Nov. 21, 2006 ATS'06 1

Spectral RTL Test Generation for Gate-Level Stuck-at Faults

Nitin Yogi and Vishwani D. AgrawalAuburn University, Department of ECE,

Auburn, AL 36849, USA

ATS'06 2Nov. 21, 2006

Outline

Need for High Level Testing Problem and Approach Spectral analysis and test generation RTL testing approach Experimental Results Conclusion

ATS'06 3Nov. 21, 2006

Need for High Level Testing

Motivations for high level testing:Reduced test generation complexity

Reduced time and cost for test developmentEarly resolution of testability issuesDifficulty of gate-level test generation for

black box cores with known functionality

ATS'06 4Nov. 21, 2006

Problem and Approach

The problem is … Develop an effective RTL ATPG method

And our approach is: Implementation-independent characterization:

RTL test generation Spectral analysis of RTL vectors

Test generated to cover faults in gate-level implementation:

Generation of spectral vectors Fault simulation and vector compaction

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Faults Modeled for an RTL Module

CombinationalLogic

FF

FF

Inputs Outputs

RTL stuck-at fault sites

A circuit is an interconnect of several RTL modules.

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Spectral Characterization of a Digital Bit-Stream

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: a complete orthogonal set of basis functions that can represent any arbitrary bit-stream.

• Walsh functions form the rows of a Hadamard matrix.

Example of Hadamard matrix of order 8time

ATS'06 7Nov. 21, 2006

Walsh Coefficients of a Bit-Stream A bit-stream is correlated with each row of Hadamard matrix.

Highly correlated basis functions => retained as essential components Others => noise.

Bit stream to analyze

Correlating with Walsh functions by multiplying with Hadamard matrix.

Essential component (others noise)

Hadamard Matrix

Bit stream

Spectral coeffs.

ATS'06 8Nov. 21, 2006

Bit-Stream Generation New spectrums are generated retaining essential components and adding

random noise. New spectrums 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 noise

Perturbation

multiplying withHadamard matrix

Ori

gin

al s

pec

tru

m

Essential component

retainedNew bit-stream

Bits changed

New spectrum

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RTL Testing Approach (Circuit Characterization)

RTL test generation: Test vectors generated for RTL faults

(PIs, POs and inputs - outputs of RTL modules and flip-flops.)

Spectral analysis: Test sequences for each input bit-stream are analyzed

using Hadamard matrix. Amount of perturbation is determined by a gradually

increasing noise level.

ATS'06 10Nov. 21, 2006

Power Spectrum: “Interrupt” Signal

Spectral Coefficients

Nor

mal

ized

Pow

er

Essential components

Noise components

Randomlevel

(1/128)

PARWANProcessorCircuit

ATS'06 11Nov. 21, 2006

Power Spectrum: “Ready” Signal

Randomlevel

(1/128)

Examples of Essential

components

Examples of Noise

components

Nor

mal

ized

Pow

er

Spectral Coefficients

PARWANProcessorCircuit

ATS'06 12Nov. 21, 2006

Power Spectrum: “DataIn[5]” Signal

Randomlevel

(1/128)

Nor

mal

ized

Pow

er

Spectral Coefficients

Examples of Essential

components

Examples of Noise

components

PARWANProcessorCircuit

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Power Spectrum: A Random SignalN

orm

aliz

ed P

ower

Averagelevel

(1/128)Spectral Coefficients

ATS'06 14Nov. 21, 2006

Selecting Minimal Vector Sequences Using ILP

Fault simulation of new sequences A set of perturbation vector sequences {V1, V2, .. , VM} are generated.

Vector sequences are fault simulated and faults detected by each is obtained.

Compaction problem Find minimum set of vector sequences which cover all the detected

faults. Minimize Count{V1, … ,VM} to obtain compressed seq. {V1,… ,VC}

where {V1, … ,VC} {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.

ATS'06 15Nov. 21, 2006

Results: Circuit Characteristics RTL Spectral ATPG technique applied to the following benchmarks:

4 ITC’99 high level RTL circuits 4 ISCAS’89 circuits. PARWAN processor (Z. Navabi, VHDL: Analysis and Modeling of Digital Systems, McGraw-Hill, 1993.)

Characteristics of benchmark circuits:

ATPG for RTL faults and 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

b01 ITC’99 2 2 5

b09 ITC’99 1 1 28

b11 ITC’99 7 6 31

b14 ITC’99 34 54 239

s1488 ISCAS’89 8 19 6

s5378 ISCAS’89 36 49 179

s9234 ISCAS’89 37 39 211

s35932 ISCAS’89 36 320 1728

PARWAN processor 11 23 53

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Results for b11-A**

No. of RTL faults

Number of Vectors

RTL test cov. (%)

CPU* seconds

No. of spec. components

Gate level test cov. (%)

240 224 76.16 530 256 74.09

* Sun Ultra 5, 256MB RAM ** Area-optimized synthesis in Mentor’s Leonardo

No. of gate-level

faults

RTL ATPG

Spectral Test SetsFlexTest Gate-level ATPG

Gate level cov. (%)

Number of vectors

CPU* seconds

Gate level cov. (%)

Number of vectors

CPU* seconds

2380 88.84 768 737 84.62 468 1866

RTL characterization:

RTL-ATPG results:

ATS'06 17Nov. 21, 2006

b11-A Circuit

0

10

20

30

40

50

60

70

80

90

100

1 10 100 1000 10000

Number of Vectors

Te

st

Co

ve

rag

e (

%) RTL spectral

ATPG

Gate-levelATPG

Randomvectors

RTL faultvectors

ATS'06 18Nov. 21, 2006

PARWAN processor

0

10

20

30

40

50

60

70

80

90

100

1 10 100 1000 10000

No. of Vectors

Te

st

co

ve

rag

e (

%)

RTL spectralATPG

Gate-levelATPG

Randomvectors

RTL faultvectors

ATS'06 19Nov. 21, 2006

ResultsCircuit name

No. of gate-level faults

RTL-ATPG spectral tests FlexTest Gate-level ATPG Random inputs

Cov. (%)

No. of vectors

CPU (secs)

Cov. (%)

No. of vectors

CPU (secs)

No. of vectors

Cov (%)

b01-A 228 99.57 128 19 99.77 75 1 640 97.78

b01-D 290 98.77 128 19 99.77 91 1 640 95.80

b09-A 882 84.68 640 730 84.56 436 384 3840 11.71

b09-D 1048 84.21 768 815 78.82 555 575 7680 6.09

b11-A 2380 88.84 768 737 84.62 468 1866 3840 45.29

b11-D 3070 89.25 1024 987 86.16 365 3076 3840 41.42

b14 25894 85.09 6656 5436 68.78 500 6574 12800 74.61

s1488 4184 95.65 512 103 98.42 470 131 1600 67.47

s5378 15584 76.49 2432 2088 76.79 835 4439 3840 67.10

s5378* 15944 73.59 1399 718 73.31 332 22567 2880 62.77

s9234 28976 17.36 64 721 20.14 6967 18241 160 15.44

s9234* 29400 49.47 832 2734 48.74 12365 4119 2176 33.06

s35932 103204 95.70 256 1801 95.99 744 3192 320 50.70

PARWAN 5380 89.11 1344 1006 87.11 718 3626 6400 76.63* Reset input added.

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Conclusion Spectral RTL ATPG technique applied to ITC’99 and

ISCAS’89 benchmarks, and a processor circuit. Vectors generated for RTL faults were spectrally

analyzed and new vectors generated through perturbation.

In most cases, Spectral RTL ATPG gave similar or better test coverage in shorter CPU time as compared to sequential ATPG

Test generation using Spectral RTL ATPG brings with it the benefits of high level testing

Techniques that will enhance Spectral ATPG are: Efficient RTL ATPG Accurate determination and use of noise components Better compaction algorithms

ATS'06 21Nov. 21, 2006

Questions ?

Thank You !