1. Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 71 Lecture 7 Fault Simulation n Problem and motivation n Fault simulation algorithms n Serial n Parallel n Deductive n Concurrent n Random Fault Sampling n Summary

2. Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 72 Problem and Motivation n Fault simulation Problem: Given  A circuit  A sequence of test vectors  A fault model Determine  Fault coverage - fraction (or percentage) of modeled faults detected by test vectors  Set of undetected faults n Motivation  Determine test quality and in turn product quality  Find undetected fault targets to improve tests

3. Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 73 Fault simulator in a VLSI Design Process Verified design netlist Verification input stimuli Fault simulatorTest vectors Modeled fault list Test generator Test compactor Fault coverage ? Remove tested faults Delete vectors Add vectors Low Adequate Stop

4. Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 74 Fault Simulation Scenario n Circuit model: mixed-level n Mostly logic with some switch-level for high-impedance (Z) and bidirectional signals n High-level models (memory, etc.) with pin faults n Signal states: logic n Two (0, 1) or three (0, 1, X) states for purely Boolean logic circuits n Four states (0, 1, X, Z) for sequential MOS circuits n Timing: n Zero-delay for combinational and synchronous circuits n Mostly unit-delay for circuits with feedback

5. Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 75 Fault Simulation Scenario (Continued) n Faults: n Mostly single stuck-at faults n Sometimes stuck-open, transition, and path-delay faults; analog circuit fault simulators are not yet in common use n Equivalence fault collapsing of single stuck-at faults n Fault-dropping -- a fault once detected is dropped from consideration as more vectors are simulated; fault- dropping may be suppressed for diagnosis n Fault sampling -- a random sample of faults is simulated when the circuit is large

6. Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 76 Fault Simulation Algorithms n Serial n Parallel n Deductive n Concurrent n Differential* * Not discussed; see M. L. Bushnell and V. D. Agrawal, Essentials of Electronic Testing for Digital, Memory and Mixed-Signal VLSI Circuits, Springer, 2000, Chapter 5.

7. Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 77 Serial Algorithm n Algorithm: Simulate fault-free circuit and save responses. Repeat following steps for each fault in the fault list: n Modify netlist by injecting one fault n Simulate modified netlist, vector by vector, comparing responses with saved responses n If response differs, report fault detection and suspend simulation of remaining vectors n Advantages: n Easy to implement; needs only a true-value simulator, less memory n Most faults, including analog faults, can be simulated

8. Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 78 Serial Algorithm (Cont.) n Disadvantage: Much repeated computation; CPU time prohibitive for VLSI circuits n Alternative: Simulate many faults together Test vectors Fault-free circuit Circuit with fault f1 Circuit with fault f2 Circuit with fault fn Comparator f1 detected? Comparator f2 detected? Comparator fn detected?

9. Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 79 Parallel Fault Simulation n Compiled-code method; best with two-states (0,1) n Exploits inherent bit-parallelism of logic operations on computer words n Storage: one word per line for two-state simulation n Multi-pass simulation: Each pass simulates w-1 new faults, where w is the machine word length n Speed up over serial method ~ w-1 n Not suitable for circuits with timing-critical and non-Boolean logic

10. Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 710 Parallel Fault Sim. Example a b c d e f g 1 1 1 1 0 1 0 0 0 1 0 1 s-a-1 s-a-0 0 0 1 c s-a-0 detected Bit 0: fault-free circuit Bit 1: circuit with c s-a-0 Bit 2: circuit with f s-a-1

11. Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 711 Deductive Fault Simulation n One-pass simulation n Each line k contains a list L k of faults detectable on it n Following true-value simulation of each vector, fault lists of all gate output lines are updated using set-theoretic rules, signal values, and gate input fault lists n PO fault lists provide detection data n Limitations: n Set-theoretic rules difficult to derive for non- Boolean gates n Gate delays are difficult to use

12. Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 712 Deductive Fault Sim. Example a b c d e f g 1 1 1 0 1 {a0}{a0} {b 0, c 0 } {b0}{b0} {b 0, d 0 } L e = L a U L c U {e 0 } = {a 0, b 0, c 0, e 0 } L g = (L e L f ) U {g 0 } = {a 0, c 0, e 0, g 0 } U {b 0, d 0, f 1 } Notation: L k is fault list for line k k n is s-a-n fault on line k Faults detected by the input vector

13. Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 713 Concurrent Fault Simulation n Event-driven simulation of fault-free circuit and only those parts of the faulty circuit that differ in signal states from the fault-free circuit. n A list per gate containing copies of the gate from all faulty circuits in which this gate differs. List element contains fault ID, gate input and output values and internal states, if any. n All events of fault-free and all faulty circuits are implicitly simulated. n Faults can be simulated in any modeling style or detail supported in true-value simulation (offers most flexibility.) n Faster than other methods, but uses most memory.

14. Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 714 Conc. Fault Sim. Example a b c d e f g 1 1 1 0 1 1 1 1 1 0 1 1 0 0 1 0 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 1 1 1 a0a0 b0b0 c0c0 e0e0 a0a0 b0b0 b0b0 c0c0 e0e0 d0d0 d0d0 g0g0 f1f1 f1f1

15. Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 715 Fault Sampling n A randomly selected subset (sample) of faults is simulated. n Measured coverage in the sample is used to estimate fault coverage in the entire circuit. n Advantage: Saving in computing resources (CPU time and memory.) n Disadvantage: Limited data on undetected faults.

16. Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 716 Motivation for Sampling n Complexity of fault simulation depends on: n Number of gates n Number of faults n Number of vectors n Complexity of fault simulation with fault sampling depends on: n Number of gates n Number of vectors

17. Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 717 Random Sampling Model All faults with a fixed but unknown coverage Detected fault Undetected fault Random picking N p = total number of faults (population size) C = fault coverage (unknown) N s = sample size N s << N p c = sample coverage (a random variable)

18. Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 718 Probability Density of Sample Coverage, c (x – C ) 2 - ───── 1 2σ 2 p (x) = Prob (x ≤ c ≤ x +dx ) = ─────── e σ (2 π) 1/2 p (x) C C +3σ C -3σ 1.0 x Sample coverage C (1 - C) Variance, σ 2 = ────── N s Mean = C Sampling error σ σ x

19. Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 719 Sampling Error Bounds C (1 - C ) | x - C | = 3 [ ────── ] 1/2 N s Solving the quadratic equation for C, we get the 3-sigma (99.7% confidence) estimate: 4.5 C 3σ = x ± ── [1 + 0.44 N s x (1 - x )] 1/2 N s Where N s is sample size and x is the measured fault coverage in the sample. Example: A circuit with 39,096 faults has an actual fault coverage of 87.1%. The measured coverage in a random sample of 1,000 faults is 88.7%. The above formula gives an estimate of 88.7% ± 3%. CPU time for sample simulation was about 10% of that for all faults.

20. Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 720 Summary n Fault simulator is an essential tool for test development. n Concurrent fault simulation algorithm offers the best choice. n For restricted class of circuits (combinational and synchronous sequential with only Boolean primitives), differential algorithm can provide better speed and memory efficiency. n For large circuits, the accuracy of random fault sampling only depends on the sample size (1,000 to 2,000 faults) and not on the circuit size. The method has significant advantages in reducing CPU time and memory needs of the simulator.