bist2
TRANSCRIPT
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Built-in self test.1
Built-in Self-Test (BIST)
• Introduction• Test Pattern Generation• Test Response Analysis• BIST Architectures• Scan-Based BIST
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Built-in self test.2
Built-in Self-Test (BIST)
• Capability of a circuit to test itself• On-line:
– Concurrent : simultaneous with normaloperation
– Nonconcurrent : idle during normal operation• Off-line:
– Functional : diagnostic S/W or F/W– Structural : LFSR-based
• We deal primarily with structural off-line testinghere.
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Built-in self test.3
Basic Architecture of BIST
• TPG: Test pattern generator• ORA Output response analyzer
TPG
Circuit Under Test(CUT)
ORA
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Built-in self test.4
Glossary of BIST
• TPG - Test pattern generator• PRPG - pseudorandom pattern generator
(Pseudorandom number generator)• SRSG – Shift register sequence generator (a
single output PRPG)• ORA – Output response analyzer• SISR – Single-input signature register• MISR – Multiple-input signature register• BILBO – Built-in logic block observer
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Built-in self test.5
Built-in Self Testing
• Test pattern generation– Exhaustive– Pseudoexhaustive– Pseudorandom
• Test response compression– One’s count– Transition count– Parity checking– Syndrome checking– Signature analysis
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Built-in self test.6
Test Pattern Generation for BIST
• Exhaustive testing• Pseudorandom testing
– Weighted and Adaptive TG• Pseudoexhaustive testing
– Syndrome driver counter– Constant-weight counter– Combined LFSR and shift register– Combined LFSR and XOR– Cyclic LFSR
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Built-in self test.7
Exhaustive Testing
• Apply all 2n input vectors, where n = # inputs toCUT
• Impractical for large n• Detect all detectable faults that does not cause
sequential behavior• In general not applicable to sequential circuits• Can use a counter or a LFSR for pattern
generator
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Built-in self test.8
Linear Feedback Shift Register(LFSR)
• Example
F/F F/F
S1 1 0S2 0 1S1 1 0 :
Z = 0 1 0 1 …2 states
0 1 1 S1 0 0 1 S2 1 0 0 S3 0 1 0 S4 1 0 1 S5 1 1 0 S6 1 1 1S7 = S0 0 1 1 :
Z Z
Z = 1 1 0 0 1 0 1 …7 states
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Built-in self test.9
Two Types of LFSRs
• Type 1: External type
• Type 2: Internal type
C 1Cn-2Cn-1C n = 1
D QQ1 Q2 Qn
D Q
C 1 C 2 C n-1 C n = 1
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Built-in self test.10
Mathematical Operations over GF(2)• Multiplication ( )
• Addition ( or simply +)⊕
• 0 1•
0 00 1
01
0 11 0
01
0 1⊕
Example: ��� =� ��� =� �� =�
��� =−� ��� =−� ��� =−�
ifthen
������� ������� •+•+•= −−−
����� =++=�
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Built-in self test.11
Analysis of LFSR using PolynomialRepresentation
• A sequence of binary numbers can berepresented using a generation function(polynomial)
• The behavior of an LFSR is determined by itsinitial “seed” and its feedback coefficients, bothcan be represented by polynomials.
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Built-in self test.12
Characteristic Polynomials
• : sequence of binarynumbers.
• Generating function :
���������� �� ����
∑∞
=
=+++++=�
���� ������
�
��
�� �������������
������������ �� �� ���� =� Let
be output sequence of an LFSR of type1
∑=
−=�
�
���� ���
�
�
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Built-in self test.13
• Let initial state be ���� −−− ������ ��
�������
���
���
�
����
�
��
���
��
�
��
�
�
�
����
�
�
�
�
�
�
�
����
��
�
���������
������
������
∑∑
∑∑
∑∑∑
∞
=
−−
−−
=
−−
∞
==
=
−
∞
=
∞
=
+++=
=
==�� ��
�� ��
�� ��
∑
∑
=
−−
−−
=
+
++=
�
�
��
��
�
�
��
��
������
�
����
�
��
������
depends on initial state and feedbackcoefficients
�� ��∴
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Built-in self test.14
Denominator
is called the characteristic polynomial of theLFSR
�
� �������� ��������� ��� ++++=
Example:
�3 �2 �1 �0
�
����� ���� ++=
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Built-in self test.15
LFSR Theory
• Definition: If period p of sequence generated by anLFSR is , then it is a maximum lengthsequence
• Definition: The characteristic polynomial associatedwith a maximum length sequence is a primitivepolynomial
• Theorem: # of primitive polynomials for an n-stageLFSR is given by
�� −�
��� �������� −= φλ
where∏ −=
�� ���
�
��
����φ
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Built-in self test.16
Primitive Polynomial• # primitive polynomials of degree n ��� �λ
6710886432204816
168241211
N
• Some primitive polynomials
1: 0 13: 4 3 1 0 25: 3 02: 1 0 14: 12 11 1 0 26: 8 7 1 03: 1 0 15: 1 0 27: 8 7 1 04: 1 0 16: 5 3 2 0 28: 3 05: 2 0 17: 3 0 29: 2 06: 1 0 18: 7 0 30: 16 15 1 07: 1 0 19: 6 5 1 0 31: 3 08: 6 5 1 0 20: 3 0 32: 28 27 1 09: 4 0 21: 2 0 33: 13 010: 3 0 22: 1 0 34: 15 14 1 011: 2 0 23: 5 0 35: 2 012: 7 4 3 0 24: 4 3 1 0 36: 11 0
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Built-in self test.17
Primitive Polynomial (Cont.)• Characteristic of maximum-length sequence:
– Pseudorandom though deterministic andperiodic
– # 1’s = # 0’s + 1
Can be used as a (pseudo)-random or exhaustivenumber generator.
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Built-in self test.18
LFSR Example
• “near” complete patterns are generated
�3 �2 �1 �0
�
����� =−
����� ���� ++=
1 0 0 00 0 0 10 0 1 10 1 1 11 1 1 11 1 1 01 1 0 11 0 1 00 1 0 11 0 1 10 1 1 01 1 0 01 0 0 10 0 1 00 1 0 01 0 0 0 (repeat)
��
��
��
��
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Built-in self test.19
LFSR Example (Cont.)
• To generate 2n patterns using LFSR
�3 �2 �1 �0
�
�
• Sequence becomes:����
����
����
����
����
…
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Built-in self test.20
What to Do if 2n is too Large?
• Using “pseudorandom” e.g. generate 232 pattern only
• Partitioning
• Using pseudo-exhaustive
� � �
Circuit under
test (CUT)
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Built-in self test.21
Constant Weight Patterns(for pseudoexhaustive testing)
• T, set of binary n-tuples, exhaustively covers allk-subspaces if for all subsets of k bits positions,each of the 2k binary patterns appears at leastonce in T, where
• Example: �� ≤
=
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
==
=
�
�
�
T can be a pseudoexhaustive test for a (n,w)-CUT if �� ≥
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Built-in self test.22
Constant Weight Patterns (Cont.)
• A binary n-tuple has weight k if it contains exactlyk 1’s
There are binary n-tuples having weight k.
• Theorem: Given n and k, T exhausitvely covers allbinary k-subspaces if it contains all binary n-tuples of weight(s) w such that w=c mod (n-k+1)for some integer c, where
�
��
��
���
≤≤−≤≤
�
��
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Built-in self test.23
Compression Techniques
• Bit-by-bit comparison is inefficient• Compress information into “signature” Response compacting or compressing
Errorindicator
Circuit under test
(CUT)
Data Compression
unit
Comparator
Inputtest
sequence T
Outputresponse
sequence R’Signature
S( R’)
Correct Signature S( R0 )
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Built-in self test.24
Compression Techniques to beDiscussed
• Ones Count• Transition Count• Parity Checking• Syndrome Checking• Signature Analysis
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Built-in self test.25
Practical Compression Techniques
• Easy to implement, part of BIST logic• Small performance degradation• High degree of compaction• No or small aliasing errors• Problems:
1. Aliasing error: signature (faulty ckt) = signature (fault-free ckt)2. Reference (good) signature calculation:
!Simulation!Golden unit!Fault tolerant
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Built-in self test.26
Ones-count Compression
• C: single-output circuit• R: output response• 1C(R) = # ones in ∑=
�
���
����� �����=
x1
x2
x3
11110000
11001100
10101010
s-a-0 fault f2
s-a-1 fault f1
10000000 = R0
11000000 = R1
10000000 = R2
z
Counter
Signature (ones count)
�����
�����
�����
===
��
��
��
Input test pattern sequence T
Raw output test response
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Built-in self test.27
Transition-count Compression
•• Does not guarantee the detection of single-bit
errors• Prob. (single-bit error masked)• Prob. (masking error)
∑=
+⊕=�
�
�� �����
�
���
T 10000000 = R0
11000000 = R1
10000000 = R2 Counter
NetworkD Q
Signature (transition count)
���
���
���
�
�
�
===
���
���
���
��
������
�
−−=
−
�
�
���
�
�
�
�
�−=
�
�
��−
�π
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Built-in self test.28
Parity-check Compression
• Detect all single bit errors• All errors consisting of odd number of bit errors
are detected• All errors consisting of even number of bit errors
are masked• Prob. (error masked)
T10000000 = R0
11000000 = R1
00000000 = R2
Network D Q
Signature (parity)
���
���
���
� ===
��
��
��
Clock
�≈
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Built-in self test.29
Syndrome Checking
• Apply random patterns.• Count the probability of 1.• The property is similar to that of ones count.
randomtest
patternCUT
Syndrome counter
Counter /
Clock
Syndrome
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Built-in self test.30
Signature Analysis• Based on linear feedback shift register (LFSR)• A linear ckt. composed of
! unit delay or D FFs! Modulo-2 scalar multipliers or adders
• Linear ckt.: Response of linear combination of inputs = Linear combination of responses of individual inputs
��� �� ���� +=+
0 1
0 1 1 0
01
+/- 0 1
0 0 0 1
01
*
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Built-in self test.31
Use LFSR as Signature Analyzer• Single-input LFSR
• Initial state• Final state
�=�
�
��
�
�
�
�
�
�
� += ���� ���� +=
Internal Type LFSRInternal Type LFSRInternal Type LFSRInternal Type LFSR⊕… …�� ��
or
: The remainder, or the signature
��
��
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Built-in self test.32
Signature Analyzer (SA)
Input sequence:
1 1 1 1 0 1 0 1 (8 bits)�
1)( ����� +++++= ������� ���1)( ����� +++=Time
01:5678
Input stream
1 0 1 0 1 1 1 11 0 1 0 1 1 1
:1 0 1
1 01
Remainder
Register contents
1 2 3 4 50 0 0 0 01 0 0 0 0
:0 1 1 1 10 0 0 1 00 0 0 0 10 0 1 0 1
�)( ���� +=Remainder
Output stream
Initial state
1 0 1 1 0 1
�1)( ��� +=Quotient
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Built-in self test.33
Signature Analyzer (SA) (Cont.)
�� +++ ����
× �� +��
= �� +++ ���
����� ���������� =+++++=+
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Built-in self test.34
Multiple-input Signature Register(MISR)
• Implementation:
C 1Cn-2Cn-1C n
D Q
D 1 D 2 D 3 D n
N
R
N
R*
Original Modified
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Built-in self test.35
Storage Cell of a SA
DCIA
Q
⊕
�i
��
�
i�
D
B
Q
⊕
Ci
��
………… …………
Normal: CK, BShift: S/T=0, A, BMISR: S/T=1, A, B
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Built-in self test.36
Performance of Signature Analyzer
• For a test bit stream of length m : # possible response = 2m, of which only one is
correct The number of bit stream producing a specific
signature is�
�
−= ��
�
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Built-in self test.37
Performance of Signature Analyzer(Cont.)
• Among these stream , only one is correct.
�
�
��
�� �−
−
≅−−= ���
������
• If n=16, then of erroneous response are detected. (Note that this is not % of faults !)
����� �� =− −
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Built-in self test.38
Generic Off-line BISTArchitecture
• Categories of architectures– Centralized or Distributed– Embedded or Separate BIST elements
• Key elements in BIST architecture– Circuit under test (CUTs)– Test pattern generators (TPGs)– Output-response analyzers (ORAs)– Distribution system for data transmission
between TPGs, CUTs and ORAs– BIST controllers
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Built-in self test.39
Centralized/ Separate BIST
TPG
DIST
CUT
CUT
DIST
ORA
BISTcontroller
Chip, board, or system
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Built-in self test.40
Distributed / Separate BIST
TPG CUT ORA
TPG CUT ORA
Chip, board, or system
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Built-in self test.41
Distributed / Embedded BIST
Chip, board, or system
TPG ORA
TPG ORA
CUT
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Built-in self test.42
Factors Affecting the Choice ofBIST
• Degree of test parallelism• Fault coverage• Level of packaging• Test time• Complexity of replaceable unit• Factory and field test-and-repair strategy• Performance degradation• Area overhead
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Built-in self test.43
Specific BIST Architectures
• Ref. Book by Abramovici, Breuer and Friedman
• Centralized and Separate Board-Level BIST (CSBL)• Built-in Evaluation and Self-Test (BEST)• Random-Test Socket (RTS)• LSSD On-Chip Self-Test (LOCST)• Self-Testing Using MISR and Parallel SRSG (STUMPS)
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Built-in self test.44
Specific BIST Architectures(Cont.)
• Concurrent BIST (CBIST)• Centralized and Embedded BIST with Boundary
Scan (CEBS)• Random Test Data (RTD)• Simultaneous Self-Test (SST)• Cyclic Analysis Testing System (CATS)• Circuit Self-Test Path (CSTP)• Built-In Logic-Block Observation (BILBO)
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Built-in self test.45
Built-In Logic Block Observation(BILBO)[1]
• Distributed• Embedded• Combinational “Kernels”• Chip level• “Clouding” of circuit• Registers based description of circuit• BILBO registers
• [1]. B. Konemann, et al., “Built-In Logic_Block ObservationTechnique,” Digest of papers 1979 Test Conf., pp.37-41, Oct.,1979
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Built-in self test.46
BILBO Registers
0
1
MU
X QD
Q
Q1
D
Q
Q
Q2
...
...
...
QD
Q
Qn-1
D
Q
Q
Qn
S0
...
Si
B2
B1
B1 B2 BILBO0 0 shift register0 1 reset1 0 MISR (input ∗ ∗ ∗ ∗ constant ∗ ∗ ∗ ∗ LFSR)1 1 parallel load (normal operation)
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Built-in self test.47
Applications of BILBO
• Bus-oriented structure
R11
C1
R21
…
R1n
Cn
R2n
BUS
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Built-in self test.48
Applications of BILBO (Cont.)
• Pipeline-oriented structure C1
…
BILBO
BILBO
C2
…
Cn
PIs
…
POs
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Built-in self test.49
Problems with BILBO
Using CBILBO
BILBO
C
MISR or TPG ?
C1
R1
R2
R2 ?
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Built-in self test.50
Transistor Level Implementation ofCBILBO
������ ++
��
��
��
��
��
��
�������������
�
�������������
�
��
��
��
��
�
�
��
��
TPG mode: C1, A2, B=0MISR mode: C1, A1, C2=0
(c) A simultaneous TPG/MISR S-Cell
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Built-in self test.51
Combination of LFSR and Scan Path
• Problem: Some hard-to-detect faults may neverbe exercised
Scan Path
CUT
SA
LFSR
Scan Path
CUT
LFSR SA
OR
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Built-in self test.52
Example 1
1 0 0
+
0 1 0
1 1 0
1 0 0
1 0 1
1 1 1
0 1 1
0 0 1
S-a-0
• The fault can never be detected
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Built-in self test.53
Example 2
….. …..32 bits
S-a-0
Or
S-a-1
S-a-0
• The faults are difficult to detect
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Built-in self test.54
Solutions:• Exhausting testing• Weighted random testing• Mixed mode vector pattern generation
• Pseudorandom vectors first• Deterministic tests followed
Do not consider the fact that the test vectorsare given in a form of testcubes with manyunspecified inputs.
4. Reseeding• Change the seeds as needed
5. Reprogram the characteristic polynomial6. Combination of two or more of the above
methods