Modeling and Simulation of Real Defects Using Fuzzy Logic

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Modeling and Simulation of Real Defects Using
Fuzzy Logic

• Amir Attarha Mehrdad Nourani
• Center for Integrated Circuits Systems
• The Univ. of Texas at DallasRichardson, TX 75083
• attarha/nourani_at_utdallas.edu

Caro Lucas Dept. of ECE The Univ. of
TehranTehran 14399, IRAN lucas_at_karun.ipm.ir
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Outline

• Prior Works
• Motivating Examples
• Fault Model
• Modeling Gates Using Fuzzy Logic
• Fault Simulation
• Test Pattern Generation
• Experimental Results
• Conclusion

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Prior Works

• Defect Analysis
• Hawkins et. al. (ITC-1994)
• Aitken (ITC-1995)
• Rodriguez-Montanes et. al. (ITC-1992)
• Bridging Fault Simulation
• Nonresistive bridging
• Di and Jess (TCAD 1996)
• Dalpasso et. al. (TCAD1997)
• Resistive bridging
• Walker et. al. (ITC-1999)
• Renovell et. al.( VTS-1995)
• Test Pattern Generation
• Larrabee et. al. (TC-1998)
• Ferguson et. al. (ITC1991)

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Ex. 1 Real Stuck at Fault

• The stuck-at-fault may or may not be detected,
  depending the value of R.

Vdd 3.3 V fault free/faulty
Circuit 1
R100
a
0.0/1.92
3.3
z
0.0/3.12
3.3
b
Circuit 2
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Ex. 2 Resistive Bridging Fault

• The resistance of bridging fault plays an
  important role in fault simulation

Vdd 3.3 V fault free/faulty
Circuit 1
Circuit 2
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Ex. 3 Internal Gate Asymmetry

• Different orientations for a gate leads to
  different interpretations for the same input
  voltages.

Orientation 1
Vdd 3.3 V fault free/faulty
1.337
0.38
3.3
1.3
0
R1.5k
0
3.3
2.3
NAND
Orientation 2
3.01
0.713
3.3
1.3
0
R1.5k
0
3.3
2.3
NAND
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Key Features

• Considering non-zero resistance values for
  bridging and stuck-at faults
• Modeling logic components as fuzzy blocks to
  improve simulation accuracy
• Using an analytical fuzzy-based analysis
  forfault simulation instead of look up tables or
  circuit-level simulators
• Test pattern generation based on the resistive
  value of faults
• A flexible method fully adaptable by new
  libraries,logic styles, and technologies.

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Real Fault Model

• There are always R, L and C associated with
  areal defect.
• Our basic fault model is a single resistive
  bridgingfault (Rbridge)
• A stuck-at fault is a bridging fault, between a
  node and Vdd or Gnd
• Resistive fault model causes intermediate
  voltages
• For accurate simulation of real faults, we need
  to
• Calculate intermediate voltages accurately at
  two nodes of the fault
• Propagate accurately the effect of the
  fault(i.e. voltage values)

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Voltage Calculation
Vdd
V1
Rbridge
V2
Gnd
NAND
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Voltage Propagation

• Logic levels depend on technology and library.
  Noise margins are not crisp and varies for gates.
• Resistive faults cause intermediate voltages

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Modeling Logic Components

• For each logic gate in the target library a fuzzy
  block is designed.
• The fuzzy block models the behavior of the gate
  accurately
• We construct such fuzzy blocks in three steps
• Step1 Find the input-output behavior
• Step2 Decide on initial structure and parameters
• Step3 Optimize the free parameters

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Step1 Find Input-Output Behavior

• All logic components in the library are simulated
  by SPICE
• To build a complete database, whole range
  ofinput voltages have to be covered
• Desired accuracy can be determined inSPICE
  simulation (e.g. 0.01 volt)
• Note that SPICE simulation is done once for each
  gate of the target library

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Step2 Decide on Initial Structure

• Fuzzy logic is able to model any nonlinear system
• Sugeno model is selected as the basic structure
  of fuzzy blocks
• Output of Sugeno model is a linear function
  ofinput variables
• The free parameters (?) of Sugeno model need to
  be optimized

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Step3 Optimize the Free Parameters

• we minimize the error function, E(?)

• tp desired output (e.g. SPICE results)
• yp approximation result (e.g. by the fuzzy block)

• Nonlinear least square Levenberg-Marquart method
  has been utilized for optimization
• The method is an iterative descent method, which
  optimizes ? (free parameters of fuzzy system)

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Initial Fuzzy Block for NOT Gate

• To initialize the system, we need to determine
  initial rules and initial values for ?I and ?I.
• The initial parameters are determined empirically
  using linear approximation.
• We partition the full range of input (universe of
  discourse) to three space, LOW, MED and
  HIGH.

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Optimized Fuzzy Block for NOT GATE

• After optimizing ?, the fuzzy model for NOT gate
  shows very high accuracy compared to the SPICE.

• The small error in the intermediate level does
  not accumulate, because the intermediate voltages
  reach Vdd or Gnd after few levels.

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Fuzzy Block for AND Gate

• The behavior of AND gate is approximated
  accurately.
• The maximum error for all input combinations is
  less than 0.03 volt.

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Fault Simulation Algorithm
Test vector v
Fault f
Evaluate the fault free circuit using logic
simulation
Fuzzy Engine
Evaluate the faulty circuit using fuzzy approach
OUT_ff
OUT_f
NO
?
YES
OUT_ffOUT_f
Fault f is detected by test vector v
Fault f is not detected by test vector v
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Fuzzy Engine
Test vector v
Fault f
Select R randomly RminltRltRmax
Determine voltages created by f (v1,v2)
ll1
Cause abnormality in level l?
yes
no
Propagate the effects of fault f as 0/1
Propagate abnormality using fuzzy logic
no
yes
Reached output?
Out_f
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Test Pattern Generation

• We limit ourselves to non-feedback bridging
  faults
• We need to force opposite logic values for 2
  sides of bridging faults.
• XOR is used to find test patterns for bridging
  faults through PODEM

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Experimental Results (Stuck-at)
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Experimental Results(Bridging)
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Conclusion

• Real defects have R, L, C where R has the most
  effect on level of voltage.
• Traditional zero-resistance model is not
  sufficient and fault coverage is too optimistic
• Detecting real defects needs accurate voltage
  analysis.
• Fuzzy logic can model the analog behavior of the
  gates in abnormal region accurately
• Fuzzy modeling improves fault simulation and test
  patterns generation efficiency