A DFT Approach for Diagnosis and A DFT Approach for Diagnosis and Process Variation-Aware Structural Test of Process Variation-Aware Structural Test of

Thermometer Coded Current Steering Thermometer Coded Current Steering DAC'sDAC's

A DFT Approach for Diagnosis and A DFT Approach for Diagnosis and Process Variation-Aware Structural Test of Process Variation-Aware Structural Test of

Thermometer Coded Current Steering Thermometer Coded Current Steering DAC'sDAC's

Rasit Onur Topaloglu and Alex OrailogluRasit Onur Topaloglu and Alex Orailoglu{ { rtopalogrtopalog | | alexalex }@cse.ucsd.edu }@cse.ucsd.eduUniversity of California, San DiegoUniversity of California, San DiegoComputer Science and Engineering Department Computer Science and Engineering Department 9500 Gilman Dr., La Jolla, CA, 92093 9500 Gilman Dr., La Jolla, CA, 92093

OutlineOutlineOutlineOutline

Current Steering Digital to Analog Converters 101Current Steering Digital to Analog Converters 101 A Process Variation-Aware Soft Fault ModelA Process Variation-Aware Soft Fault Model Process Variation EstimationProcess Variation Estimation Reduction of Diagnosis Time Using Design for Testability Reduction of Diagnosis Time Using Design for Testability

Hardware Hardware Experimental ResultsExperimental Results

Current Steering Digital to Analog Converters 101Current Steering Digital to Analog Converters 101 A Process Variation-Aware Soft Fault ModelA Process Variation-Aware Soft Fault Model Process Variation EstimationProcess Variation Estimation Reduction of Diagnosis Time Using Design for Testability Reduction of Diagnosis Time Using Design for Testability

Hardware Hardware Experimental ResultsExperimental Results

IntroductionIntroductionIntroductionIntroduction

Higher precision applications drive Digital to Analog Higher precision applications drive Digital to Analog Converter (DAC) resolutions to higher bits day by dayConverter (DAC) resolutions to higher bits day by day

Higher bit resolutions increase circuit complexity, Higher bit resolutions increase circuit complexity, hence increase hence increase test timetest time and difficulty and difficulty

In thermometer coded circuits, In thermometer coded circuits, controllabilitycontrollability is is limited as each bit increment sums current of a new limited as each bit increment sums current of a new source with previous onessource with previous ones

Diagnosis of a fault or test is usually handled by Diagnosis of a fault or test is usually handled by exhaustivelyexhaustively trying all input codes trying all input codes

Higher precision applications drive Digital to Analog Higher precision applications drive Digital to Analog Converter (DAC) resolutions to higher bits day by dayConverter (DAC) resolutions to higher bits day by day

Higher bit resolutions increase circuit complexity, Higher bit resolutions increase circuit complexity, hence increase hence increase test timetest time and difficulty and difficulty

In thermometer coded circuits, In thermometer coded circuits, controllabilitycontrollability is is limited as each bit increment sums current of a new limited as each bit increment sums current of a new source with previous onessource with previous ones

Diagnosis of a fault or test is usually handled by Diagnosis of a fault or test is usually handled by exhaustivelyexhaustively trying all input codes trying all input codes

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(110) input shown for an 8-bit binary CSDAC (Current Steering DAC)

Binary-Coded Current Steering Binary-Coded Current Steering PrinciplePrincipleBinary-Coded Current Steering Binary-Coded Current Steering PrinciplePrinciple

Input digital code selects current sources to be Input digital code selects current sources to be added to analog output added to analog output

IIoutout is the analog output is the analog output Current sources are in fact implemented by current Current sources are in fact implemented by current

mirrors using a common on-chip reference current mirrors using a common on-chip reference current

Input digital code selects current sources to be Input digital code selects current sources to be added to analog output added to analog output

IIoutout is the analog output is the analog output Current sources are in fact implemented by current Current sources are in fact implemented by current

mirrors using a common on-chip reference current mirrors using a common on-chip reference current

Individual Current DistributionsIndividual Current DistributionsIndividual Current DistributionsIndividual Current Distributions

Soft faults for exponentially valued current sources Soft faults for exponentially valued current sources would contribute integral and differential non-linearity would contribute integral and differential non-linearity (INL and DNL) degradation during certain transitions (INL and DNL) degradation during certain transitions e.g. transition from 2^n-1 to 2^n e.g. transition from 2^n-1 to 2^n

Soft faults for exponentially valued current sources Soft faults for exponentially valued current sources would contribute integral and differential non-linearity would contribute integral and differential non-linearity (INL and DNL) degradation during certain transitions (INL and DNL) degradation during certain transitions e.g. transition from 2^n-1 to 2^n e.g. transition from 2^n-1 to 2^n

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Impact of Binary Coding on INL and Impact of Binary Coding on INL and DNLDNLImpact of Binary Coding on INL and Impact of Binary Coding on INL and DNLDNL

Transitions from Transitions from 2^n-1 to 2^n activate totally differents 2^n-1 to 2^n activate totally differents sets of current sourcessets of current sources

Due to limited spatial correlation between these Due to limited spatial correlation between these groups, DNL will tend to get larger, which implicitly groups, DNL will tend to get larger, which implicitly tend to enlarge INLtend to enlarge INL

In thermometer-coded (TC-CSDACs), in these In thermometer-coded (TC-CSDACs), in these transitions, one more current source is added only, and transitions, one more current source is added only, and hence outputs of these two codes highly correlated due hence outputs of these two codes highly correlated due to the 2^n-1 common elements to the 2^n-1 common elements

Transitions from Transitions from 2^n-1 to 2^n activate totally differents 2^n-1 to 2^n activate totally differents sets of current sourcessets of current sources

Due to limited spatial correlation between these Due to limited spatial correlation between these groups, DNL will tend to get larger, which implicitly groups, DNL will tend to get larger, which implicitly tend to enlarge INLtend to enlarge INL

In thermometer-coded (TC-CSDACs), in these In thermometer-coded (TC-CSDACs), in these transitions, one more current source is added only, and transitions, one more current source is added only, and hence outputs of these two codes highly correlated due hence outputs of these two codes highly correlated due to the 2^n-1 common elements to the 2^n-1 common elements

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INL: max difference between overall real and

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(0111111) input for an 8-bit thermometer coded CSDAC

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Thermometer-Coded CSDACs (TC-Thermometer-Coded CSDACs (TC-CSDACs)CSDACs)Thermometer-Coded CSDACs (TC-Thermometer-Coded CSDACs (TC-CSDACs)CSDACs)

(110) in binary is (0111111) in thermometer code(110) in binary is (0111111) in thermometer code

Equal weighting of current sources prevents Equal weighting of current sources prevents significant impact for faulty sourcessignificant impact for faulty sources

Error correction capability is another attractive Error correction capability is another attractive reason for choosing thermometer code reason for choosing thermometer code ex:0111011 not possible as 1’s should be ex:0111011 not possible as 1’s should be consecutiveconsecutive

(110) in binary is (0111111) in thermometer code(110) in binary is (0111111) in thermometer code

Equal weighting of current sources prevents Equal weighting of current sources prevents significant impact for faulty sourcessignificant impact for faulty sources

Error correction capability is another attractive Error correction capability is another attractive reason for choosing thermometer code reason for choosing thermometer code ex:0111011 not possible as 1’s should be ex:0111011 not possible as 1’s should be consecutiveconsecutive

(0111111) input for an 8-bit thermometer coded CSDAC

Current sources indexed with fixed bit positionsCurrent sources indexed with fixed bit positions

Fixed indexes imply a controllability restrictionFixed indexes imply a controllability restriction Diagnosis time for a faulty current source Diagnosis time for a faulty current source

exponentially increases as compared to binary coded exponentially increases as compared to binary coded CSDACSCSDACS

Current sources indexed with fixed bit positionsCurrent sources indexed with fixed bit positions

Fixed indexes imply a controllability restrictionFixed indexes imply a controllability restriction Diagnosis time for a faulty current source Diagnosis time for a faulty current source

exponentially increases as compared to binary coded exponentially increases as compared to binary coded CSDACSCSDACS

Diagnosis Restriction of TC-Diagnosis Restriction of TC-CSDACsCSDACsDiagnosis Restriction of TC-Diagnosis Restriction of TC-CSDACsCSDACs

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ex: In a 16-bit converter, current sources indexed by consecutive number laid out on separate corners

Design Considerations for TC-Design Considerations for TC-CSDACsCSDACsDesign Considerations for TC-Design Considerations for TC-CSDACsCSDACs

Current sources laid out in common-centroid layout Current sources laid out in common-centroid layout style to minimize impact of process variationsstyle to minimize impact of process variations

A number of most significant bits (MSB’s) and least A number of most significant bits (MSB’s) and least significant bits (LSB’s) are grouped within themselves significant bits (LSB’s) are grouped within themselves to further reduce process variation impactsto further reduce process variation impacts

Current sources laid out in common-centroid layout Current sources laid out in common-centroid layout style to minimize impact of process variationsstyle to minimize impact of process variations

A number of most significant bits (MSB’s) and least A number of most significant bits (MSB’s) and least significant bits (LSB’s) are grouped within themselves significant bits (LSB’s) are grouped within themselves to further reduce process variation impactsto further reduce process variation impacts

A Practical TC-CSDAC ArchitectureA Practical TC-CSDAC ArchitectureA Practical TC-CSDAC ArchitectureA Practical TC-CSDAC Architecture

m MSB’s are m MSB’s are interpolatedinterpolated by n LSB’s by n LSB’s where B, total number where B, total number of bits, is m+n of bits, is m+n

Input to the TC-CSDAC Input to the TC-CSDAC is binary, hence is binary, hence binary binary to thermometer to thermometer decodersdecoders used in the used in the circuitcircuit

Proposed fault model Proposed fault model can be applied to MSB can be applied to MSB and LSB parts and LSB parts separately separately

m MSB’s are m MSB’s are interpolatedinterpolated by n LSB’s by n LSB’s where B, total number where B, total number of bits, is m+n of bits, is m+n

Input to the TC-CSDAC Input to the TC-CSDAC is binary, hence is binary, hence binary binary to thermometer to thermometer decodersdecoders used in the used in the circuitcircuit

Proposed fault model Proposed fault model can be applied to MSB can be applied to MSB and LSB parts and LSB parts separately separately

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Process-Aware Structural Soft Fault Process-Aware Structural Soft Fault ModelModelProcess-Aware Structural Soft Fault Process-Aware Structural Soft Fault ModelModel

Process variations should not be mistaken as faultsProcess variations should not be mistaken as faults

The proposed fault model:The proposed fault model: one current source might one current source might have an additional deviation from process variation have an additional deviation from process variation effected value due to any modeled or un-modeled faulteffected value due to any modeled or un-modeled fault

Process variations should not be mistaken as faultsProcess variations should not be mistaken as faults

The proposed fault model:The proposed fault model: one current source might one current source might have an additional deviation from process variation have an additional deviation from process variation effected value due to any modeled or un-modeled faulteffected value due to any modeled or un-modeled fault

Current sources are systematically correlated due Current sources are systematically correlated due to their close locations on dieto their close locations on die

Current sources can be represented as a sum of Current sources can be represented as a sum of independent components through a technique independent components through a technique called Principal Component Analysis (PCA)called Principal Component Analysis (PCA)

Principal components corresponding to largest Principal components corresponding to largest eigenvalues account for most of the variationeigenvalues account for most of the variation

Ratio of selected eigenvalues to all eigenvalues Ratio of selected eigenvalues to all eigenvalues can be used to ensure a minimum variationcan be used to ensure a minimum variation

Current sources are systematically correlated due Current sources are systematically correlated due to their close locations on dieto their close locations on die

Current sources can be represented as a sum of Current sources can be represented as a sum of independent components through a technique independent components through a technique called Principal Component Analysis (PCA)called Principal Component Analysis (PCA)

Principal components corresponding to largest Principal components corresponding to largest eigenvalues account for most of the variationeigenvalues account for most of the variation

Ratio of selected eigenvalues to all eigenvalues Ratio of selected eigenvalues to all eigenvalues can be used to ensure a minimum variationcan be used to ensure a minimum variation

I : normalized current source variablesU : eigenvectors of correlation matrixC : principal components

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Estimation of Process VariationsEstimation of Process VariationsEstimation of Process VariationsEstimation of Process Variations

Estimation of Process VariationsEstimation of Process VariationsEstimation of Process VariationsEstimation of Process Variations

A reduced number of principal components, M<N, is A reduced number of principal components, M<N, is equivalent to deleting some of the columnsequivalent to deleting some of the columns

Then, M of these equations can be chosen to obtain an Then, M of these equations can be chosen to obtain an M equation-M unknown systemM equation-M unknown system

The choice is made for consecutively indexed sources, The choice is made for consecutively indexed sources, as each source individually requires two measurements as each source individually requires two measurements due to controllability restrictiondue to controllability restriction

A reduced number of principal components, M<N, is A reduced number of principal components, M<N, is equivalent to deleting some of the columnsequivalent to deleting some of the columns

Then, M of these equations can be chosen to obtain an Then, M of these equations can be chosen to obtain an M equation-M unknown systemM equation-M unknown system

The choice is made for consecutively indexed sources, The choice is made for consecutively indexed sources, as each source individually requires two measurements as each source individually requires two measurements due to controllability restrictiondue to controllability restriction

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Process Variation-Aware Test Process Variation-Aware Test NominalsNominalsProcess Variation-Aware Test Process Variation-Aware Test NominalsNominals

M sources are measured for each chip, U is calculated M sources are measured for each chip, U is calculated from correlation matrix, hence only C values are left to from correlation matrix, hence only C values are left to be determinedbe determined

Once C values are calculated, unmeasured N-M source Once C values are calculated, unmeasured N-M source I values can be calculatedI values can be calculated

Hence, these steps provide Hence, these steps provide process-variation aware process-variation aware nominal valuesnominal values for each current source using few for each current source using few measurements, as N>>M even for 98% variationmeasurements, as N>>M even for 98% variation

M sources are measured for each chip, U is calculated M sources are measured for each chip, U is calculated from correlation matrix, hence only C values are left to from correlation matrix, hence only C values are left to be determinedbe determined

Once C values are calculated, unmeasured N-M source Once C values are calculated, unmeasured N-M source I values can be calculatedI values can be calculated

Hence, these steps provide Hence, these steps provide process-variation aware process-variation aware nominal valuesnominal values for each current source using few for each current source using few measurements, as N>>M even for 98% variationmeasurements, as N>>M even for 98% variation

Acquiring Principal Components On-Acquiring Principal Components On-ChipChipAcquiring Principal Components On-Acquiring Principal Components On-ChipChip

Analog current is measured for up to principal component number of times; as low as ~ 6 measurements Analog current is measured for up to principal component number of times; as low as ~ 6 measurements satisfactory to account for 98% variationsatisfactory to account for 98% variation

No additional hardware is required to take these measurements, for ex. 6 consequent input codes, No additional hardware is required to take these measurements, for ex. 6 consequent input codes, (0..0000000),(0..0000001),(0..0000011),.., (0..0111111), can be used to get these measurements (0..0000000),(0..0000001),(0..0000011),.., (0..0111111), can be used to get these measurements

Analog current is measured for up to principal component number of times; as low as ~ 6 measurements Analog current is measured for up to principal component number of times; as low as ~ 6 measurements satisfactory to account for 98% variationsatisfactory to account for 98% variation

No additional hardware is required to take these measurements, for ex. 6 consequent input codes, No additional hardware is required to take these measurements, for ex. 6 consequent input codes, (0..0000000),(0..0000001),(0..0000011),.., (0..0111111), can be used to get these measurements (0..0000000),(0..0000001),(0..0000011),.., (0..0111111), can be used to get these measurements

Correlation ModelCorrelation ModelCorrelation ModelCorrelation Model

Output of a current source is spatially correlated to neighboring sources on layout as a result of silicon manufacturing stepsOutput of a current source is spatially correlated to neighboring sources on layout as a result of silicon manufacturing steps A spatial distanceA spatial distance22 correlation model is used correlation model is used According to the correlation model, the correlation starts from a number close to 1 and decreases towards 0 with distance According to the correlation model, the correlation starts from a number close to 1 and decreases towards 0 with distance

between each pair of sourcesbetween each pair of sources

Output of a current source is spatially correlated to neighboring sources on layout as a result of silicon manufacturing stepsOutput of a current source is spatially correlated to neighboring sources on layout as a result of silicon manufacturing steps A spatial distanceA spatial distance22 correlation model is used correlation model is used According to the correlation model, the correlation starts from a number close to 1 and decreases towards 0 with distance According to the correlation model, the correlation starts from a number close to 1 and decreases towards 0 with distance

between each pair of sourcesbetween each pair of sources

Design for Test (DFT) HardwareDesign for Test (DFT) HardwareDesign for Test (DFT) HardwareDesign for Test (DFT) Hardware

One more decoder One more decoder and some and some combinational gates combinational gates added to the original added to the original decoderdecoder

Similar modification Similar modification done for row done for row selection hardwareselection hardware

test_sel=0 : original test_sel=0 : original modemode

test_sel=1 : one test_sel=1 : one column is selected column is selected using Ci inputs and using Ci inputs and setting row_sel=1setting row_sel=1

One more decoder One more decoder and some and some combinational gates combinational gates added to the original added to the original decoderdecoder

Similar modification Similar modification done for row done for row selection hardwareselection hardware

test_sel=0 : original test_sel=0 : original modemode

test_sel=1 : one test_sel=1 : one column is selected column is selected using Ci inputs and using Ci inputs and setting row_sel=1setting row_sel=1

Instead of exhaustively measuring current sources, Instead of exhaustively measuring current sources, particular groups of them are summed & measuredparticular groups of them are summed & measured

This reduces the diagnosis time from quadratic to This reduces the diagnosis time from quadratic to linearlinear

Process-variation aware nominal test points are used Process-variation aware nominal test points are used for each source to create variation aware nominalsfor each source to create variation aware nominals

One row selected such that the sum of current One row selected such that the sum of current sources within are deviating from the average of sources within are deviating from the average of remaining row sums; similarly for columnsremaining row sums; similarly for columns

Instead of exhaustively measuring current sources, Instead of exhaustively measuring current sources, particular groups of them are summed & measuredparticular groups of them are summed & measured

This reduces the diagnosis time from quadratic to This reduces the diagnosis time from quadratic to linearlinear

Process-variation aware nominal test points are used Process-variation aware nominal test points are used for each source to create variation aware nominalsfor each source to create variation aware nominals

One row selected such that the sum of current One row selected such that the sum of current sources within are deviating from the average of sources within are deviating from the average of remaining row sums; similarly for columnsremaining row sums; similarly for columns

Reduction of Diagnosis Time using Reduction of Diagnosis Time using DFTDFTReduction of Diagnosis Time using Reduction of Diagnosis Time using DFTDFT

1 12 15 3

13 5 7 109 8 6 144 16 11 2

Even a minor 20% deviational soft fault around process variation Even a minor 20% deviational soft fault around process variation estimated values can be caught with ~100% efficiency!estimated values can be caught with ~100% efficiency!

Even a minor 20% deviational soft fault around process variation Even a minor 20% deviational soft fault around process variation estimated values can be caught with ~100% efficiency!estimated values can be caught with ~100% efficiency!

Experimental ResultsExperimental ResultsExperimental ResultsExperimental Results

Error Rates for Process EstimationError Rates for Process EstimationError Rates for Process EstimationError Rates for Process Estimation

Examination of normalized error in last column reveals that Examination of normalized error in last column reveals that difference between real and estimated values are almost difference between real and estimated values are almost negligible using 6 principal components negligible using 6 principal components

Examination of normalized error in last column reveals that Examination of normalized error in last column reveals that difference between real and estimated values are almost difference between real and estimated values are almost negligible using 6 principal components negligible using 6 principal components

Increasing bit requirements indicate detection of lower deviational faults Increasing bit requirements indicate detection of lower deviational faults due to averaging of non-faulty sources approaching the population meandue to averaging of non-faulty sources approaching the population mean

Increasing bit requirements indicate detection of lower deviational faults Increasing bit requirements indicate detection of lower deviational faults due to averaging of non-faulty sources approaching the population meandue to averaging of non-faulty sources approaching the population mean

Robustness for Increased Robustness for Increased RequirementsRequirementsRobustness for Increased Robustness for Increased RequirementsRequirements

A process variation aware DFT method is proposedA process variation aware DFT method is proposed Even minor soft faults can be caught with the proposed Even minor soft faults can be caught with the proposed

technique due to accounting of process variationstechnique due to accounting of process variations A fast diagnosis procedure is proposed with reasonable A fast diagnosis procedure is proposed with reasonable

addition of DFT HWaddition of DFT HW The proposed technique becomes more robust for The proposed technique becomes more robust for

increased bit requirementsincreased bit requirements

A process variation aware DFT method is proposedA process variation aware DFT method is proposed Even minor soft faults can be caught with the proposed Even minor soft faults can be caught with the proposed

technique due to accounting of process variationstechnique due to accounting of process variations A fast diagnosis procedure is proposed with reasonable A fast diagnosis procedure is proposed with reasonable

addition of DFT HWaddition of DFT HW The proposed technique becomes more robust for The proposed technique becomes more robust for

increased bit requirementsincreased bit requirements

ConclusionsConclusionsConclusionsConclusions