Pinaki Mazumder. Digital Testing 1 PODEM. PODEM Algorithm. PODEM Flow Chart

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1 POEM Algorithm POEM IBM introduced semiconductor RAM memory into its mainframes late 970 s Memory had error correction and translation circuits improved reliability -ALG unable to test these circuits! Search too undirected! Large XOR-gate trees! Must set all external inputs to define output Needed a better ATPG tool POEM: Path-Oriented Ecision Making (Goel 98) Like Algorithm, POEM is circuit-based, fault-oriented ATPG algorithm Signal values are explicitly assigned at the primary inputs only; other values are computed by implication Justification is not needed Backtracking means reassigning primary inputs when a contradiction occurs; implicit enumeration technique A simple backtrace heuristic is used to select the next primary input line and the value to assign to it New concepts introduced: Expand binary decision tree only around primary inputs Use X-PATH-CHECK to test whether -frontier still there Objectives -- bring ATPG closer to propagating ( ) to PO Backtracing 0 POEM Flow Chart EXIT ONE EXIT Untestable Fault Start Assign a binary values to an unassigned PI eterming implications of all assigned PIs NO YES Test generated? NO Test possible with additional PIs? NO Is there an untried combination of values on assigned values YES MAYBE Set untried combination of value on assigned PIs Step. Assign binary value to unassigned PI Step : etermine implications of all assigned PIs Test Generated? If so, done. Test possible with more assigned PIs? If maybe, go to Step Is there untried combination of values on assigned PIs? If not, exit: untestable fault Set untried combination of values on assigned PIs using objectives and backtrace. J K L M N G SA Find the Test vector that tests SA fault at G. -rive: G && {G G5} && G7. G G G 4 G 5 G 6 G 7 4 Then, go to Step igital Testing

2 POEM Example How POEM Works J K L M G SA G G G 4 4 G 7 a Backtrace.(c, ) e c d b f Backtrace (b, ) N G 5. Initial objective (f = ) Iteration Objective Backtrace Implication -Front G. = 0 J= G. = 0 K= G 6. = {G } G. = M= G. = {G, G 5} 4 G5.= N= G5. = ' {G, G7} 5a G 7.= L=0 G 7.5 = {G, G 7} 5b Retry L= G 7.5 = None Test: (JKMNL)=() J= K= M= N= L= J=0 K=0 M=0 N=0 L=0 G 6. B acktrace (b, ). PI assignment (b =) 4. Imply 5. B acktrace (c, ) 6. PI assignment (a = 0) 7. Imply (d = 0) 4 5 Comparison Between -ALG & POEM PI = Initial assignment PI = unused alternative assignment PI = Node removed PI 4 = Backtrack No test Start All PI s are set to X PI =0 unused alternative assignment PI = Initial assignment No remaining alternative PI 4 = 0 PI 4 = 0 PI 4 = PI 5 = PI 5 = Backtrack No test 6 -Algorithm b a c e b ecision Implication Comment B=' E=', A=0, a=0 Activate fault b= C=' Propagate via G F=0 Z=' End of -rive 4 H=0 e=0 Jusitify F 5 c=0 A B H B/ E Test = (a, b, c, e)= (000) Order of PI assignment: a, b, e, c. C F G 7 Order of PI assignment: a, c, b, e. Z ecision Implication Comment Initial objective (B, 0) a=0 Backtrace, Imply c=0 A=0, B=', E= Backtrace, Imply b= b'=0, C=' Objective (b,), Imply 4 e=0 POEM H=0, F=0, Z=' Objective (F,0); Imply; Success Test = (a, b, c, e)= (000) igital Testing

3 -ALG v.s. POEM Example Fault s sa -Algorithm POEM Primitive -cube of Failure Emphasis on -propagation Too much backtracking (undoing a previous decision and making a different choice) in some circuits. All possible choices may have to be tried in the worst case Some faults require multiple path sensitization Less backtracking Sets a subset of inputs one by one Propagates after initial objective is reached Comparison of speed between POEM & -Algorithm sa Run Time Fault Coverage # of Cells POEM -ALG POEM -ALG ckt # ckt # ckt # ckt #4, ckt # Example 7. Backtrack Example Step s sa Need alternate propagation -cube for v Initial objective: Set r to to sensitize fault 0 sa sa 0 igital Testing

4 Example Step s sa FAN: Fan-out Oriented ATPG Algorithm Backtrace from r sa FAN: Fan-out Oriented ATPG Algorithm (Fujiwara & Shimono, 98) Representative of POEM-based ATPG algorithms that add various heuristic speed-up features FAN drops or alters some of basic features of POEM: it halts backtracking at certain internal lines it tries to satisfy multiple objectives at once (multiple backtrace) it allows backward as well as forward implications it makes quick and easy assignments directly FAN -- Fujiwara and Shimono (98) POEM Fails to etermine Unique Signals New concepts: Immediate assignment of uniquely-determined signals Unique sensitization Stop Backtrace at head lines Multiple Backtrace Backtracing operation fails to set all inputs of gate L to Causes unnecessary search 4 5 igital Testing 4

5 FAN -- Early etermination of Unique Signals POEM Makes Unwise Signal Assignments etermine all unique signals implied by current decisions immediately Avoids unnecessary search Blocks fault propagation due to assignment J = Unique Sensitization of FAN with No Search Headlines Path over which fault is uniquely sensitized FAN immediately sets necessary signals to propagate fault Headlines H and J separate circuit into parts, for which test generation can be done independently 8 9 igital Testing 5

6 Contrasting ecision Trees Multiple Backtrace FAN breadth-first passes time POEM decision tree FAN decision tree POEM depth-first passes 6 times 0 Comparison Between POEM & FAN Random ckt # circuit characteristic # of gates # of I/O # of fanout/# of faults computing time avarage # of backtracks SPS POEM FAN SPS POEM FAN ECC 78 /5 8/ ALU 00 /40 454/ ALU / 579/ % 60% L = length of random test n log( / Q ) σ n : # of PIs Q :etection quality # f i t t ll i th dt ti f h df lt Apply deterministic ALU 00 78/ 806/ ALU /08 00/ Fault Coverage Random Phase HTF: Hard-to-detect-fault MTF: most difficult to detect fault igital Testing 6

7 History of Algorithm Speedups Algorithm -ALG POEM FAN TOPS SOCRATES Waicukauski et al. EST TRAN Recursive learning Tafertshofer et al. Est. speedup over -ALG (normalized to -ALG time) ATPG System 89 ATPG System 8765 ATPG System 005 ATPG System Year igital Testing 7