aug 11, 2006yogi/agrawal: spectral functional atpg1 spectral characterization of functional vectors...
Post on 20-Dec-2015
216 views
TRANSCRIPT
Aug 11, 2006 Yogi/Agrawal: Spectral Functional ATPG 1
Spectral Characterization of Functional Vectors for
Gate-level Fault Coverage Tests
Nitin Yogi and Vishwani D. AgrawalAuburn University
Department of ECE, Auburn, AL 36849, [email protected], [email protected]
Aug 11, 2006 Yogi/Agrawal: Spectral Functional ATPG 2
Outline
• Verification and Testing• Problem and Approach• Spectral analysis and generation of test
sequences• Test sequence compaction• Experimental Results• Conclusion• References
Aug 11, 2006 Yogi/Agrawal: Spectral Functional ATPG 3
Verification and Testing• Verification vectors
– are mandatory and required; to check for functional correctness of a digital system
– are generated based on the behavior of the system– have been found useful in detection of manufacture
defects like timing faults– have low stuck-at fault coverage (poor defect level), but
no yield loss
• Manufacturing tests– may be non-functional; cannot be used for verification– have high test generation complexity– have high stuck-at fault coverage
Aug 11, 2006 Yogi/Agrawal: Spectral Functional ATPG 4
Problem and Approach
• The problem:– To develop manufacturing tests from verification
vectors.
• Our approach: – Implementation-independent characterization:
• Functional vectors obtained either from design verification phase or by exercising various functions of the circuit.
• Characterization of verification vectors for spectral components and the noise level for each PI of the circuit.
– Test generation for gate-level implementation:• Generation of spectral vectors• Fault simulation and vector compaction
Aug 11, 2006 Yogi/Agrawal: Spectral Functional ATPG 5
Verification vectors
A
B
FC
GD
E
1 / 0
1 / 00 / 0
0 / 0
1 / 0
X / 00 / 0
X / 1
X / 0
State Diagram (b02 ckt.)
4 bit multiplier
A B
4 b
its
4 b
its
8 b
its
Behavioral Description (s344 ckt.)
Cases to verify:
Y
A B
Non-zero Non-zero
0 Non-zero
Non-zero 0
0 0
Max no. Max no.
Other cases …
Cases to verify : all state transitions
Input / output
Aug 11, 2006 Yogi/Agrawal: Spectral Functional ATPG 6
Walsh Functions and Hadamard Spectrum
1 1 1 1 1 1 1 11 -1 1 -1 1 -1 1 -11 1 -1 -1 1 1 -1 -11 -1 -1 1 1 -1 -1 11 1 1 1 -1 -1 -1 -11 -1 1 -1 -1 1 -1 11 1 -1 -1 -1 -1 1 11 -1 -1 1 -1 1 1 -1
H8 =
w0
w1
w2
w3
w4
w5
w6
w7
Wal
sh f
unct
ions
(or
der
8)
• Walsh functions form an orthogonal and complete set of basis functions that can represent any arbitrary bit-stream.
• Walsh functions are the rows of the Hadamard matrix.
• Example of Hadamard matrix of order 8:
Aug 11, 2006 Yogi/Agrawal: Spectral Functional ATPG 7
Characterizing a Bit-Stream
• A bit-stream is correlated with each row of Hadamard matrix.• Highly correlated basis Walsh functions are retained as essential
components and others are regarded as noise.
Bit stream to analyze
Correlating with Walsh functions by multiplying with Hadamard matrix.
Essential component (others noise)
Hadamard Matrix
Bit stream
Spectral coeffs.
Aug 11, 2006 Yogi/Agrawal: Spectral Functional ATPG 8
Test Vector Generation• Spectrum for new bit-streams consists of the essential components
and added random noise.• Essential component plus noise spectra are converted into bit-
streams by multiplying with Hadamard matrix.• Any number of bit-streams can be generated; all contain the same
essential components but differ in their noise spectrum.
Perturbation
Generation of test vectors by multiplying with Hadamard matrix
Spectral components
Essential component
retainedNew test vector
Aug 11, 2006 Yogi/Agrawal: Spectral Functional ATPG 9
Spectral Testing Approach (Circuit Characterization)
• Verification vector generation:– Verification vectors are generated to exercise various functions
of the circuit including its corner cases.
• Spectral analysis:– Verification sequences for each input are analyzed using
Hadamard matrix.– Essential components are determined by comparing their power
Hi2 with the average power per component M2.
– Condition to pick-out essential components:
where K is a constant
– The process starts with the highest magnitude component and is repeated till the criteria is not satisfied.
KM
Ηi2
2
Aug 11, 2006 Yogi/Agrawal: Spectral Functional ATPG 10
s298 Spectral Coeffs.
-70
-60
-50
-40
-30
-20
-10
0
10
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64
Coefficients
Ma
gn
itu
de
Input 1
Input 2
Input 3
Circuit s298: Coefficient Analysis
Examples of essential
components
Examples of noise
components
Aug 11, 2006 Yogi/Agrawal: Spectral Functional ATPG 11
Functional Verification Vectors for Spectral ATPG
• Start with functional verification vectors.• Characterize verification vectors for Walsh
spectrum and noise level.• Generate new sequences by adding random
noise to the Walsh spectrum.• Use fault simulator (Flextest) and integer linear
program (ILP) to compact sequences.
Aug 11, 2006 Yogi/Agrawal: Spectral Functional ATPG 12
Selecting Minimal Vector Sequences Using ILP
• A set of perturbation vector sequences {V1, V2, .. , VM} is generated, fault simulated and faults detected by each is obtained.
• Compaction problem: Find minimum set of vector sequences that cover all detected faults.
• Minimize Count{V1, … ,VM} to obtain compressed seq. {V1,… ,VC} where {V1, … ,VC} {V1, … , VM} Count{V1, … ,VC} ≤ Count{V1, … ,VM} Fault Coverage{V1, … ,VC} = Fault Coverage{V1, … ,VM}
• Compaction problem is formulated as an Integer Linear Program (ILP) [1].
[1] P. Drineas and Y. Makris, “Independent Test Sequence Compaction through Integer Programming," Proc. ICCD’03, pp. 380-386.
Aug 11, 2006 Yogi/Agrawal: Spectral Functional ATPG 13
ILP formulation• Each vector sequence in {V1, V2, .. , VM} is fault simulated
with the circuit in unknown state• Faults detected by each sequence is obtained• Variable xi defined for each vector seq. Vi
such that xi = 0 : vec. seq. Vi not selected = 1 : vec. seq. Vi selected
• Constraint equation formulated for each detected fault fk. • For example, if fault f3 is detected by vec. sequences V3, V4
and V11, then the constraint equation is
x3 + x4 + x11 ≥ 1• Solve for objective function:
Minimize
Mi
iix
1
Aug 11, 2006 Yogi/Agrawal: Spectral Functional ATPG 14
Experimental Circuits• Spectral ATPG technique applied to the following benchmarks:
– three ISCAS’89 circuits.– one ITC’99 high level RTL circuit– Parwan microprocessor
• Characteristics of benchmark circuits:
• Fault simulation performed using commercial sequential ATPG tool Mentor Graphics FlexTest.
• Results obtained on Sun Ultra 5 machines with 256MB RAM.
Circuit Benchmark PIs POs FFs Function
s298 ISCAS’89 3 6 14 Traffic light controller
s344 ISCAS’89 9 11 15 4 x 4 add-shift multiplier
s349 ISCAS’89 9 11 15 4 x 4 add-shift multiplier
b02 ITC’99 2 1 4 Finite-state machine
Aug 11, 2006 Yogi/Agrawal: Spectral Functional ATPG 15
ATPG Results
CircuitNo. of gate
faults
Functional Vectors
Spectral ATPG Gate-level ATPG
No. of vecs.
Fault Cov. (%)
No. of vecs.
Fault Cov. (%)
CPU (s)
No. of vecs.
Fault Cov. (%)
CPU (s)
s298 698 75 81.23 192 84.74 21 152 85.89 45
s344 1020 57 87.45 256 91.08 51 150 90.78 23
s349 1030 57 87.09 256 90.68 51 150 90.39 26
b02 148 13 85.47 128 93.92 10 38 94.26 1
Aug 11, 2006 Yogi/Agrawal: Spectral Functional ATPG 16
Functional Spectral ATPG: s298
Spectral ATPG
Gate-level ATPG
Functional vectors
Random vectors
Aug 11, 2006 Yogi/Agrawal: Spectral Functional ATPG 17
Functional Spectral ATPG: ITC’99 Benchmark b02 (FSM)
Aug 11, 2006 Yogi/Agrawal: Spectral Functional ATPG 18
Parwan Microprocessor
Reference: Z. Navabi, Analysis and Modeling of Digital Systems, NY: McGraw-Hill, 1993.
Aug 11, 2006 Yogi/Agrawal: Spectral Functional ATPG 20
Conclusion• Spectral ATPG technique for verification vectors
is applied to three ISCAS’89 and one ITC’99 benchmark circuits.
• Coverage of functional vectors can be effectively improved to match that of a gate-level ATPG by the proposed method.
• Test generation using Spectral ATPG brings with it all the benefits of high level testing
• Techniques that will enhance Spectral ATPG are:– Accurate determination and use of noise components– Better compaction algorithms
Aug 11, 2006 Yogi/Agrawal: Spectral Functional ATPG 21
References
• N. Yogi and V. D. Agrawal, “High-Level Test Generation for Gate-Level Fault Coverage,” Proc. 15th IEEE North Atlantic Test Workshop, May 2006, pp. 65-74.
• N. Yogi and V. D. Agrawal, “Spectral RTL Test Generation for Gate-Level Stuck-at Faults,” Proc. 19th IEEE Asian Test Symp., November 2006.
• N. Yogi and V. D. Agrawal, “Spectral RTL Test Generation for Microprocessors,” submitted.