P1253553558ngyUf

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Mismatch analysis for high speed, deep
sub-micron blocks and simulation
methodologyTask ID906.001
Task Leader Alex Orailoglu, UC
San DiegoStudents Rasit Onur
Topaloglu, UC San Diego, 2007Industrial
Liaisons Hosam Haggag, National
Semiconductor Corp. Patrick Drennan, Freescale
Semiconductor, Inc. Mien Li, Advanced Micro
Devices, Inc.
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Technical Thrust Circuit designAnticipated
Result Mismatch simulation and testing
methods, with possible implementation in an EDA
environmentTask Description Provide
measurement, simulation, test and verification
methods for mismatch for deep-submicron
technologies
Task Deliverables Report on developing a
mismatch test methodology ? Report on developing
level 1 sensitivity functions
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Executive Summary
Accomplishments During the Past Year ?
Devised a test generation methodology to target
mismatch ? Devised a general methodology to
derive sensitivity functions for mismatch ?
Devised Forward Discrete Probability Propagation
Method for estimation of high level parameter
probability distributionsFuture Direction ?
Implementation of these techniques at behavioral
levels will enable ability to use along with
HDL, ex.Verilog-AMS
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Executive Summary
Technology Transfer Industrial Interactions
? Monthly telephone communications to National
Semiconductor on project progress ?
Internship at National Semiconductor
Publications ?SRC Deliverable Reports (
P007960 and P009498 ) ?On Mismatch in the Deep
Sub-micron Era From Physics to Circuits ,
ASPDAC 2004
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Mismatch for Next GenerationTask ID 1184.001
Task Leader Alex Orailoglu, UC
San DiegoStudents Ayse K. Coskun,
UC San Diego, 2008 Chengmo Yang, UC San Diego,
2008Industrial Liaisons Hosam Haggag,
National Semiconductor Corp.
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Technical Thrust Circuit designAnticipated
Result A wafer-aware and design-to-avoid
mismatch design flow for mixed-signal and RF
circuits implemented in an EDA environment. Task
Description Provide mismatch-immune design
and analysis methodologies including parasitics
and passives
Task Deliverables Report on MINT
modelsReport on mismatch verification and
diagnosis, Nov04
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Executive Summary
Technology Transfer Industrial Interactions
? Monthly telephone communications to National
Semiconductor on project progress
Future Direction ? Discovery of mismatch
integrated models and diagnosis Techniques to
target mismatch
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Outline
Test of Mismatch
Motivation
Mismatch Amplification
Excitation Plots
Mismatch Factor
Test Generation
Forward Discrete Probability Propagation
Probability Discretization Theory
Q, F, B, R Operators and r-domain
Experimental Results
Conclusions
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Test of Mismatch
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Motivation for Testing

• Functional testing is not the only method for
  digital circuits

• While testing for stuck-at faults, other faults
  typically discovered also

Find an analogous specialized test for mismatch
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Mismatch Amplification
Activate the defect, then propagate
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Excitation Plots
max-mismatch diagonal
no-mismatch diagonal
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Deteriorating Effects of Mismatch
Gain _at_100kHz vs. Widths of matched pair
no-mismatch diagonal
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Separation of Responses
Frequency response
DC response

• Fault-free responses sit on no-mismatch diagonal

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Mismatch Factor
Matrix representation of response
High MF gt small mismatch causes appreciable
impact
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Other Observed Excitation Plots
Sens. of AC gain to bias
Sens. of AC gain to VDD

• MF still effective due to symmetric nature

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Test Algorithm

• Mismatch (mm) pair,
• physical parameter,
• worst-case (V,T),
• obtain MFs
• select largest ones.

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Input and Analysis Choices
Use circuit specs to constraint ranges ex. AC or
VDD range
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Test Generation Ex. high coverage
W, mm1
VDD1, VDD2, T1, T2
Each entry ? excitation plot ? MF ? analysis type
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Test Generation Example low cost
W
VDD1, VDD2, T1, T2, mm1, mm2,..,mmN
Each entry ? excitation plot ? MF ? analysis type
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Test Set for Low Cost Example
AC2GHZ Apply 1mV input AC at 3.3V, 300K,
find AC gain
DCVin1.4V Apply 1.4V input DC 2.7V, 200K,
find DC gain
IDDQ At 3.3V, 300K, find power supply
current
Apply 1mV input AC at 2.7V, 200K then change
Vbias1 by 10 and repeat
SAC2GHz
Vbias1
Apply 1mV input AC at 2.7V, 200K then change
Vbias2 by 10 and repeat
SAC100kHz
Vbias2
At 2.7V, 200K, find power supply current then
change Vbias2 by 10 and repeat
SIDDQ
Vbias2
W

• This test set targets the Width mismatch in the
  circuit

If mismatch in Width parameter present, results
differ appreciably
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Test Set Size and Verification

• Reduction in number of test vectors intrinsic

• Apply this test set before any functional test,
  as this test catches most hard faults

• Test number can be reduced to analysis
  typesphysical parameters

• Test number is analysis typesphysical
  parametersmismatch pairs for increased fault
  coverage

• As simulation based, verification also intrinsic

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Outline
Test of Mismatch
Motivation
Mismatch Amplification
Excitation Plots
Mismatch Factor
Test Generation
Forward Discrete Probability Propagation
Probability Discretization Theory
Q, F, B, R Operators and r-domain
Experimental Results
Conclusions
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Forward Discrete Probability Propagation
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Motivation for Probability Propagation

• Estimation of circuit parameters needed to
  examine effects of process variations

• Gaussian assumption attributed to device
  parameters no longer accurate

Find a novel propagation method
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Shortcomings of Monte Carlo

• Non-determinism Not manually applicable

• Limited for certain distributions Random number
  generators only provide certain distributions

• Accuracy May miss points that are less likely
  to occur due to random sampling limited by the
  performance of random number generator

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Probability Discretization Theory QN Operator
p and r domains
pdf(X)
p-domain
r-domain
Certain operators easy to apply in r-domain
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Characterizing an spdf
spdf(X) or ?(X)
r-domain
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F Operator

• F operator implements a function over spdfs

• Function applied to individual impulses

• Individual probabilities multiplied

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Band-pass, Be, Operator
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Re-bin, RN, Operator
Resulting spdf(X)
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The Necessity of Re-binning

• Non-linear nature of functions cause accumulation
  in certain ranges

Band-pass and re-bin operations needed after F
operation
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Error Analysis

• If quantizer uniform and ? small, quantization
  error random variable Q is uniformly distributed

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Connectivity Graph Used in Experiments

• Connectivity Graphs can tie physical parameters
  to circuit parameters

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Algorithm Implementing the F Operator
While each random variable has its spdf computed
For each rv. which has all ancestor spdfs
computed
For each sample in X1
For each sample in Xr
Place an impulse with height p1,..,pr at
xf(v1,..,vr)
Apply B and R algorithms to this rv.
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Algorithm for the B and R Operators
Find maximum and minimum values wi within impulses
Divide this range into M bins
For each bin
Place a quantizing impulse at the center of the
bin with a height pi equal to the sum of all
impulses within bin
Find maximum probability, pi-max, of quantized
impulses within bins
Eliminate impulses within bins which have a
quantized impulse with smaller probability than
error-ratepi-max
Find new maximum and minimum values wi within
impulses
Divide this range into N bins
For each bin
Place an impulse at the center of the bin with
height equal to sum of all impulses within bin
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Q, F, B, R on a Connectivity Graph

• Repeated until we get the high level distribution

Useful for device characterization also
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Experimental Results
?(X) for Vth

• Impulse representation for threshold voltage and
  transconductance are obtained through FDPP on the
  graph

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Monte Carlo FDPP Comparison
Pdf of Vth
Pdf of ID
solid FDPP dotted Monte Carlo

• A close match is observed after interpolation

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Monte Carlo FDPP Comparison with a Low Sample
Number
Pdf of ?F
Pdf of ?F
solid FDPP,100 samples
noisy Monte Carlo, 1000 and 100000 samples
respectively

• Monte Carlo inaccurate for moderate number of
  samples

• Indicates FDPP can be manually applied without
  major accuracy degradation

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Monte Carlo FDPP Comparison
one-to-many relationships and custom pdfs
P1
P2
P3
P4
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Conclusions

• A specialized test selection mechanism for
  mismatch is introduced

• Test of Mismatch is a deterministic, general and
  low-cost methodology

• Forward Discrete Probability Propagation is
  introduced as an alternative to Monte Carlo based
  methods

• FDPP should be preferred when low probability
  samples are important, algebraic intuition
  needed, custom pdfs are present or one-to-many
  relationships are present