Introduction• Many integrated circuits (ICs) contain fabrication

defects upon manufacture

• Die yields may only be 20-50% for high end circuits

• ICs must be carefully tested to screen out faulty parts before integration in systems

Example

Need 23 = 8 inputs to exhaustively test a 3 input AND gate.

Need 2N inputs to exhaustively test an N-input circuitMany ICs have > 100pins

2100 = 1.27 X 1030

Applying 1030 tests in 109 tests per Sec (1GHz !) will require 1021 Sec i.e. 400 billion centuries

Only a few input combinations can be applied in practice – 25% approx

VLSI Realization Process

Determine requirements

Write specifications

Design synthesis and Verification

Fabrication

Manufacturing test

Chips to customer

Customer’s need

Test development

Verification vs TestVerification

Verifies correctness of design. Performed by simulation,

hardware emulation, or formal methods.

Performed once prior to manufacturing.

Responsible for quality of design.

Test Verifies correctness of

manufactured hardware. Two-part process:

1. Test generation: software process executed once during design

2. Test application: electrical tests applied to hardware

Test application performed on every manufactured device.

Responsible for quality of devices.

Faults, Errors and Failures• Fault(Defect): A physical defect within a circuit or a

system– May or may not cause a system failure

• Error: Manifestation of a fault that results in incorrect circuit (system) outputs or states– Caused by faults

• Failure: Deviation of a circuit or system from its specified behavior– Fails to do what it should do– Caused by an error

» Defect ---> Error ---> Failure

• Electrical Effects:– Shorts – Opens– Transistor Stuck-On/Open– Resistive Shorts and Opens– Change in Threshold Voltages

• Logic Effects:– Logic Stuck-At-0/1– Slower Transition (Delay Faults)– AND-Bridging, OR-Bridging

Faults:

Single Stuck-at Fault• Three properties define a single stuck-at fault

• Only one line is faulty• The faulty line is permanently set to 0 or 1• The fault can be at an input or output of a gate

Test Generation

E

B F

C

A

Ds-a-1

0/1

0

1

1 0

1

10

0/1

Cannot detect the fault

Fault detected

Controllability for a digital circuit is defined as the difficulty or efforts of setting a particular logic signal to a 0 or a 1.

Observability for a digital circuit is defined as the difficulty or efforts of observing the state of a logic signal.

These measures are important for circuit testing, because while there are methods of observing the internal signals of a circuit, they are prohibitively expensive.

Sandia Controllability/Observability Analysis Program, Called as SCOAP consists of six numerical measures for each signal (l) in the circuit:

Line = l

The three combinational measures are related to the number of signals that may be manipulated to control or observe l.

The three sequential measures are related to the number of time-frames (or clock cycles) needed to control or observe.

The controllability range between 1 and infinity. The observability lie between 0 and infinity.

E

BF

C

A

D

Find Output Controllability of the following circuits

Z

Y

A

B

C

G1

G2

G3

G4

G5

F

H

G

Z

Y

A

B

C

G1

G2

G3

G4

G5

F

H

GControllabilitiesCC1(F)=CC1(A)+CC1(B)+CC1( C)+1=4CC0(F)=min{CC0(A),CC0(B),CC0( C)}+1=2CC1(H)=min{CC0(A),CC0(B)}+1=2CC0(H)=CC1(A)+CC1(B)+1=3CC1(G)=CC0( C)+1=2CC0(G)=CC1( C)+1=2CC1(Y)=min{CC1(F),CC1(H)}+1=3CC0(Y)=CC0(F)+CC0(H)+1=6CC1(Z)=min{CC0(H),CC0(G)}+1=3CC0(Z)=CC1(H)+CC1(G)+1=5

Assume that controllability of all inputs and observability of all outputs is 1

Comb. Controllability

Circled numbers give level number. (CC0, CC1)

Controllability Through Level 2

Final Combinational Controllability