Predictive Statistical Analysis of Embedded Meander Resistors Via Measurement of Canonical Building Blocks

1
Predictive Statistical Analysis of Embedded
Meander Resistors Via Measurement of Canonical
Building Blocks
Doctoral Dissertation (Temp) by Lawrence A.
Carastro School of Electrical and Computer
Engineering Georgia Institute of Technology 2001
2
Proposal Objective

• The objective of this proposed research
• Further develop a passive device modeling
  methodology
• Predicts electrical behavior and statistical
  variation of embedded passive devices on a
  generic substrate
• Methodology will accurately model new passive
  devices
• Deembedding many building blocks from which they
  are built
• From just a few test structures
• Nonlinear optimizer used to find optimal models
  for building blocks
• Fitting extensive high frequency measurements of
  test structures behavior
• Key results of this research are
• Number of test structures needed is much less
  than number of parameters and building blocks to
  be extracted
• Extracted models of building blocks are very
  predictive of behavior of new devices built from
  them
• Methodology is much faster than other finite
  element like methods
• Statistical variations in modeled device can be
  extracted from building block models

3
Difficulties/Solution

• This Methodology has been very successful in
  modeling
• Both 2D and 3D passive device structures
• However, problems with this method
• Lie in long convergence time experienced when
  using optimization routine
• An initial guess and a range of possible element
  values is required by optimizer
• Inaccurate initial guesses coupled with
  non-inclusive element value ranges and an
  excessive number of optimized elements
• Lead to long convergence times or no convergence
  at all
• One solution to this problem is to decrease
  number of optimized element values
• By using physical equations to calculate lumped
  element circuit value

4
Semi-Empirical Model
Cint
R
L
nin
nout
C1
C2
Rsub12
Csub1
Csub2
Rsub1
Rsub2
Didnt Work
Semi-Empirical Sub Circuit Model for Planar
Inductors

• Paper entitled IC compatible planar inductors on
  silicon
• More physical semiempirical model has been
  developed
• Several components in lumped element equivalent
  circuit are modeled by functions related to
  inductor layout and material parameters
• Blue are solved using physical equations
• Red are deembedded using optimization routine
  actual measured data
• This research will prove
• Using semiempirical lumped element model and/or
  equations
• Improvement can be made by decreasing convergence
  time and/or avoiding failure of optimization tool

5
Statistical Variation Prediction

• Research will also focus on statistical variation
  of deembedded element values of building block
  models
• Will demonstrate that variation in complete
  equivalent circuit models, based only on circuit
  building blocks
• Used to predict such variations in actual
  fabricated devices
• Thirty-two meander resistor test structures, and
  thirty-two 9-segment meander resistors
• Fabricated in MiRC cleanroom
• Scattering parameter measurements ranging in
  frequencies from 50MHz to 20GHz
• Taken from all resistor structures
• Measured s-parameter data from each resistor test
  structure
• Used to deembed element values of improved lumped
  element equivalent circuit of that structure
• Using a non-linear optimization algorithm in
  Hspice
• This process will yield a unique equivalent
  circuit model for each of thirty-two test
  structures

DONE
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Statistical Variation Prediction

• Mean and absolute deviation relative variation
• Calculated for each component of each unique
  equivalent circuit model
• A Monte Carlo Analysis
• Using Hspice, yielding a range of 1000 500
  s-parameter curves
• (For resistor test structures z-parameters are
  more informative than s-parameters)
• (z-parameters for test structures, both measured
  and predicted, will be calculated)
• S-parameter polar coordinates were used
• Measured s-parameter magnitude and phase curves
  (input impedance curves) from each complete
  9-segment meander resistors
• Compared to curves generated by Monte Carlo
  analysis
• To determine if measured input impedance curves
  reside in range of curves generated by Monte
  Carlo analysis
• Comparison between Monte Carlo results and
  measured data
• Statistical variations of component values
  provide an accurate representation of overall
  9-segment meander resistor performance

DONE
7
Automation ofModeling Methodology

• A modeling methodology showcased previously
  entitled Automatic and accurate lumped-model
  generation of millimeter wave passive components
  using EM simulator
• Uses an EM solver to calculate coefficients in
  design equations
• Basically, designer inserts size and EM solver
  solves unknown coefficients
• Yields element values of lumped element circuits
• Method is completely automated
• Using shell-scripts as interface between user and
  computer
• Therefore, to further simplify this proposed
  research
• Unix scripts will be developed which will also
  act as interface between user and computer
• Automatically generating Hspice circuit files

DONE
8
Work Remaining

• Improvement to Existing Lumped Element Equivalent
  Circuit
• Investigate how current lumped element equivalent
  circuit can be improved by using equations from
  semiempirical lumped element model
• Using existing s-parameter data to model a
  9-segment meander resistor using a version of
  both methodologies by
• Using semiempirical lumped element circuit to
  model 30?m metal segments
• Using design equations from semiempirical model
  to calculate inductor and resistor values of
  existing PEEC
• Fabrication
• Thirty-two meander resistor test structures and
  thirty-two 9-segment meander resistor devices
• Physically designed using Magic Layout Tool on
  Sun Sparcstation 20 series workstation
• A mask of physical design needs to be obtained
  and used in MiRC cleanroom for fabrication of
  above-mentioned devices

DONE
9
Work Remaining

• Measurement
• High frequency s-parameter measurements
• Obtained from all fabricated devices
• Using HP 8510C network analyzer in conjunction
  with a Cascade Microtech probe station and
  ground-signal-ground configuration probes
• Calibration will be accomplished
• Using a supplied substrate and application of
  line-reflect-match (LRM) calibration method
• Data will be gathered for each test structures
• At over 200 frequency points between 50MHz and
  20GHz
• Stored by means of data acquisition software
• Deembedding
• Element values of equivalent circuits
  representing each test structure
• Deembedded using measured s-parameter data from
  each device
• Inserted into non-linear optimization algorithm
  in Hspice
• Process yields a unique equivalent circuit model
  for each of the thirty-two meander resistor test
  structures

DONE
10
Work Remaining

• Statistical Calculations and Monte Carlo
  Simulations
• Statistical variations in deembedded element
  values from all test structures calculated
• The statistical variations for each element value
  will be inserted into Hspice Monte Carlo
  simulation tool to create a range consisting of
  1000 500 s-parameter curves
• Monte Carlo Simulations vs. Actual Measured
  Devices
• A comparison of Monte Carlo simulation results to
  actual measured data from 9-segment meander
  resistors
• To show that behavior variations in fabricated
  structures are a subset of predicted variations
  obtained from the Monte Carlo results
• Automation Using Unix Shell-Scripts
• Final completion of unix shell-scrips need to be
  accomplished to automate deembedding and
  simulation process of Hspice

DONE
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Deembedding Procedure
Pad
Semi-Empirical
Didnt Converge Well
No Substrate Resistance
Material Square
With Substrate Resistance
Test Structure 1
Building Blocks
Circuit Model Topologies
1Block
Semi-Empirical
Didnt Converge Well
No Substrate Resistance 1Block Corner
Multi Block
With Substrate Resistance 1Block Corner
Deembed
No Substrate Resistance MultiBlock Corners
Coupled Pair
Test Structure 2
With Substrate Resistance No MultiBlk Corners

• Using different circuit configurations to improve
  Test Structure Measured vs. Modeled agreement

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Test Structure 1 S11R Comparisons
No Substrate Resistance Deembedded 3 percent
Error Between Measured vs. Modeled
Substrate Resistance Deembedded 2.5 percent
Error Between Measured vs. Modeled

• S11 measured vs. modeled percent mismatch error
• Two circuit topologies used
• 32 fabricated structures and 32 modeled
  structures
• Model including deembedded substrate resistance
  has lower percent error

13
Test Structure 1 S21R Comparisons
No Substrate Resistance Deembedded 0.5 percent
Error Between Measured vs. Modeled
Substrate Resistance Deembedded 0.75 percent
Error Between Measured vs. Modeled

• S21 measured vs. modeled percent mismatch error
• Two circuit topologies used
• 32 fabricated structures and 32 modeled
  structures
• Model without deembedded substrate resistance has
  lower percent error

14
Test Structure 2 S11R Comparisons
No Substrate Resistance Deembedded / MultiBlk
Corner 2.5 percent Error Between Measured vs.
Modeled
Substrate Resistance Deembedded / MultiBlk
Corner 6 percent Error Between Measured vs.
Modeled
Substrate Resistance Deembedded / 1Blk
Corner 10 percent Error Between Measured vs.
Modeled
No Substrate Resistance Deembedded / 1Blk
Corner 4 percent Error Between Measured vs.
Modeled
15
Test Structure 2 S21R Comparisons
No Substrate Resistance Deembedded / MultiBlk
Corner 1.0 percent Error Between Measured vs.
Modeled
Substrate Resistance Deembedded / MultiBlk
Corner 3 percent Error Between Measured vs.
Modeled
Substrate Resistance Deembedded / 1Blk
Corner 10 percent Error Between Measured vs.
Modeled
No Substrate Resistance Deembedded / 1Blk
Corner 1.5 percent Error Between Measured vs.
Modeled
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Circuit Configuration Choice
Test Structure 1
Test Structure 2
Building Blocks
Building Blocks
PEECs
PEECs

• No Substrate Resistance Deembedded and Inserting
  a Deembedded Multi-Block Corner
• Had the minimum overall percent error

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Multi-Block U-Shaped Bend
Test Structure 2
Close-Up

• Current visualization software tool shows
  non-uniform current distribution as it flows
  through the U-Shaped Bend building block

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Statistical Variations
30 u
Line Specs 1
c_sq_1 UNIF(1.262198980e-13, 9.72E-01)
rsq_1 UNIF(2.510000000e-06, 0.00E00) lsq_1
UNIF(1.816762077e-11, 4.91E-02) csq_1
UNIF(6.520000000e-26, 9.69E-01) r_sub_sq
10mega
Corner and Coupled Lines Specs 1
.param cou_l_1
UNIF(2.205573309e-01, 2.97E-01) c_cou_1
UNIF(6.714851620e-24, 8.15E-01) r2_1
UNIF(6.652141530e-01, 4.43E-01) c2_1
UNIF(1.357575649e-15, 2.34E-01) l2_1
UNIF(4.295089543e-12, 3.34E-01) c_co2cr_1
UNIF(8.071681342e-12, 3.66E-01) r_sub_corrn
10mega

• Statistical variations for each element were
  calculated and inserted
• Hspice Monte Carlo simulation tool to create a
  range consisting of 500 s-parameter curves

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9 Segment Modeled Resistor

• The MonteCarlo analysis setup varied element
  values of each individual building block
• Numbered 1 through 89

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S11/S21 MagnitudeMonteCarlo vs. Measured Results
MonteCarlo vs. Actual Measured Devices From 45MHz
to 20GHz For S11/S21 Magnitude

• MonteCarlo analysis consisted of 500 simulations
• Varying 89 material squares using statistical
  element data
• Deembedded from 32 Test Structure 1 devices, and
  32 Test Structure 2 devices
• MonteCarlo predicted range is outlined in red
• Accurately predicts measured 9 Segment Resistors
  into the GHz

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S11/S21 MagnitudeMonteCarlo vs. Measured Results
2.28GHz
4.5GHz
1.7GHz
943MHz
MonteCarlo Range (Red) vs. Actual Measured
Devices From 45MHz to 10GHz For S11 Magnitude
MonteCarlo Range (Red) vs. Actual Measured
Devices From 45MHz to 10GHz For S21 Magnitude

• 9 Segment Resistor measurements begin to deviate
  from MonteCarlo predicted range at 943MHz for S11
  magnitude and 2.28GHz for S21 magnitude
• The second curves deviated at 1.7GHz for S11
  magnitude and 4.5GHz for S21 magnitude

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S11 Mag. Statistical Comparisons
2.0GHz
2.0GHz
1.04GHz
1.04GHz
Correlation Coefficient For S11 MonteCarlo vs.
Measured At Each Frequency Point From 45MHz to
7.5GHz
Mean Percent Error For S11 MonteCarlo vs.
Measured At Each Frequency Point From 45MHz to
7.5GHz (With TrendLine)
T-Test For S11 MonteCarlo vs. Measured At Each
Frequency Point From 45MHz to 7.5GHz (With
TrendLine)
1.04GHz
2.0GHz

• Statistical comparisons between MC predicted
  range and actual measured data for S11 magnitude
  show first deviations at 1.04GHz
• MC prediction begins to fail at approximately
  2.0GHz for S11 magnitude

23
S21 Mag. Statistical Comparisons
4.7GHz
4.7GHz
2.45GHz
2.45GHz
Correlation Coefficient For S11 MonteCarlo vs.
Measured At Each Frequency Point From 45MHz to
7.5GHz
Mean Percent Error For S11 MonteCarlo vs.
Measured At Each Frequency Point From 45MHz to
7.5GHz (With TrendLine)
T-Test For S11 MonteCarlo vs. Measured At Each
Frequency Point From 45MHz to 7.5GHz (With
TrendLine)
2.45GHz
4.7GHz

• Statistical comparisons between MC predicted
  range and actual measured data for S21 magnitude
  show first deviations at 2.45GHz
• MC prediction begins to fail at approximately
  4.7GHz for S21 magnitude

24
S11/S21 PhaseMonteCarlo vs. Measured Results
MonteCarlo vs. Actual Measured Devices From 45MHz
to 20GHz For S11/S21 Phase

• MonteCarlo analysis consisted of 500 simulations
• Varying 89 material squares using statistical
  element data
• Deembedded from 32 Test Structure 1 devices, and
  32 Test Structure 2 devices
• MonteCarlo predicted range is outlined in red
• Appears to overlap measured data to 20GHz

25
S11/S21 PhaseMonteCarlo vs. Measured Results
MonteCarlo Range (Red) vs. Actual Measured
Devices From 45MHz to 10GHz For S11 Phase
MonteCarlo Range (Red) vs. Actual Measured
Devices From 45MHz to 10GHz For S21 Phase

• Actual measured data for S11 phase fits
  MonteCarlo predicted range when the 9 Segment
  Resistor turns capacitive
• A 3 or 4 degree mismatch at low frequencies is
  trivial compared to the Inductive /- 90 degree
  phase shift of an Inductor or Capacitor

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Automated Analysis Flow
Model Circuit Description
Number of TS1 TS2 Measured Devices
TS1 Initial Guess TS2 Initial Guess
TS1 TS2 .cir Files
Deembedded Element Values For TS1
HSPICE OPTIMIZATION TS1 TS2
TS1 TS2 Measured S-Parameters
Deembedded Element Values For TS2
Save Optimization Files
Calculate Error Measured vs. Modeled For TS1
TS2
PLOT
HSPICE SIMULATION TS1 TS2 MODEL RESISTOR
Extract S-Parameters From .out files Separate
Into Single Real/Imag, Real, Imag Master Files
Save .cif Files
Statictical Analysis In Excel
PLOT
Relative Variation of Element Values
HSPICE MONTECARLO ANALYSIS
Convert MC Model Resistor S-Parameter To Polar
Coordinates
Model Circuit Generation
PLOT
Model Resistor Measured S-Parameters
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Automated Analysis Flow

• The user enters the description of the modeled
  resistor
• Number of single Material Squares, number of
  Corners, and number of Turns (Coupled Material
  Squares)
• The user enters the number of measured devices
• This research used 32 measured devices
• The user enters the initial guess for each
  element value
• This research used the semi-empirical equations
  first, then used the initial values found in
  Ravis work
• Ravis values produced a closer measured vs.
  modeled fit
• The automated flow
• Constructs the correct resistor (modeled) .cir
  file
• Deembeds the element values from all measured
  devices (TS1 TS2)
• Simulates all Test Structures and Resistor Models
• Runs the MonteCarlo Analysis
• Saves all .cir files, S-parameters, and
  optimizations runs
• Converts and Localizes all data to be view using
  MS Excel
• The entire process completes in approximately 24
  hours