VLSI System Testing. Introduction
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1 ECE 538 VLSI System Testing Krish Chakraarty Test Generation: Part ECE 538 Krish Chakraarty Introduction Classification of test generation methods Fault tale analysis Boolean difference method Propagation, implication and justification procedures -algorithm 9-V algorithm (multiple path sensitization) ECE 538 Krish Chakraarty 2
2 General Approaches Systematic (algorithmic) Fault tale analysis Boolean difference method Fault-oriented methods (-algorithm, POEM) Fault-independent methods (critical path tracing) Exhaustive/pseudoexhaustive Random/pseudorandom ECE 538 Krish Chakraarty 3 Fault Tale Analysis 2-input OR gate a z Test Fault a/0 a/ /0 / z/0 z/ a 00 x x x 0 x x 0 x x x etermine fault tale via simulation and solve covering prolem Covering prolems are NP-complete Computationally infeasile ECE 538 Krish Chakraarty 4 2
3 Fault-Oriented ATPG Procedure Generate_Tests() egin repeat egin Select uncovered fault f Generate test for f Evaluate current fault coverage end until fault coverage > limit, or time runs out end ECE 538 Krish Chakraarty 5 Boolean ifference The Boolean difference of F(x, x 2, x 3,, x n ) with respect to x i is given y F x i = F(x, x 2,,, x 3,, x n ) F(x, x 2,,0, x 3,, x n ) Cofactor w.r.t. x i Cofactor w.r.t. x i Boolean difference provides input comination for sensitized path A test pattern for x i /0 is an input comination that makes x F i x = i A test pattern for x i / is an input comination that makes x i F x = i ECE 538 Krish Chakraarty 6 3
4 a c d e Boolean ifference f g h i j k z To find a test for a/0 or a/, determine the Boolean difference of output z with respect to a: z a =? How to handle internal faults, e.g. j/0? ECE 538 Krish Chakraarty 7 Key Terminology Backtrace: move a goal value ackwards in a circuit to a primary input Backtrack: return to a previous decision point in an algorithm and make an alternative decision -frontier: Set of gates closest to primary output with or on some input Implication: etermine unique signal values that are forced y signal values already assigned Justification: etermine values to unspecified inputs of gates whose outputs are specified (ackward) Propagation (-drive): etermine path values needed to propagate an error signal to a primary output (forward) ECE 538 Krish Chakraarty 8 4
5 Testing Fanout-Free Circuits No (reconvergent) fanout Propagation path from any line is unique Each line justification prolem is independent of all others Test generation for line l/v in a fanout-free circuit egin set all values to X (unknown) Justify(l,v) if v = 0 then Propagate(l,) else Propagate(l,) end ECE 538 Krish Chakraarty 9 Testing Fanout-Free Circuits Error propagation: Propagate(l,err) /* err is or */ egin set l to err if l is PO then return k = the fanout gate of l c = controlling value of k i = inversion of k for every input j of k other than l Justify(j,c) Propagate(k,err i) end l err err ECE 538 Krish Chakraarty 0 5
6 Testing Fanout-Free Circuits Justify(l,val) egin set l to val if l is PI then return /* l is a gate (output) */ c = controlling value of l i = inversion of l inval = val i if(inval = c) then for every input j of l Justify(j,inval) else egin Select one input (j) of l Justify(j,inval) end Line Justification ECE 538 Krish Chakraarty X 0 X 0 l l Functional vs Structural Testing Functional ATPG generate complete set of tests for circuit input-output cominations 29 inputs, 65 outputs: 2 29 patterns Using GHz ATE, would take 2.5 x 0 22 years Structural test: No redundant adder hardware, 64 it slices Each with 27 faults (using fault equivalence) At most 64 x 27 = 728 faults (tests) Takes s on GHz ATE esigner gives small set of functional tests augment with structural tests to oost coverage to 98 + % ECE 538 Krish Chakraarty 2 6
7 Algorithm Completeness efinition: Algorithm is complete if it ultimately can search entire inary decision tree, as needed, to generate a test Untestale fault no test for it even after entire tree searched Cominational circuits only untestale faults are redundant, showing the presence of unnecessary hardware ECE 538 Krish Chakraarty 3 -Algorithm a c d A B B/ E C G z e H F ecision Implication Comment B = E =, A = 0, a = 0 Activate fault = C = Propagate via C F = 0 z = End of -drive H = 0 e = 0 Justify F c = 0 () Test: ace = 000 Justify A ECE 538 Krish Chakraarty 4 7
8 -Algorithm a c d A B B/ E C G z e H F ecision Implication Comment B = E =, A = 0, a = 0 Activate fault H = F = Propagate via F C = 0 z = End of -drive = 0 e = 0 Justify C c = 0 or e = 0 Test: ace = 0000 Justify A ECE 538 Krish Chakraarty 5 c a d Fault e/0 f e g -Algorithm j h i k z Single path sensitization does not always work! ecision Implication Action e =, c = 0 i =, f =, h = 0 Activate fault, propagate via i j = k = 0 z = Contradiction End of -drive d =, = g = 0, e = 0 Justify j = 0, k = 0 (Backtrack) c = 0, d = 0 i = j = propagate through i and j ECE 538 Krish Chakraarty 6 8
9 Comments on the -Algorithm Based on propagation (primary procedure), justification and implication In complete form, guarantees test generation ut may require multiple path sensitization (computationally expensive) Practical restrictions: Single path sensitization only Limits placed on acktracking time (aorted faults) ECE 538 Krish Chakraarty 7 9-V Algorithm Nine logic values, specified as good/ad pairs: /, 0/0, /0, 0/, u/u, /u, 0/u, u/0, u/ Example of logic operations:.x = /0.u/u = u/0, i.e. provides more information than the X outcome for 5-valued algera Reduces acktracking When there are k possile paths for error propagation, -algorithm may try all 2 k - cominations of paths 9-V enumerates only k ways of propagation ECE 538 Krish Chakraarty 8 9
10 Path Sensitization Fault Sensitization 2 Fault Propagation 3 Line Justification ECE 538 Krish Chakraarty 9 Path Sensitization Try path f h k L locked at j, since there is no way to justify the on i 0 ECE 538 Krish Chakraarty 20 0
11 Path Sensitization Try simultaneous paths f h k L and g i j k L locked at k ecause -frontier (chain of or ) disappears ECE 538 Krish Chakraarty 2 Path Sensitization Final try: path g i j k L test found! 0 0 ECE 538 Krish Chakraarty 22
12 Random Test Generation Flow chart for method Use to get tests for 60-80% of faults, then switch to - algorithm or other ATPG for rest ECE 538 Krish Chakraarty 23 2
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