A Novel Wavelet Transform Based Transient Current Analysis for Fault Detection and Localization

1
DAC 2002
A Novel Wavelet Transform Based Transient
Current Analysis for Fault Detection and
Localization Swarup Bhunia, Kaushik Roy
Purdue University
2
Outline

• Background
• Overview of Wavelet Transform
• Fault Detection
• Fault Localization
• Simulation Results
• Test Issues
• Power-grid issue
• Process variation
• Measurement noise
• Variation of mother wavelet
• Conclusions and Future Work

3
Background
Current Based Testing of Scaled CMOS Circuits
IDDQ Testing
IDDT Testing
Leakage Tolerant Techniques
Multiple Parameter IDDQ
Delta IDDQ
Wavelet Transform Based Method
Time Domain Signature Based Methods
DFT Based Methods
4
Wavelet Transform

• A square-integrable wave-like function (mother
  wavelet) used as basis
• Translated and dilated mother wavelet used in
  decomposition
• W(a,b) is the transform coeff of f(t) for given a
  (scale) and b (translation).

5
Wavelet Transform
Sine Wave
Mother Wavelet (db10)
6
Why Wavelet?
Temporal
Spectral
Temporal Spectral
7
Fault Detection Using Wavelet

• Based on current signature comparison
• Steps -
• Compute Wavelet Coeffs of IDD Waveform from the
  DUT for Vector I0-gtI1
• Apply I0-gtI1 to Fault-free Device, Compute
  Wavelet Coeffs of IDD Waveform
• Calculate the Mean Square Error (MSE)
• Fault Detected if MSE gt Test-Margin
• Better Detection Sensitivity - Signature
  Comparison Considers both Time and Frequency
  Components Unlike DFT-based Techniques

8
Fault Detection

• Fault Detection Sensitivity computed as

• Significantly better detection sensitivity than
  DFT
• Charge-based method has the least sensitivity
• Experiment
• 8-bit fabricated shift register
• Open faults on the clock line
• Sampling at 2 GHz
• Matlab wavelet toolbox
• Only 4 low freq components are considered

9
Fault Localization by Delay Measurement

• Basic idea
• Time domain information from wavelet coefficients
  can be used to compute delay
• The delay can be considered as a measure of
  propagation time to the faulty cell
• More input vectors needed to identify the region
  of fault with better resolution

• Wavelet is more effective for delay measurement
  than pure time domain methods, which suffers from
  aliasing

10
Fault Localization
Set of Inverters in Cascade
11
Fault Localization

• Delay Measurement from the wavelet Coeff

Wavelet Coeff at Four Different scales
12
Localization Example

• Part of a test circuit with a bridging fault (R1)

13
Fault Localization Steps
Localization

• Apply a vector that detects fault
• Compute the Delay
• Partition the circuit into Faulty and Fault-Free
  Set
• Apply next vector for finer faulty region

Partition

• Traverse the gates in topological order
• Compute excitation and Tpd at output of a gate
• If excitation occurs and delay is between min/max
  Tpd - consider the gate in the faulty set

14
Simulation Results

• Experiment
• Hspice simulation of 2 circuits as input
• 800 cells from Leda library (0.25TSMC)
• Shorts modeled with 100?, opens 1M?
• Matlab wavelet toolbox for wavelet transform
• only four low frequency spectral components of
  wavelet used
• Terminating condition applied to reduce
  simulation time

Detection and Localization Results for 2 Test
Circuits
15
Test Design Issues

• Power-grid Issue
• Does detection and localization work for
  mesh-like power supply network?

• Process Variation
• Presence of both time and frequency domain data
  renders better detectability for wavelet

• Measurement noise
• wavelet can model the measured signal better
  than DFT

• Selection of mother wavelet
• Different mother wavelets are good for different
  circuits

16
Impact of Power Supply Grid
VDD
Current Source
Rp
Lp
VDD pin
VDD
VDD
VDD
17
Power Grid Issue
18
Impact of Process Variation

• Process variation modeled by changing transistor
  threshold (VTH) in Hspice simulation
• Test margin for detection need to be relaxed. RMS
  error does not change much
• Localization still effective but the resolution
  decreases a bit

19
Conclusions and Future Work

• Wavelet based fault detection and localization
  appears very promising
• Can be effective to detect cross-talk induced
  delay faults and other delay faults
• Can be applied to analog and mixed-signal
  circuits
• Test generation is very important for fault
  localization
• More investigation about practical application of
  this method is being explored