Techniques and Algorithms for Techniques and Algorithms for Fault Grading of FPGA Fault Grading of FPGA

Interconnect Test ConfigurationsInterconnect Test Configurations

Techniques and Algorithms for Techniques and Algorithms for Fault Grading of FPGA Fault Grading of FPGA

Interconnect Test ConfigurationsInterconnect Test ConfigurationsMehdi Baradaran Tahoori and

Subhasish MitraIEEE Transactions on Computer-Aided Design of

Integrated Circuit and SystemsLaboratory of Reliable ComputingDepartment of Electrical EngineeringNational Tsing Hua UniversityHsinchu, Taiwan

2004/3/25 Yen-Lin Peng 2

OutlineOutline Introduction FPGA model Interconnect fault model Previous work Testing for opens Testing for shorts Algorithms and implementation details Generalization for arbitrary logic Results Summary and Conclusion

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IntroductionIntroduction Almost 80% of transistors in an FPGA are

programmable switches and buffers

In order to test an FPGA, it needs test configurations and test vectors

The objective of this paper is to develop techniques to calculate fault coverage for a given set of test patterns

Switch- and gate-level fault simulation and fault-emulation technique are too time consuming

CLBs are configured as transparent logic

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FPGA modelFPGA model

CLB

LineSegments IOB

SwitchMatrix

Logicblock

Mux

N1 N2 N3

W1

W2

W3

E1

E2

E3

S1 S2 S3

SRAM

PIP

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Interconnect Fault ModelInterconnect Fault Model The stuck-at faults can be modeled as shorts to

VDD and ground lines

Fault list consists of All line segments and PIP stuck-opens faults The bridging fault of all connectable pair and

possible nonconnectable pair Interconnect Faults

Open Short Stuck-at

Line segmentopen

PIPstuck-open

Short Between

Line segments

PIPstuck-closed

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Previous Work (1)Previous Work (1) Fault emulation

The test configuration is modified to obtain a faulty configuration and then test vectors are applied

It is very time consuming Needs whole test configurations and test vectors

Unable to deal with shorts between lines which cannot be directly connected

1 00 1

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Previous Work (2)Previous Work (2) Fault simulation

Switch-level fault simulation Due to the very large number of transistors in the

FPGA, this method takes too much time Gate-level fault simulation

All interconnect and routing details are eliminated and only gate-to-gate connectivity information is preserved

&

&

+

1 1 1 1

1 1

&

& +

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Testing for Opens (1)Testing for Opens (1) Used and neighbor sets

Open detection in switch matrices Multiple independent paths Detectable and undetectable stuck-open faults

N1 N2 N3

W1

W2

W3

E1

E2

E3

S1 S2 S3Used set

Neighbor Set N1 N2 N3

W1

W2

W3

E1

E2

E3

S1 S2 S3

Circuit-->undetectable

ABCD

G

F E

H

L

FF

FF

open fault can be detected

open fault cannot be detected

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Testing for Opens (2)Testing for Opens (2) Modeling of opens in line segments

Extension to the Entire FPGA

ABC

D G

F

E H

I J

K

equivalent

LUT1 LUT2

F=XZ

Y

X

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Testing for Shorts (1)Testing for Shorts (1) Stuck-closed PIP detection in switch matrices

Detectable and undetectable stuck-closed faults

N1 N2 N3

W1

W2

W3

E1

E2

E3

S1 S2 S3

detectable

undetectable

W1

W3

E1

E3

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Testing for Shorts (2)Testing for Shorts (2) Short detection in the entire FPGA

The bridging fault between two routing resources, A and B, is detectable if A and B are a connectable pair via a PIP(P) P is in the neighbor set P stuck-closed fault is detectable A and B belong to different unrelated nets

Bridging faults in nonconnectable pairs Inductive fault analysis toolscandidate list

0

Bridging Fault

wire A

wire B

0

PIP Stuck-Closed

wire A

wire B

A

N1 N2 N3

W1

W2

W3

E1

E2

E3

S1 S2 S3

B

W1

W3

E1

E3

Net 1

Net 2

Logic Cell

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Flowchart for Fault Coverage Flowchart for Fault Coverage CalculationCalculation

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Algorithms and Implementation Algorithms and Implementation DetailsDetails

LUTs are configured as transparent logic

The test configurations are converted to the appropriate graph models

Switch matrices point are translated to nodes of graph

PIPs and line segments are converted to graph edges

Transparent logic

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Fault Coverage for OpensFault Coverage for Opens Undetectable open faulttest configuration which

form cycles in the graph model

Modified Depth First Search

ABCD

G

F E

H

L

FF

FF

open fault can be detected

open fault cannot be detected

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Fault Coverage for ShortsFault Coverage for Shorts Find-Connectables on the use set graph in order to

find all connected pairs in the graph DFS

For each neighbor set, check that if its ends are connected through a path in used set Floyd-Warshall algorithm

N1 N2 N3

W1

W2

W3

E1

E2

E3

S1 S2 S3

detectable

undetectable

W1

W3

E1

E3

Net 1

Net 2

Logic Cell

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Flowchart for The Complete MethodFlowchart for The Complete Method

1 1

Z=X

11

Z=F(X,Y)

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ResultsResults Implemented using C++

A set of 100 test configurations

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Summary and ConclusionSummary and Conclusion Presented a new technique to calculate the fault

coverage of a set of test configurations for FPGA interconnects

This method is very fast