ECE 269 VLSI System Testing Krish Chakrabarty Delay Fault Testing 2 Acknowledgment Mahmut Yilmaz Outline Motivation Probabilistic Delay Fault Model and Output Deviations for Screening Small Delay Defects SDDs Gate and Signal Transition Probability Definitions Propagation of Signal Transition Probabilities Output Deviations Based on Delay Differences Pattern Selection and Re ordering Path Length and Output Deviation Correlation Analysis Simulation Results Conclusions 2 Motivation Decreasing feature sizes Process technology scales down continuously Very Deep Submicron VDSM designs 3 Motivation Increasing Defect Rates Resistive shorts bridges Cc Resistive opens All of them are sources of small delay defects 90nm Cc 45nm Pictures from M Tehranipoor L 10 tOX 3 VTH 30 More effective crosstalk 4 Increased sensitivity to process variations Motivation Shortcomings of current methods Stuck at fault model Not sufficient for high quality test RI SDUWV Small delay defects Traditional transition test ATPG does not target SDDs Large delay defects Inclined to select short activation paths The pattern generation methods usually GGLWLRQ DO GHOD use SCOPE measure SDDs are observable on short slack paths long paths Recently developed timing aware ATPG tools Recent versions of Mentor Graphics FastScan Cadence True Time ATPG Synopsys TetraMax Are they doing as good as expected Real defect causes are covered 5 Motivation Long ATPG Run time Industrial timing aware ATPG tools take very long time to generate transition test patterns They usually perform path enumeration This may be unacceptable due to time to market constraints Timing aware ATPG tool Mentor Graphics FastScan 2007 2 6 Probabilistic Delay Fault Model and Output Deviations for Small Delay Defects Gate Delay Defect Probabilities DDP The probability that the delay of a gate is larger than a delay limit For each input transition the gate has a different delay distribution Set a critical delay limit for the gate Dcrt Dcrt Relaxed limit can be set to MAX delay reported by STA DDP The probability that the gate delay is more than Dcrt for the given input transition Probability 00 10 11 01 Dcrt Dcrt Delay 7 Probabilistic Delay Fault Model and Output Deviations for Small Delay Defects Delay Defect Probability Matrix DDPM With DDP for all possible input transitions we can form a matrix of DDPs Delay Defect Probability Matrix Example DDPM for an OR2 gate entries are arbitrary At most one of the probabilities can be non zero OR2 Initial Input State IN0 IN1 Prob PL H PH L 00 01 10 11 IN0 0 2 0 0 0 0 0 5 0 0 1 IN1 0 1 0 0 0 2 0 0 0 0 1 Inputs 8 H L Probabilistic Delay Fault Model and Output Deviations for Small Delay Defects Signal Transition Probabilities Transition Delay Fault TDF test patterns will force signal transitions on circuit nets Assuming that there are only two possible signal values Low and High each net may have one of the four different signal transitions Low Low Signal value stays at low Low High Signal value changes from low to high High Low Signal value changes from high to low High High Signal value stays at high Each of these events has a probability to occur Each net has a vector of signal transition probabilities Net PL L PL H PH L PH H 9 Probabilistic Delay Fault Model and Output Deviations for Small Delay Defects Propagation of Signal Transition Probabilities STPs The nets connected to the test application points Initialization nets INs Initialized with 0 DDP During signal propagation through circuit use DDPM of the gates to update signal transition probabilities The probability that net A will have the expected signal transition PEXPECTED Deviation 1 PEXPECTED 10 Probabilistic Delay Fault Model and Output Deviations for Small Delay Defects Rules of STP Propagation 1 If output does not change the deviation on output net is 0 2 If any one of the multiple input transitions can cause the output transition only the maximum deviation provider is considered 3 If multiple input transitions are required for an output transition all required input transitions are considered Deviation increase through a sensitized path Proven 11 Probabilistic Delay Fault Model and Output Deviations for Small Delay Defects An example arbitrary DDPMs Expected signal transitions are shown in dark boxes Initialization of signal transition probabilities on INs 12 Probabilistic Delay Fault Model and Output Deviations for Small Delay Defects An example There is no transition on net E The probability of a delay fault deviation is 0 13 Probabilistic Delay Fault Model and Output Deviations for Small Delay Defects An example XOR2 Initial Input State Prob PL H PH L 00 01 10 11 IN0 0 3 0 0 0 4 0 0 2 0 3 0 IN1 0 3 0 0 0 4 0 0 1 0 4 0 Inputs The output changes due to IN1 Probability of a delay fault 0 4 14 Probabilistic Delay Fault Model and Output Deviations for Small Delay Defects An example The output deviation for each observable output for an input pattern is the probability that the output value is different from the expected value Output Deviations Q1 0 52 Q2 0 664 15 Probabilistic Delay Fault Model and Output Deviations for Small Delay Defects An example Relative deviations at the observation points are considered Absolute values depends on many effects For the applied test pattern Q2 has longer delay 16 Output Deviations Q1 0 52 Q2 0 664 Pattern Selection and Re ordering Pattern Selection heuristic method Determine the number of patterns to be selected S For each observation point OP select the pattern which creates the highest output deviation Repeat for all OPs until you select S patterns If a pattern is already selected for an OP select the next highest deviation pattern for the corresponding OP Pattern Re ordering After selection sort the patterns by the maximum deviation they create at an observation point Top off ATPG Run top off transition delay fault ATPG to increase the fault coverage if necessary 17 Pattern Selection Observation points Q1 Q2 Q3 P1 P2 P1 P2 P5 P9 P3 P1 P4 P5 P7 P6 Selected Patterns We will select 3 patterns Patterns are ordered according to the deviation that they caused at the corresponding observation point 18 Pattern Selection Q1 Q2 Q3 P1 P2 P1 P2 P5 P9 P3 P1 P4 P5 P7 P6 Start with the first observation point Select P1 Selected Patterns P1 19 Pattern Selection Continue with Q2 Select P2 Q1 Q2 Q3 Selected Patterns P1 P2 P1 P1 P2 P5 P9 P2 P3 P1 P4 P5 P7 P6 20 Pattern Selection Continue with Q3 P1 has already selected Select P9 Q1 Q2