EEDG/CE 6303: Testing and Testable Design
Mehrdad Nourani
Dept. of EE
Univ. of Texas at Dallas
Session 01
Introduction
VLSI Test Philosophy
Testing
Source: IEEE Spectrum
Test Philosophy
A Pass/Fail test:
Prob(P|PQ) = 0.95
70% Pass Quality
Prob(PQ) = 0.7
? % Passed
All Students
30% Fail Quality
Prob(FQ) = 0.3
Prob(F|FQ) = 0.95
PQ: student is pass quality
FQ: student is fail quality
? % Failed
P: student passes the test
F: student fails the test
Test Philosophy (contd)
Conditional Probability: P[A|B]=P[AB]/P[B]
Rewrite the relation:P[AB]=P[A|B].P[B]=P[B|A].P[A]=P[BA]
If A and B are independent: P[A|B]=P[A] or P[AB]=P[A].P[B]
Bays Theorem:
Simple form: P[A|B]=P[B|A].P[A]/P[B]
General Form for mutually exclusive & exhaustive events Eis:
P[A]=i=1n P[A|Ei].P[Ei] or
P[Ei|A]=P[EiA]/P[A]=P[A|Ei].P[Ei]/i=1n P[A|Ei].P[Ei]
Probability of Passing/Failing the Exam:
Prob( P) Prob( P | PQ ) Prob( PQ ) Prob( P | FQ ) Prob( FQ )
0.95 0.70 0.05 0.30 0.68
Pr ob( F ) 1 Pr ob( P) 1 0.68 0.32
Test Philosophy (contd)
Students risk (manufacturers risk or yield loss):
Prob( PQ | F )
Prob( F | PQ ) Prob( PQ ) 0.05 0.7
0.11
Prob( F )
0.32
11% of failed students (chips) should have passed
Teachers risk (consumers risk):
Prob( FQ | P)
Prob( P | FQ ) Prob( FQ ) 0.05 0.3
0.022
Prob( P)
0.68
2.2% of students (chips) passed the tests should
have failed
7
VLSI Chips Present and Future
Year
1997-2001
2003-2006
2009-2012
0.25 0.15
0.13 0.10
0.07 0.05
Millions of Transistors/cm2
4 10
18 39
84 180
Number of wiring layers
67
78
89
50 385
60 520
70 750
100 900
160 1475
260 2690
Clock Rate, MHz
200 730
530 1100
840 1830
Voltage, V
1.2 2.5
0.9 1.5
0.5 0.9
Power, W
1.2 61
2 96
2.8 109
Feature Size, m
Die Size, mm2
Pin count
Ntrans.
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VLSI Fabrication Process
A seed crystal is dipped into the
melted silicon to initiate singlecrystal growth
Diameter: 75 230 mm
Growth rate: 30 180 mm/hour
The output is a silicon ingot
Using diamond blades, the wafers
are produced (thickness = 0.25
1 mm)
At least one surface is polished to
a flat, scratch-free mirror finish
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VLSI Fabrication Process (contd)
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What May Go Wrong?
Shorts between two points
(bridges)
Open in a line
Improper doping
Masking error
Improper thickness of a line
Particles on surface
Electron migration due to
heat
Corrosion
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What Can be Done?
1. Wafer probe testing.
2. Use microscope to find
faulty dices. Mark with a
small ink. Reject after
separation. Package the
unmarked dies.
3. Test for electrical and
mechanical characteristics.
4. Final inspection for
cosmetic defects.
5. Pack and ship.
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Test Definition
Testing of a system is an experiment in which
the system is exercised and its resulting
responses are analyzed to ascertain whether it
behaved correctly
How to send input data (test patterns)?
How to collect output results (test signatures)?
How long the system should run?
How to make the conclusion?
How to locate the cause of misbehavior (diagnosis)?
What causes misbehavior?
What test equipment are needed?
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Test Importance
Test is an integral part of any manufacturing
process.
Production Cost = Fabrication & Packaging + Testing
According to Semiconductor Industry Association
(SIA) roadmap, the cost of testing a die will surpass
its manufacturing cost in the near future.
Each VLSI chip needs to be tested. Sampling is
not adequate. Why?
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When and Where to Test
Try to detect defects at the earliest point
possible.
Costs increases dramatically (typically by an
order of magnitude) as faulty components find
their way to the higher level of integration
Rule of 10:
$1 to detect a faulty chip. Throw it out!
$10 to find (and replace) a bad IC on a board.
$100 to find a bad PC board in a system.
$1000 to find a bad component in the fielded system
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Taxonomy of Testing
Failure: incorrect operation of a system.
Fault: the physical failure mechanism.
Fault effect: the logical effect of a fault on a
signal or carrying net.
Error:
The condition (or state) of a system containing a
fault, i.e. deviation from correct state (e.g. wrong
component, incorrect wiring).
An instance of an incorrect operation of a system
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Taxonomy of Testing (contd)
An error does not necessarily lead to a failure.
Example:
Failure: one of the operational tires on your car goes
flat.
Error: existence of erroneous state of air pressure.
Defect: physical problems due to imperfect
manufacturing process.
Defects are not directly attributable to a human error.
Examples: shorts, opens, improper doping profiles,
mask misalignment
Sometimes fabrication defects and errors are
collectively referred to as physical faults
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Taxonomy of Testing (contd)
Fault model: the basic assumptions regarding
the nature of the logical (malignant) fault.
A fault is detected by observing an error
caused by it.
Briefly:
Defect Fault Error Failure
(e.g. dust particle stuck-at-1 erroneous
logic value circuit failing)
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Taxonomy of Testing (contd)
Yield (Y): the probability (usually expressed as
percent) that items (e.g. ICs) will not be
defective (fraction of manufactured parts that is
defect-free).
For VLSI chips yields range from 10% to 90%
depending on the process, circuit complexity, lambda
(), etc.
Y=1 (100%) means defect-free production.
Y=0 (0%) means all circuits are faulty.
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Taxonomy of Testing (contd)
Fault coverage (FC) is a measure to grade the quality of
a test:
FC=
Number of faults detected
100%
Total number of faults
FC=1 (100%)
FC=0 (0%)
: all possible faults detected
: no fault detected.
Defect level (DL): the probability of shipping a defective
product (the fraction of bad parts that pass all tests).
An empirical/analytical equation:
DL 1 Y (1FC) 100%
Both Y and FC must be continually improved to maintain
reliability of shipped products
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Defect Level Formula
Because tests may not be complete, a defective
chip may pass the tests.
Assumptions:
a chip has exactly n stuck-at faults.
Let m be the number of detected faults (m n)
the probability of a fault occurrence is independent of
the occurrence of another fault (i.e., there is no fault
clustering) and that all faults are equally likely with
probability p
A is the event that a part is free of defects, and B
that a part has been tested for m defects while none
were found.
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Defect Level Formula (cont.)
The Fault Coverage of a test is:
The Process Yield is defined as:
Considering: P( A B) P( A) (1 p)n
FC m / n
Y (1 p) n P( A)
P( B) (1 p) m
We will get:
P( A B) P( A B) / P( B) (1 p)n /(1 p)m (1 p)n(1m / n)
DL can now be expressed as:
DL 1 P( A B) 1 Y (1 FC )
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Defect Level (cont.)
DL is expressed as: DL 1 P( A B) 1 Y (1FC )
For large values of Y (i.e., a manufacturing process
with a high yield), it approaches a straight line
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Defect Level (cont.)
Example: Assume a manufacturing process with
Y = 0.5 and a FC = 0.8, then:
DL 1 0.5(10.8) 0.1295
This means that 12.95% of the shipped parts
are defective!
If a DL=200 PPM (i.e., DL = 0.0002) is required,
given Y = 0.5, then:
FC 1 (log(1 DL) / log Y ) 0.99971
This is a FC of 99.971%
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Type of Faults
Permanent fault: always being present after
their occurrence (in existence long enough to be
observed at test time).
Intermittent fault: existing only during some
intervals (appears and disappears at regular
intervals).
Transient fault: a one-time occurrence, e.g.
caused by a temporary change in some
environmental factors (appears and disappears
in short time intervals). These faults are crucial
for real-time systems.
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Failure Mechanisms
Failure mechanisms describe the physical and
electrical causes for faults. They can be divided
into 3 classes:
1.Electrical stress
Poor design leading to electrical overstress, or careless handling
causing static damage
2.Intrinsic failure mechanisms
Inherent to the semiconductor material itself.
Examples: Crystal defects, dislocations and processing defects
3.Extrinsic failure mechanisms
Originate in the packaging and interconnection process
Examples: Poor bonding, corrosion, etc.
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Failure
Mechanisms
Electrical
stress
Intrinsic
failure
mechanisms
Failure
mechanism
class
Extrinsic
failure
mechanisms
Electrical overstress
Electrostatic discharge
Gate oxide breakdown
Ionic contamination
Surface charge spreading
Charge effects
Slow trapping
Hot electrons
Secondary slow trapping
Piping
Dislocations
Packaging
Metallization
Corrosion
Electromigration
Contact migration
Microcracks
Bonding (purple plague)
Die attachments failure
Particle contamination
Radiation
External
Intrinsic
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