFs to 0 by scanning in zeros

72
Circuit Initialization
  • Full-scan BIST shift in scan chain seed before
    starting BIST
  • Partial-scan BIST critical to initialize all
    FFs before BIST starts
  • Otherwise we clock Xs into MISR and signature is
    not unique and not repeatable
  • Discover initialization problems by
  • Modeling all BIST hardware
  • Setting all FFs to Xs
  • Running logic simulation of CUT with BIST hardware

73
Summary BIST
  • LFSR pattern generator and MISR response
    compacter preferred BIST methods
  • BIST has overheads test controller, extra
    circuit delay, Input MUX, pattern generator,
    response compacter, DFT to initialize circuit
    test the test hardware
  • BIST benefits
  • At-speed testing for delay stuck-at faults
  • Drastic ATE cost reduction
  • Field test capability
  • Faster diagnosis during system test
  • Less effort to design testing process
  • Shorter test application times

74
IEEE 1149.1 Boundary Scan Standard
75
System Test Logic
76
Serial Board / MCM Scan
77
Parallel Board / MCM Scan
78
Tap Controller Signals
  • Test Access Port (TAP) includes these signals
  • Test Clock Input (TCK) -- Clock for test logic
  • Can run at different rate from system clock
  • Test Mode Select (TMS) -- Switches system from
    functional to test mode
  • Test Data Input (TDI) -- Accepts serial test
    data and instructions -- used to shift in vectors
    or one of many test instructions
  • Test Data Output (TDO) -- Serially shifts out
    test results captured in boundary scan chain (or
    device ID or other internal registers)
  • Test Reset (TRST) -- Optional asynchronous TAP
    controller reset

79
Summary Bound. Scan
  • Functional test verify system hardware,
    software, function and performance pass/fail
    test with limited diagnosis high (100)
    software coverage metrics low (70) structural
    fault coverage.
  • Diagnostic test High structural coverage high
    diagnostic resolution procedures use fault
    dictionary or diagnostic tree.
  • SOC design for testability
  • Partition SOC into blocks of logic, memory and
    analog circuitry, often on architectural
    boundaries.
  • Provide external or built-in tests for blocks.
  • Provide test access via boundary scan and/or
    analog test bus.
  • Develop interconnect tests and system functional
    tests.
  • Develop diagnostic procedures.

80
IDDQ Test
81
Basic Principle of IDDQ Testing
  • Measure IDDQ current through Vss bus

82
Capacitive Coupling of Floating Gates
  • Cpb capacitance from poly to bulk
  • Cmp overlapped metal wire to poly
  • Floating gate voltage depends on capacitances and
    node voltages
  • If nFET and pFET get enough gate voltage to turn
    them on, then IDDQ test detects this defect
  • K is the transistor gain

83
Sematech Results
  • Test process Wafer Test Package Test
  • Burn-In Retest Characterize
    Failure Analysis
  • Data for devices failing some, but not all, tests.

84
Summary IDDQ Test
  • IDDQ tests improve reliability, find defects
    causing
  • Delay, bridging, weak faults
  • Chips damaged by electro-static discharge
  • No natural breakpoint for current threshold
  • Get continuous distribution bimodal would be
    better
  • Conclusion now need stuck-fault, IDDQ, and delay
    fault testing combined
  • Still uncertain whether IDDQ tests will remain
    useful as chip feature sizes shrink further

85
References
  • M.L. Bushnell and V. D. Agrawal, Essentials of
    Electronic Testing for Digital, Memory and
    Mixed-Signal VLSI Circuits, Boston Kluwer
    Academic Publishers, 2000, ISBN 0-7923-7991-8.
  • For the material on a course taught by the
    authors at Rutgers University, and a complete
    bibliography from the above book, see website
  • http//cm.bell-labs.com/cm/cs/who/va
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