Overview ECE 3: TESTING AND TESTABLE DESIGN OF DIGITAL SYSTES Logic and Fault Modeling Motivation Logic Modeling Model types Models at different levels of abstractions Models and definitions Fault Modeling Why model faults? Some real defects in VLSI and PCB Common fault models Stuck-at faults Transistor faults Summary 9/6/22 2 Motivation Models are often easier to work with Models are portable Models can be used for simulation, thus avoiding expensive hardware/actual circuit implementation Nearly all engineering systems are studied using models All the above apply for logic as well as for fault modeling Logic Modeling Model types Behavior System at I/O level Timing inf provided Internal details missing Functional DC behavior no timing Structural Gate level description External representation Internal representation Models are often described using an hierarchy 9/6/22 3 9/6/22 4 A B C a b Hierarchical Model: A Full-Adder HA D E d HA2 HA F e HA; inputs: a, b; outputs: c, f; AND: A, (a, b), (c); AND: A2, (d, e), (f); OR: O, (a, b), (d); NOT: N, (c), (e); 9/6/22 c f Carry Sum FA; inputs: A, B, C; outputs: Carry, Sum; HA: HA, (A, B), (D, E); HA: HA2, (E, C), (F, Sum); OR: O2, (D, F), (Carry); Modeling level Function, behavior, RTL Logic Switch Timing Circuit description Modeling Levels Programming language-like HDL Connectivity of Boolean gates, flip-flops and transistors Transistor size and connectivity, node capacitances Transistor technology data, connectivity, node capacitances Signal values Circuit Tech. Data, active/ Analog Continuous Digital timing passive component voltage, time and analog connectivity current circuit 9/6/22 6,,, X and Z, and X Analog voltage Timing Clock boundary Zero-delay unit-delay, multipledelay Zero-delay Fine-grain timing Application Architectural and functional Logic and test Logic Timing
Logic Models and definitions* Combinational circuit models Function expressed as truth-table or cubes Cubes and cube intersection can be used during simulation Sequential Circuits Structure represented as a collection of flip-flops feeding combinational logic Time frame expansion is possible Binary Decision Diagrams (BDD) *Ref: Abramovici et. Al, Digital system testing and testable design Logic Models and definitions (2) Program model of a circuit Express circuit (gate level) as a program consisting of interconnected logic operations Execute the program to determine circuit output for varying inputs RTL model Higher level model of the circuit HDL model Examples at this level are veriloghdl and VHDL 9/6/22 7 9/6/22 8 Logic Models and definitions (3) netlist Format: Two Examples Structural model External representation in the form of netlist Examples of this are uw format, iscas format, EDIF, Some keyword used in such representation Primary inputs and Primary outputs Gates: AND, OR, NOT, Storage: latch, flip-flop Connections: lines, nets Fanin: number of inputs to a gate Fanout : number of lines a signal feeds Fanoutfree circuit: every line or gate has a fanout of one uw format # gate connected to PI 4, ; 2 PI 3, 6; 3 not ; 4 not 6; and 7; 6 and 7; 7 or; 7 PO # gate #outputs # inputs input gate # input 2 8 fanoutfrom 9 fanoutfrom 2 input 2 fanoutfrom 2 fanoutfrom 2 3 not iscas format (comb.) 4 not 9 and 2 3 8 6 and 2 4 7 or 2 6 7 output 9/6/22 9 9/6/22 Logic Models and definitions (4) Structural model Internal representation in the form of tables Tables of gates and storage elements (names) Tables of connections Tables of fanin and fanouts Objective is to make the storage and search processes (integral part of simulation) more efficient Knowledge of data structures and algorithms is very useful Logic Models and definitions () Additional useful terms Graph representation Reconvergent fanouts Stems and branches Logic levels in a circuit levelization of a circuit 9/6/22 9/6/22 2 2
Why Model Faults? I/O function tests inadequate for manufacturing (functionality versus component and interconnect testing) Real defects (often mechanical) too numerous and often not analyzable A fault model identifies targets for testing A fault model makes analysis possible Effectiveness measurable by experiments Some Real Defects in Chips Processing defects Missing contact windows Parasitic transistors Oxide breakdown Material defects Bulk defects (cracks, crystal imperfections) Surface impurities (ion migration) Time-dependent failures Dielectric breakdown Electromigration Packaging failures Contact degradation Seal leaks 9/6/22 3 Ref.: M. J. Howes and D. V. Morgan, Reliability and Degradation - Semiconductor Devices and Circuits, Wiley, 98. 9/6/22 4 Defect classes Observed PCB Defects Shorts Opens Missing components Wrong components Reversed components Bent leads Analog specifications Digital logic Performance (timing) Occurrence frequency (%) 6 3 6 8 Ref.: J. Bateson, In-Circuit Testing, Van Nostrand Reinhold, 98. 9/6/22 Common Fault Models Single stuck -at faults Transistor open and short faults Memory faults PLA faults (stuck-at, cross-point, bridging) Functional faults (processors) Delay faults (transition, path) Analog faults For more examples, see Section 4.4 (p. 6-7) of the book. 9/6/22 6 Stuck-at Faults Single stuck-at faults What does it achieve in practice? Fault equivalence Fault dominance and checkpoint theorem Classes of stuck-at faults and multiple faults 9/6/22 7 Single Stuck-at Fault Three properties define a single stuck-at fault Only one line is faulty The faulty line is permanently set to or The fault can be at an input or output of a gate Example: XOR circuit has 2 fault sites ( ) and 24 single stuck-at faults a b c d e s-a- g h i f k Test vector for h s-a- fault Faulty circuit value Good circuit value j () () z 9/6/22 8 3
Single Stuck-at Faults (contd.) How effective is this model? Empirical evidence supports the use of this model Has been found to be effective to detect other types of fauls Relates to yield modeling Simple to use 9/6/22 9 Fault Equivalence Number of fault sites in a Boolean gate circuit = #PI + #gates + # (fanout branches). Fault equivalence: Two faults f and f2 are equivalent if all tests that detect f also detect f2. If faults f and f2 are equivalent then the corresponding faulty functions are identical. Fault collapsing: All single faults of a logic circuit can be divided into disjoint equivalence subsets, where all faults in a subset are mutually equivalent. A collapsed fault set contains one fault from each equivalence subset. 9/6/22 2 AND Equivalence Rules sa WIRE OR NOT sa sa sa Equivalence Example Faults in red removed by equivalence collapsing NAND NOR sa sa FANOUT sa 2 9/6/22 2 Collapse ratio = ----- =.62 32 9/6/22 22 Fault Dominance If all tests of some fault F detect another fault F2, then F2 is said to dominate F. Dominance fault collapsing: If fault F2 dominates F, then F2 is removed from the fault list. When dominance fault collapsing is used, it is sufficient to consider only the input faults of Boolean gates. See the next example. In a tree circuit (without fanouts) PI faults form a dominance collapsed fault set. If two faults dominate each other then they are equivalent. F s-a- Dominance Example s-a- s-a- All tests of F2 F2 s-a- s-a- s-a- A dominance collapsed fault set Only test of F 9/6/22 23 9/6/22 24 4
Checkpoints Primary inputs and fanout branches of a combinational circuit are called checkpoints. Checkpoint theorem: A test set that detects all single (multiple) stuck-at faults on all checkpoints of a combinational circuit, also detects all single (multiple) stuck-at faults in that circuit. Total fault sites = 6 Checkpoints ( ) = 9/6/22 2 Classes of Stuck-at Faults Following classes of single stuck-at faults are identified by fault simulators: Potentially-detectable fault -- Test produces an unknown (X) state at primary output (PO); detection is probabilistic, usually with % probability. Initialization fault -- Fault prevents initialization of the faulty circuit; can be detected as a potentially-detectable fault. Hyperactive fault -- Fault induces much internal signal activity without reaching PO. Redundant fault -- No test exists for the fault. Untestable fault -- Test generator is unable to find a test. 9/6/22 26 Multiple Stuck-at Faults A multiple stuck-at fault means that any set of lines is stuck-at some combination of (,) values. The total number of single and multiple stuck-at faults in a circuit with k single fault sites is 3 k -. A single fault test can fail to detect the target fault if another fault is also present, however, such masking of one fault by another is rare. Statistically, single fault tests cover a very large number of multiple faults. Transistor (Switch) Faults MOS transistor is considered an ideal switch and two types of faults are modeled: Stuck-open -- a single transistor is permanently stuck in the open state. Stuck-short -- a single transistor is permanently shorted irrespective of its gate voltage. Detection of a stuck-open fault requires two vectors. Detection of a stuck-short fault requires the measurement of quiescent current (I DDQ ). 9/6/22 27 9/6/22 28 Stuck-Open Example Stuck-Short Example A B pmos V DD C Vector : test for A s-a- (Initialization vector) Vector 2 (test for A s-a-) Two-vector s-op test can be constructed by ordering two s-at tests (Z) A B pmos V DD Stuckopen Stuckshort C Test vector for A s-a- (X) I DDQ path in faulty circuit Good circuit state nmos Good circuit states Faulty circuit states 9/6/22 29 nmos Faulty circuit state 9/6/22 3
Summary Modeling of logic circuit offers many advantages Many modeling levels exist and are used Gate level models are most prevalent in logic testing Fault models are analyzable approximations of defects and are essential for a test methodology. For digital logic single stuck-at fault model offers best advantage of tools and experience. Many other faults (bridging, stuck-open and multiple stuck-at) are largely covered by stuck-at fault tests. Stuck-short and delay faults and technology-dependent faults require special tests. Memory and analog circuits need other specialized fault models and tests. 9/6/22 3 6