1. A DFT Approach for Diagnosis and Process Variation-Aware Structural Test of Thermometer Coded Current Steering DAC's Rasit Onur Topaloglu and Alex Orailoglu { rtopalog | alex }@cse.ucsd.edu University of California, San Diego Computer Science and Engineering Department 9500 Gilman Dr., La Jolla, CA, 92093 { rtopalog | alex }@cse.ucsd.edu { rtopalog | alex }@cse.ucsd.edu Rasit Onur Topaloglu and Alex Orailoglu { rtopalog | alex }@cse.ucsd.edu University of California, San Diego Computer Science and Engineering Department 9500 Gilman Dr., La Jolla, CA, 92093 { rtopalog | alex }@cse.ucsd.edu { rtopalog | alex }@cse.ucsd.edu

2. OutlineOutline Current Steering Digital to Analog Converters 101 Current Steering Digital to Analog Converters 101 A Process Variation-Aware Soft Fault Model A Process Variation-Aware Soft Fault Model Process Variation Estimation Process Variation Estimation Reduction of Diagnosis Time Using Design for Testability Hardware Reduction of Diagnosis Time Using Design for Testability Hardware Experimental Results Experimental Results Current Steering Digital to Analog Converters 101 Current Steering Digital to Analog Converters 101 A Process Variation-Aware Soft Fault Model A Process Variation-Aware Soft Fault Model Process Variation Estimation Process Variation Estimation Reduction of Diagnosis Time Using Design for Testability Hardware Reduction of Diagnosis Time Using Design for Testability Hardware Experimental Results Experimental Results

3. IntroductionIntroduction Higher precision applications drive Digital to Analog Converter (DAC) resolutions to higher bits day by day Higher precision applications drive Digital to Analog Converter (DAC) resolutions to higher bits day by day Higher bit resolutions increase circuit complexity, hence increase test time and difficulty Higher bit resolutions increase circuit complexity, hence increase test time and difficulty In thermometer coded circuits, controllability is limited as each bit increment sums current of a new source with previous ones In thermometer coded circuits, controllability is limited as each bit increment sums current of a new source with previous ones Diagnosis of a fault or test is usually handled by exhaustively trying all input codes Diagnosis of a fault or test is usually handled by exhaustively trying all input codes Higher precision applications drive Digital to Analog Converter (DAC) resolutions to higher bits day by day Higher precision applications drive Digital to Analog Converter (DAC) resolutions to higher bits day by day Higher bit resolutions increase circuit complexity, hence increase test time and difficulty Higher bit resolutions increase circuit complexity, hence increase test time and difficulty In thermometer coded circuits, controllability is limited as each bit increment sums current of a new source with previous ones In thermometer coded circuits, controllability is limited as each bit increment sums current of a new source with previous ones Diagnosis of a fault or test is usually handled by exhaustively trying all input codes Diagnosis of a fault or test is usually handled by exhaustively trying all input codes

4.  4I2II I out (110) input shown for an 8-bit binary CSDAC (Current Steering DAC) Binary-Coded Current Steering Principle Input digital code selects current sources to be added to analog output Input digital code selects current sources to be added to analog output I out is the analog output I out is the analog output Current sources are in fact implemented by current mirrors using a common on-chip reference current Current sources are in fact implemented by current mirrors using a common on-chip reference current Input digital code selects current sources to be added to analog output Input digital code selects current sources to be added to analog output I out is the analog output I out is the analog output Current sources are in fact implemented by current mirrors using a common on-chip reference current Current sources are in fact implemented by current mirrors using a common on-chip reference current

5. Individual Current Distributions Soft faults for exponentially valued current sources would contribute integral and differential non-linearity (INL and DNL) degradation during certain transitions e.g. transition from 2^n-1 to 2^n Soft faults for exponentially valued current sources would contribute integral and differential non-linearity (INL and DNL) degradation during certain transitions e.g. transition from 2^n-1 to 2^n I 4I4I II I ref W 2 /L 2 W 1 /L 1 4I I ref W 2 /L 2 W 1 /L 1

6. Impact of Binary Coding on INL and DNL Transitions from 2^n-1 to 2^n activate totally differents sets of current sources Transitions from 2^n-1 to 2^n activate totally differents sets of current sources Due to limited spatial correlation between these groups, DNL will tend to get larger, which implicitly tend to enlarge INL Due to limited spatial correlation between these groups, DNL will tend to get larger, which implicitly tend to enlarge INL In thermometer-coded (TC-CSDACs), in these transitions, one more current source is added only, and hence outputs of these two codes highly correlated due to the 2^n-1 common elements In thermometer-coded (TC-CSDACs), in these transitions, one more current source is added only, and hence outputs of these two codes highly correlated due to the 2^n-1 common elements Transitions from 2^n-1 to 2^n activate totally differents sets of current sources Transitions from 2^n-1 to 2^n activate totally differents sets of current sources Due to limited spatial correlation between these groups, DNL will tend to get larger, which implicitly tend to enlarge INL Due to limited spatial correlation between these groups, DNL will tend to get larger, which implicitly tend to enlarge INL In thermometer-coded (TC-CSDACs), in these transitions, one more current source is added only, and hence outputs of these two codes highly correlated due to the 2^n-1 common elements In thermometer-coded (TC-CSDACs), in these transitions, one more current source is added only, and hence outputs of these two codes highly correlated due to the 2^n-1 common elements 7 8 Digital Analog DNL: max of stepwise differences INL: max difference between overall real and ideal lines

7.  III I out (0111111) input for an 8-bit thermometer coded CSDAC IIII II Thermometer-Coded CSDACs (TC-CSDACs) (110) in binary is (0111111) in thermometer code (110) in binary is (0111111) in thermometer code Equal weighting of current sources prevents significant impact for faulty sources Equal weighting of current sources prevents significant impact for faulty sources Error correction capability is another attractive reason for choosing thermometer code ex:0111011 not possible as 1’s should be consecutive Error correction capability is another attractive reason for choosing thermometer code ex:0111011 not possible as 1’s should be consecutive (110) in binary is (0111111) in thermometer code (110) in binary is (0111111) in thermometer code Equal weighting of current sources prevents significant impact for faulty sources Equal weighting of current sources prevents significant impact for faulty sources Error correction capability is another attractive reason for choosing thermometer code ex:0111011 not possible as 1’s should be consecutive Error correction capability is another attractive reason for choosing thermometer code ex:0111011 not possible as 1’s should be consecutive

8. (0111111) input for an 8-bit thermometer coded CSDAC Current sources indexed with fixed bit positions Current sources indexed with fixed bit positions Fixed indexes imply a controllability restriction Fixed indexes imply a controllability restriction Diagnosis time for a faulty current source exponentially increases as compared to binary coded CSDACS Diagnosis time for a faulty current source exponentially increases as compared to binary coded CSDACS Current sources indexed with fixed bit positions Current sources indexed with fixed bit positions Fixed indexes imply a controllability restriction Fixed indexes imply a controllability restriction Diagnosis time for a faulty current source exponentially increases as compared to binary coded CSDACS Diagnosis time for a faulty current source exponentially increases as compared to binary coded CSDACS Diagnosis Restriction of TC-CSDACs  III I out IIII II

9. 112153 135710 98614 416112 ex: In a 16-bit converter, current sources indexed by consecutive number laid out on separate corners Design Considerations for TC-CSDACs Current sources laid out in common-centroid layout style to minimize impact of process variations Current sources laid out in common-centroid layout style to minimize impact of process variations A number of most significant bits (MSB’s) and least significant bits (LSB’s) are grouped within themselves to further reduce process variation impacts A number of most significant bits (MSB’s) and least significant bits (LSB’s) are grouped within themselves to further reduce process variation impacts Current sources laid out in common-centroid layout style to minimize impact of process variations Current sources laid out in common-centroid layout style to minimize impact of process variations A number of most significant bits (MSB’s) and least significant bits (LSB’s) are grouped within themselves to further reduce process variation impacts A number of most significant bits (MSB’s) and least significant bits (LSB’s) are grouped within themselves to further reduce process variation impacts

10. A Practical TC-CSDAC Architecture m MSB’s are interpolated by n LSB’s where B, total number of bits, is m+n m MSB’s are interpolated by n LSB’s where B, total number of bits, is m+n Input to the TC-CSDAC is binary, hence binary to thermometer decoders used in the circuit Input to the TC-CSDAC is binary, hence binary to thermometer decoders used in the circuit Proposed fault model can be applied to MSB and LSB parts separately Proposed fault model can be applied to MSB and LSB parts separately

11. II For each die, a current source will have a fixed value picked up from its probability density function, caused by process variations probability I source Process-Aware Structural Soft Fault Model Process variations should not be mistaken as faults Process variations should not be mistaken as faults The proposed fault model: one current source might have an additional deviation from process variation effected value due to any modeled or un-modeled fault The proposed fault model: one current source might have an additional deviation from process variation effected value due to any modeled or un-modeled fault Process variations should not be mistaken as faults Process variations should not be mistaken as faults The proposed fault model: one current source might have an additional deviation from process variation effected value due to any modeled or un-modeled fault The proposed fault model: one current source might have an additional deviation from process variation effected value due to any modeled or un-modeled fault

12. Current sources are systematically correlated due to their close locations on die Current sources are systematically correlated due to their close locations on die Current sources can be represented as a sum of independent components through a technique called Principal Component Analysis (PCA) Current sources can be represented as a sum of independent components through a technique called Principal Component Analysis (PCA) Principal components corresponding to largest eigenvalues account for most of the variation Principal components corresponding to largest eigenvalues account for most of the variation Ratio of selected eigenvalues to all eigenvalues can be used to ensure a minimum variation Ratio of selected eigenvalues to all eigenvalues can be used to ensure a minimum variation Current sources are systematically correlated due to their close locations on die Current sources are systematically correlated due to their close locations on die Current sources can be represented as a sum of independent components through a technique called Principal Component Analysis (PCA) Current sources can be represented as a sum of independent components through a technique called Principal Component Analysis (PCA) Principal components corresponding to largest eigenvalues account for most of the variation Principal components corresponding to largest eigenvalues account for most of the variation Ratio of selected eigenvalues to all eigenvalues can be used to ensure a minimum variation Ratio of selected eigenvalues to all eigenvalues can be used to ensure a minimum variation I : normalized current source variables U : eigenvectors of correlation matrix C : principal components Estimation of Process Variations

13. A reduced number of principal components, M<N, is equivalent to deleting some of the columns A reduced number of principal components, M<N, is equivalent to deleting some of the columns Then, M of these equations can be chosen to obtain an M equation-M unknown system Then, M of these equations can be chosen to obtain an M equation-M unknown system The choice is made for consecutively indexed sources, as each source individually requires two measurements due to controllability restriction The choice is made for consecutively indexed sources, as each source individually requires two measurements due to controllability restriction A reduced number of principal components, M<N, is equivalent to deleting some of the columns A reduced number of principal components, M<N, is equivalent to deleting some of the columns Then, M of these equations can be chosen to obtain an M equation-M unknown system Then, M of these equations can be chosen to obtain an M equation-M unknown system The choice is made for consecutively indexed sources, as each source individually requires two measurements due to controllability restriction The choice is made for consecutively indexed sources, as each source individually requires two measurements due to controllability restriction 

14.  Process Variation-Aware Test Nominals M sources are measured for each chip, U is calculated from correlation matrix, hence only C values are left to be determined M sources are measured for each chip, U is calculated from correlation matrix, hence only C values are left to be determined Once C values are calculated, unmeasured N-M source I values can be calculated Once C values are calculated, unmeasured N-M source I values can be calculated Hence, these steps provide process-variation aware nominal values for each current source using few measurements, as N>>M even for 98% variation Hence, these steps provide process-variation aware nominal values for each current source using few measurements, as N>>M even for 98% variation M sources are measured for each chip, U is calculated from correlation matrix, hence only C values are left to be determined M sources are measured for each chip, U is calculated from correlation matrix, hence only C values are left to be determined Once C values are calculated, unmeasured N-M source I values can be calculated Once C values are calculated, unmeasured N-M source I values can be calculated Hence, these steps provide process-variation aware nominal values for each current source using few measurements, as N>>M even for 98% variation Hence, these steps provide process-variation aware nominal values for each current source using few measurements, as N>>M even for 98% variation

15. Acquiring Principal Components On-Chip Analog current is measured for up to principal component number of times; as low as ~ 6 measurements satisfactory to account for 98% variation Analog current is measured for up to principal component number of times; as low as ~ 6 measurements satisfactory to account for 98% variation 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 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 Analog current is measured for up to principal component number of times; as low as ~ 6 measurements satisfactory to account for 98% variation Analog current is measured for up to principal component number of times; as low as ~ 6 measurements satisfactory to account for 98% variation 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 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

16. Correlation Model Output of a current source is spatially correlated to neighboring sources on layout as a result of silicon manufacturing steps Output of a current source is spatially correlated to neighboring sources on layout as a result of silicon manufacturing steps A spatial distance 2 correlation model is used A spatial distance 2 correlation model is used According to the correlation model, the correlation starts from a number close to 1 and decreases towards 0 with distance between each pair of sources According to the correlation model, the correlation starts from a number close to 1 and decreases towards 0 with distance between each pair of sources Output of a current source is spatially correlated to neighboring sources on layout as a result of silicon manufacturing steps Output of a current source is spatially correlated to neighboring sources on layout as a result of silicon manufacturing steps A spatial distance 2 correlation model is used A spatial distance 2 correlation model is used According to the correlation model, the correlation starts from a number close to 1 and decreases towards 0 with distance between each pair of sources According to the correlation model, the correlation starts from a number close to 1 and decreases towards 0 with distance between each pair of sources

17. Design for Test (DFT) Hardware One more decoder and some combinational gates added to the original decoder One more decoder and some combinational gates added to the original decoder Similar modification done for row selection hardware Similar modification done for row selection hardware test_sel=0 : original mode test_sel=0 : original mode test_sel=1 : one column is selected using Ci inputs and setting row_sel=1 test_sel=1 : one column is selected using Ci inputs and setting row_sel=1 One more decoder and some combinational gates added to the original decoder One more decoder and some combinational gates added to the original decoder Similar modification done for row selection hardware Similar modification done for row selection hardware test_sel=0 : original mode test_sel=0 : original mode test_sel=1 : one column is selected using Ci inputs and setting row_sel=1 test_sel=1 : one column is selected using Ci inputs and setting row_sel=1

18. Instead of exhaustively measuring current sources, particular groups of them are summed & measured Instead of exhaustively measuring current sources, particular groups of them are summed & measured This reduces the diagnosis time from quadratic to linear This reduces the diagnosis time from quadratic to linear Process-variation aware nominal test points are used for each source to create variation aware nominals Process-variation aware nominal test points are used for each source to create variation aware nominals One row selected such that the sum of current sources within are deviating from the average of remaining row sums; similarly for columns One row selected such that the sum of current sources within are deviating from the average of remaining row sums; similarly for columns Instead of exhaustively measuring current sources, particular groups of them are summed & measured Instead of exhaustively measuring current sources, particular groups of them are summed & measured This reduces the diagnosis time from quadratic to linear This reduces the diagnosis time from quadratic to linear Process-variation aware nominal test points are used for each source to create variation aware nominals Process-variation aware nominal test points are used for each source to create variation aware nominals One row selected such that the sum of current sources within are deviating from the average of remaining row sums; similarly for columns One row selected such that the sum of current sources within are deviating from the average of remaining row sums; similarly for columns Reduction of Diagnosis Time using DFT 112153 135710 98614 416112

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

20. Error Rates for Process Estimation Examination of normalized error in last column reveals that difference between real and estimated values are almost negligible using 6 principal components Examination of normalized error in last column reveals that difference between real and estimated values are almost negligible using 6 principal components

21. Increasing bit requirements indicate detection of lower deviational faults due to averaging of non-faulty sources approaching the population mean Increasing bit requirements indicate detection of lower deviational faults due to averaging of non-faulty sources approaching the population mean Robustness for Increased Requirements

22. A process variation aware DFT method is proposed A process variation aware DFT method is proposed Even minor soft faults can be caught with the proposed technique due to accounting of process variations Even minor soft faults can be caught with the proposed technique due to accounting of process variations A fast diagnosis procedure is proposed with reasonable addition of DFT HW A fast diagnosis procedure is proposed with reasonable addition of DFT HW The proposed technique becomes more robust for increased bit requirements The proposed technique becomes more robust for increased bit requirements A process variation aware DFT method is proposed A process variation aware DFT method is proposed Even minor soft faults can be caught with the proposed technique due to accounting of process variations Even minor soft faults can be caught with the proposed technique due to accounting of process variations A fast diagnosis procedure is proposed with reasonable addition of DFT HW A fast diagnosis procedure is proposed with reasonable addition of DFT HW The proposed technique becomes more robust for increased bit requirements The proposed technique becomes more robust for increased bit requirements ConclusionsConclusions