# Design for Testability (DfT)

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Design for Testability (DfT)

OUTLINE Motivation Background and Definitions
Boolean Difference and Testing of Digital Circuits Combinational Circuit Testing Path Sensitization D-Algorithm

How do we know that our Design works?
f(x) x=(x0,x1,..,xn) q=(q0,q1,…qn) Fault!!!

System Validation Techniques
Simulation Validate a model of the system. Emulation Build a prototype and validate. Testing Check the correctness of actual system. Formal Verification Mathematically show the ’Equivalence’ of the specification and the implementation.

Definitions: Errors and Faults
Error : Incorrect operation of the system. Cause of Error are Faults Design error, fabrication error, fabrication defect, physical defects. Logical Fault: Faults which result in a change in logic value at a point in a circuit. Fault Model: The effect of a fault is represented by a model Stuck-at-fault Bridging fault Stuck-open fault Linking faults: Memories

Fault Probabilities

Fault Probabilities Dynamic Faults Static Faults
Timing Failures Components out of specification Static Faults Short-circuits Breaks Intermittent Faults (Environmental Faults) Single-Event Upsets - SEUs ESD Particles Magnetic Fields

Testing Techniques General Method Generation of Stimuli Test Time
The behavior (Response) of the system is observed by applying a sequence of test inputs (Stimuli). Generation of Stimuli Test various cases Random Patterns: Random Testing Algorithmic Test Pattern Generation Combinational Circuit Sequential Circuit Test Time Time to generate tests and apply them to the circuit under test Fault Coverage Percentage of all the faults detected by a set of test patterns

Test Cost and Quality Cost of quality Cost Cost of the fault Cost of
testing Quality Optimum test 100% 0%

Design for Testability( DFT)
To take into account the testing aspects during the design process so that testing is simpler and faster. Reduce test effort Reduce test time Reduce cost of test equipment Increase product quality Limitations Hardware overhead ( 5-30%) Performance degradation Increase in design complexity

Fault Models Stuck Fault Model Single-Stuck Fault Model
Stuck-at-0 (S-a-0) & Stuck-at-1 model (S-a-1) Single-Stuck Fault Model Heuristic Model, multiple faults do occur. Model appears to be valid most of the times Other Stuck Fault Models Variants including Stuck-at-open, Stuck-at-short

Faults Model : Assumptions
For Combinational Circuits Logical faults only Only those faults which can be modeled as a signal stuck-at-0 or stuck-at-1. Single fault Permanent fault For Sequential Circuits State table of the faulty sequential circuit is different from the good circuit.

Fault-oriented Test Pattern Generation
Combinational circuit with n inputs 2n possible patterns (exhaustive test) Find minimum number of necessary input patterns Problem: Some nodes may not be testable because of circuit structure

Fault Detection in Logic Circuits
Number of possible faults Equivalent faults For an n-input AND gate, any input s-a-0 is equivalent to the output s-a-0. The same test (all 1’s) is required to test any of these faults. x1 s-a-1 x1 s-a-0 x1 x2 x3 z Gate x2 s-a-1 x2 s-a-0 x3 s-a-1 x3 s-a-0 N input gate may have 2(N+1) stuck at faults z s-a-1 z s-a-0

Testability Controllability Observability
Can we control all nodes to establish whether there is a fault? Observability Can we observe and distinguish between the behavior of a faulty node and a free node?

Detectable Stuck-At Fault
& b e 1 S-a-0 c 1 d 1100 Good Circuit 00 1 Faulty Circuit 10

The fault cannot be detected because the circuit has redundancy. Example: Good Circuit 1 1 0 X 1 0 X 0 1 S-a-0 a & b e 0 1 0 X 1 1 0 X 1 1 1 d Faulty Circuit

Undetectable faults In general, untestable faults are due to redundancy Conversely, redundant circuits are not fully testable Fan-out may also cause untestable faults

Undetectable faults D A C B E Z F Consider Z=AC+BC - to avoid hazard we add the term AB => Z=AC+BC+AB => Impossible to test F/0

Undetectable faults’ fix
Z F Z2 Solution: Add internal wires to propagate an internal value to a new output

Ad Hoc DFT Techniques Test Point Insertion O C
OP Test Point Insertion C1 C1 C2 C2 CP0 CP1 Demultiplexing Control Points Multiplexing Observation points CP1 CP2 CPN Demu x OP1 OP2 OPN Mu x O C m m

Test Generation for Combinational Circuits
Truth Table and Fault Matrix Example: x1 x2 x z z z zz z z Truth table approach not practical if number of inputs is large. & 1 x1 x2 x2 x3 x1 x3 z s-a-0 and  s-a-1

Testing Sequential Circuits
Testing of sequential circuits is harder than combinational circuits Sequential Circuit Testing requires verification of the state table Verify Reachability of all states Verify all transitions Assumption: Only the inputs and outputs are accessible, internal flip-flops are not accessible

Testing Sequential Circuits
Fortunately for us, ad-hoc testing techniques (like scan-chains) has made the internal flip-flops accessible, so the last assumption does not hold! In case access to internal flip-flops is too costly, standard sequential test methods still have to be applied, see Appendix.

Testing Sequential Circuits – Scan-based Techniques
Sequential Circuits have poor controllability and poor observability PO Comb. Part PO PI Comb. Part PI Scanout Scanin

Full Scan and Partial Scan
Connect all the storage elements to form a long shift register (scan chain) The storage elements can be easily tested by shifting in a pattern and observing the output Testing of sequential circuit testing can be now treated as testing of combinational circuit Full scan is costly and slow Partial Scan Select a subset of storage elements to be included in the scan chain

Random Access Scan To achieve controllability and observability of all registers Access one register at a time PO Comb. Part PI Memory Scan-in Scan-out Scan Address

Board Level DFT: Boundary Scan
Every input and output port of a chip is included in a special scan chain PI Test Data In Test Clock Test Mode Test Data Out Main Logic SO SI PO

Boundary Scan Cell SO PI PO M u x M u x ClockDR UpdateDR SI

JTAG Standard (IEEE 1149.1) Boundary Scan-path Boundary-Scan cell

Summary of DfT Testing of complex digital systems is a hard but very important task. Test Pattern Generation is most important in testing Testing contributes substantially to the cost and effort required to design a new product. Methods are required to reduce this cost and effort. Design for testability Reuse of proven designs Formal Methods

Test Pattern Generation - part I Built-In Self Test (BIST) Methods

+ Testing a Circuit Circuit Under Test Test Pattern Generator
Response Analyzer Test Equipment Pulse and Function generators Oscilloscope Logic Analyzers Computers Specialized Zigs + Test Engineer

Self-Test a Circuit – Built-In Self Test (BIST)
Circuit Under Test Test Pattern Generator Response Analyzer Package the test equipment along with the circuit! Test Engineer

BIST: Requirements Generation of Test patterns for testing
DFT is very important Algorithm has to be very simple and easy to implement in hardware Comparing Response It is not possible to store the response in memory: area overhead Related to Test Pattern Generation Compression of Test Patterns and Response is essential for BIST design

Test Generation and Response Compression
Circuit Under Test Data Compression Unit Signature S(R) Input Test Sequence T Output Response R Correct Signature Test Generator Unit Comparator Error Indicator

General Aspects of Compression
A simple hardware implementation It should not slow down normal operations Good Compression The signatures of good and faulty circuit should be different Small size of signature. Signature size should be log of data size. Issues: How to generate signatures for good circuit?

Generic Off-line BIST Architectures
Classification Centralized or Distributed BIST circuitry Embedded or Separate BIST Key Elements of BIST Test pattern Generator (TPG) Output Response Analyzers (ORA) Circuit Under Test (CUT) A Distribution system for transmitting data from TPG to CUT and from CUT to ORAs. A BIST Controller

Test Pattern Generation for BISTs
Exhaustive Testing Exhaustive Test Pattern Generators Pseudo-Random testing Weighted test generator Adaptive Test Generator Pseudo-Exhaustive testing Constant Weight Counter Combined LFSR and Shift Register Combined LFSR and XOR Cyclic LFSR

Exhaustive Testing Apply all possible 2n test patterns to a n input circuit. A binary counter can be used Or a maximum length autonomous LFSR can be used (add special circuit to generate all zeros). Normally applied when number of inputs are less than 25.

Pseudorandom Testing Patterns are generated deterministically but have characteristics of random patterns. Pseudo-random patterns without replacement can be generated using autonomous LFSRs. Test length can be chosen to achieve the desired fault coverage. This can be determined using fault simulation. Limitation LFSR tend to produce patterns with equal numbers of 1’s and 0’s For some circuit it is better to bias the distribution of 0’s and 1’s of the pattern generator. For example testing of AND requires more 1’s in the test pattern.

Weighted Test Generation
Generate Test Patterns with the desired distribution of 1’s and 0’s. Such a generator can be constructed using a LFSR and a combinational circuit. Different parts of the circuit may require different distribution of 0’s and 1’s.

Also employs weighted test pattern generation. Fault simulation is used to determine weights for various faults. Different distributions are used for different class of faults. A Test Pattern Generator (TPG) is designed to produce the required distributions. Advantage: Small test lengths Disadvantage: Costly TPG hardware

Pseudo-exhaustive Testing
Requires fewer tests but has the advantage of exhaustive testing. Segments the circuit into parts and each segment is exhaustively tested. Logical Segmentation Cone Segmentation Sensitized path segmentation Physical Segmentation

Compression Methods for BISTs
Basic Idea – Apply sequence, check signature after finishing... Simple Analyzers Ones-count Compression Transition-count Compression Signature Analyzers Single-Input Signature Response (SISR) Multi-Input Signature Response Analyser (MISR) Generic BIST architectures BILBO

Ones-Count Compression
Assume a single output circuit C. Let the response of C to a test sequence be R = r1, r2, , rm .In ones counting the signature 1C(R) is the number of 1s appearing in R, i.e. 1C(R) =  ri where 0  1C(R)  m. i x1 x2 x3 & R R R2 f2 s-a-0 X & X s-a-1 f1 z

Ones Count Compression: Analysis
x1 x2 x3 Circuit Counter Signatures: 1C(R0) = 1 1C(R1) = 2 1C(R2) = 0 Clock Masking Probability The probability of an erroneous output sequence having the same number of 1’s as the correct sequence. Theorem: The masking probability for ones-count compression for a combinational network circuit asymptotically approaches (m)-1/2.

Transition-Count Compression
The Transition Count signature is the number of 0-1 and 1-0 transitions in the output response sequence R. Let the response of C to a test sequence be R = r1, r2, , rm. In transition counting the signature TC(R) is TC(R) =  (ri ri+1) i=1 x1 x2 x3 & R0 TC(R0)= R1 TC(R1)= R2 TC(R2)= 0 f2 s-a-0 X & X s-a-1 f1 z

Transition Count Compression: Analysis
Transition Detector x1 x2 x3 Circuit D Counter D Q Theorem: The masking probability for transition count compression for a combinational network circuit asymptotically approaches (m)-1/2

Signature Analysis Period of Linear Feed back shift register depends upon Feed back connections Intial value of register Masking probability is inversely related to the period + S S S S S S S S7 =S 1 1

LFSR as a Single-Input Signature Register (SISR)
Cn-2 C1 Cn Cn-1 D Q + D Q + + + + : Modulo-2 addition( an ex-or gate) : If Ci=1 then there is a connection otherwise no connection Ci This Circuit can be used to compress the response with masking probability = 2-n .

Multiple-Input Signature Registers
Method 1: Time Multiplex the signature analyzer for each output. That is repeat the test sequence for each output.This will require long test time. Method 2: Use Multiple Input Signature Register (MISR). D1 D2 D3 Dn + + + + Cn-2 Cn Cn-1 C1 Error Masking Probability = 2-n

Generic BIST Architectures
CUT DIST DIST TPG ORA CUT BIST Controller TPG CUT ORA TPG CUT ORA

Build-In Logic Block Observer (BILBO)
Motivation: It is difficult to self test a circuit which has a large number of (Inputs+Outputs+Storage Cells). You require PRSG for inputs, MISR for outputs PRSG and MISR for storage cells. Solution: Clustering of storage cells into registers and make these registers carry out multiple jobs. BILBO is one such scheme. Registers can be configured for : Normal Operation As PRSG As MISR As Scan Register

BILBO Registers B1 B2 Operation 1 1 Normal Operation
X X Xn Xn B1B2 Si D Q D Q So D Q D Q EXOR EXOR B1 B Operation Normal Operation Shift Register mode PRPG or MISR

BIST design with BILBO Registers
Example: R1 To Test C1 R1 as PRPG R2 as MISR To Test C2 R2 as PRPG R3 as MISR C1 R2 C2 R3

Summary of BIST BIST of a system requires techniques for
Data Compression Test Pattern Generation Linear Feedback Shift Registers are good for doing both Important concerns Masking Probability Fault coverage Overhead Data Compression and Test Generation Functions can be combined in one register (BILBOs)

Test Pattern Generation – part II Automatic Test Pattern Generation (ATPG)

Automatic Test Pattern Generation (ATPG)
With Scan-chains available, deterministic tests are preferred. Generic test method: Prepare a Fault list Repeat Write a test check fault cover (one test may cover more than 1 fault) delete covered faults from list until fault cover target is reached or only un-testable faults remain.

ATPG Example To test A/0 (A stuck-at-0), set A=1.
B C D Z E F To test A/0 (A stuck-at-0), set A=1. To propagate A/0, set B=1 To propagate result to Z, F must be 0 Thus, Either C=0 or D=0 or C=D=0 are solutions (3 possibilities) => (110-,11-0) The test pattern (1101/0) is good because it also covers E/1, D/0, F/1 and Z/1

Traditional algebra: speed Boolean algebra: change
Boolean Derivatives Traditional algebra: speed Boolean algebra: change y = F(x) y 0,1, F(X) 0,1 y F(X) will change if xi changes F(X) will not change if xi changes x xi xk

Boolean Derivatives Boolean function: Y = F(x) = F(x1, x2, … , xn)
Boolean partial derivative:

Example: Functional Description
F( x1, x2 ,x3) = x1x2+ x2x3+ x3x1 Fault: x1 stuck-at-1 = x2 x3 The function F will have different output, when x2 x3 = 1, that is x2=0 and x3 =1 OR x2= 1 and x3 = 0

Boolean Difference: Test pattern generation
For a point Xi s-a-1 The solution of the equation Gives all the tests for Xi stuck-at-1 For a point Xi s-a-0 Gives all the tests for Xi s-a-0

Boolean derivatives Useful properties of Boolean derivatives:
Test generation algorithm: Solve the differential equation if F(x) is independent of xi if F(x) depends always on xi

If F(x) is independent of xi
Boolean derivatives Useful properties of Boolean derivatives These properties allow to simplify the Boolean differential equation to be solved for generating test pattern for a fault at xi If F(x) is independent of xi

Boolean derivatives Calculation of the Boolean Difference w.r.t. x5
Given: Calculation of the Boolean Difference w.r.t. x5

A Complete Test: Intermediate circuit points must also be tested
Example & AB BC CA F h s-a-1 Test for h s-a-1 ABC = 1 A = 1; B= 1; C= 0.

Example: Complete Test using Boolean Derivatives
Z F

Fault Cover Check Test Pattern A B C D E F Z Sa0 Sa1 0000 X 0001 0010
0011 Redundant Redundant Redundant 0111 1000 1001 1010 1011 1100 Essential 1110 Essential One of these

Path Sensitization The method consists of two steps: Example Circuit
Identify a sensitized path from the fault site to output Check for consistency of the assignments to the inputs Example Circuit 11 X1 X2 G1& 7 S-a-0 G5 13 1/0 10 G7& 15 X3 X4 G2& 8 0X G4 1 1/0 1 1 G6 14 12 11 XX X5 X6 G3& 9 X Good value Bad value

Path Sensitization Node 1/0 1 X 13 12 11 10 9 8 7 6 5 4 3 2 14 15 G1
X 13 12 11 10 9 8 7 6 5 4 3 2 14 15 G1 G5 G7 G4 G6 G3 G2 Gates

Path Sensitization: Sensitization of multiple paths
Example: Fault 6 s-a-0 G4 8 5 1 G1 1 9 X1 X2 X3 X4 G5 1 1/0 1 G8 0/1 1 2 G2 6 12 3 1 10 G6 1/0 4 1 1 G3 7 1 G7 11 1 1

Path Sensitization: Sensitization of multiple paths
Example (Continued) G4 8 1 G1 5 1 X1 X2 X3 X4 9 G5 1 G8 1/0 1 0/1 1 0/1 2 G2 6 12 1 10 3 G6 1/0 1 4 G3 7 1 1 G7 11 1

D-Algorithm The ideas of Path sensitization method are formalized.
D-Notation The signal can take value from the set { 0,1,x,D,D } 1 D Good Circuit Faulty Circuit

Singular Cover Singular Cube is a compact representation of the truth table of a component. Example: 2-input AND gate Singular Cover Truth Table A B C A B C x 0 x

Primitive D-Cube Model of the component in the presence of fault.
Example: 2-input NOR gate Fault Primitive D-Cube A s-a A B C A s-a D C s-a D C s-a X X 1 A B C

Propagation D-Cube Model of a good component in a faulty circuit.
Must propagate the fault from the inputs to one of the outputs. Example: 2-input NOR gate A B C D D D D D D

D-intersection This is a method to propagate fault from the component to the output and to make consistency check. Example D 1 x 5 4 3 2 Primitive D-Cube G1 4 1 2 G2 3 5 X1 X2 X3 Z Propagation D-Cube Cube Intersection Fault Node 2 s-a-0

D-Algorithm: Forward Drive
1 2 X1 X2 X3 X4 G1 5 G3& 7 G5& 9 3 G2& G4 8 8 4 6 Primitive D-Cube of Fault G x D 1 2 3 4 5 6 7 8 9 G2 x D G4 D Propog. D-Cube G D G D x D G5 1 D x D 1 D

D-Algorithm: Consistency Check
1 x G1 G3 9 8 7 6 5 4 3 2 Singular Cover G x 1 G x 0

Re-convergent Fanout Example: Point 6 s-a-0 G4 8 1 G1 5 1 X1 X2 X3
9 G5 1 1 G8 1 2 G2 6 12 1 10 3 G6 1/0 1 4 G3 7 1 G7 11 1

D-Algorithm: Sensitizing Multiple Paths
X1 X2 X3 X 1 D G2 G5&G6 G8 G4 G7 G1 G3

D-Algorithm: Worst Case and Time Complexity
In the worst case the D-Algorithm will have to consider all combinations of path. In a circuit with N components, the number of combinations of paths from fault to output are: k2N. Worst case time complexity of D-Algorithm: O(2N). Fortunately, in practice average time complexity is much smaller (N2). If size of circuit grows by 10, number of tests required grows by 100.

Appendix

Testing Sequential Circuits

Testing Sequential Circuits
Testing of sequential circuits is harder than combinational circuits Sequential Circuit Testing requires verification of the state table Verify Reachability of all states Verify all transitions Assumption: Only the inputs and outputs are accessible, internal flip-flops are not accessible

Case Study Example Pattern Detector X S0 S1S2 S3 S1,0 S1,0S1,0 S0,1
State X= 0 X= 1 Pattern Detector Z S0 S1 S2 S3 1/0 0/0 0/1 (0110)

Homing Sequence Def.: Smallest input sequence which brings the machine to a known state. Therefore ‘00’ is the homing sequence for the machine {S0,S1,S2,S3} 1 {S1,S1,S1,S3} {S0,S2,S3,S0} 1 {S1,S1,S1,S1} {S2,S2,S2,S0}

Distinguishing Sequence
Definition: Smallest input sequence which produces a different output for each starting state. Example 2: mod-4 counter Example 1 does not have a common distinguishing sequence for all states. The common distinguishing sequence for Example 2 is ’1111’. S0 S1 S2 S3 Output = 0001 Output = 0010 Output = 0100 Output = 1000 X Mod-4 counter Z State X= 0 X= 1 S0 S1S2 S3 S0,0 S1,0S2,0 S3,0 S1,0 S2,0 S3,0 S0,1

Transfer Sequence Definition: Smallest input sequence which takes the machine from state i to state j, for all states i and j. Example 1: Example 2: i j Sequence S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S

Checking Experiment: Steps
1. Go to a known starting state by using a homing sequence or a distinguishing sequence. 2. Check reachability of all the states 3. Check all transitions

Checking Experiment: Step 1 Known Initial State
Example 1 Homing Sequence: 00 Known State : S1 Example 2 Distinguishing Sequence: Final State : If output = 0001 then S0 else if output = 0010 then S1 else if output = 0100 then S2 else S3;

Checking Experiment: Step2 Check reachability of all states
Example 2: Known Intial State : say S1 Check reachability to S2 Give transfer sequence for S1 to S2, that is, 1 Distinguish S2 by distinguishing sequence 1111: Output should be 0100 and final state S2. Check reachability to S3 Give transfer sequence for S2 to S3, that is, 1 Distinguish S3 by distinguishing sequence 1111 Output should be 1000 and final state S3 Check reachability to S0

Checking Experiment: Step3 Check various transitions
Example 2: Present State = S0 Check transition ( S0,0)  S0/0 Give 0 and check output to be 0 To check next state as S0 give distinguishing sequence 1111 and check output to be 0001. Check transition ( S0,1)  S1/0 Give 1 and check output to be 0 To check next state as S1 give distinguishing sequence 1111 and check output to be 0010. Similarly all other transitions.