standard cell approach to 3d interconnect crosstalk modeling
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Standard Cell Approach to 3D Interconnect Crosstalk Modeling
Dr. A.A. IlumokaAssociate Professor, University of Hartford, CT, USAVisiting Prof, Georgia Institute of Technology ,USA
Visiting Prof, Imperial College, London
Interconnect Effects
Interconnect is Interconnect is 70% chip area70% chip area
DelayDelay
CrosstalkCrosstalk
Logic Logic HazardsHazards
Poor SignalPoor Signal IntegrityIntegrity
Major Issues in Nanoscale VLSI Design
Interconnect Coupling Noise Low Power Design Wafer Scale Integration Thermal Modelling Hardware/Software Co-Design
Interconnect Effects
Delay - due to self parasitic effects. Accounts for up to 70% of clock cycle time in dense high-speed circuits
Crosstalk - due to mutual parasitic effects. Electromagnetic coupling between signal paths
Delay Noise
Extensive work Well characterised Elmore Delay equations Passive Multi-port models ED A tools
Interconnect Modelling
Several approaches reported: Distributed model for lossy Tx Lines (Frye &
Chen) Simplified Pole/Zero Descriptions of circuit
behaviour (Brews) Graph-based approaches - risk graphs
generated for each region (Xue, Kuh & Wang) Reduced-Order Modelling Techniques
(Feldman, Kamon, White)
Problems with Interconnect Modelling
Difficulty Modelling 3D Effects
Difficulty modelling effect of several non-correlated variables ( wire geometry, insulating medium properties)
Lack of re-usability - need to recalculate models for changes in interconnect
Example-based Learning
Map set of Inputs to set of Outputs
Many network formulations
General form: f(x)= Σ ci Gi(x,W)
In p u t 1 In p u t 2 In p u t 3
N eu ra l N etw ork O u tp u ts
AI to the rescue Neural NetworksAI to the rescue Neural Networks
Neural Nets
f(x) = Σ ci Gi (x ,W) (sum over i) x = (x1, x2, x3,…….) are inputs f(x) is output: weighted sum of
activation functions Gi W : weights which parameterize Gi c: coefficients which modify Gi
Types of ANN’s
Many network formulations depending on problem type
SLP: if Gi are sigmoids, suitable for low dim problems
MLP: if f(x) applied as input to another net, more cx problems
Radial Basis - if Gi are Gaussian, suitable for classification problems
Modular Artificial Neural Network (MANN)
All animal brains exhibit some degree of regional specialisation wrt function
Specific parts of the human brain are known to have certain functions e.g. sleep control, memory etc
Certain neural nets called MANN’sMANN’s function in analogous way
MANN
Jacobs, Nowlan and Hinton, (MIT) 1991 Group of sub nets called local experts
competing to learn different aspects of a problem
Competitive learning controlled by a gating network
Useful for high dim problems with input data space stratification
MANN Architecture
G ate In p u t 1 G ate In p u t 2 G ate In p u t 3
N eu ra l N e tw ork O u tp u ts
In p u t 1 In p u t 2 In p u t 3
L oca l E xp ert L
In p u t 1 In p u t 2 In p u t 3
N eu ra l N et In p u ts
In p u t 1 In p u t 2 In p u t 3
L oca l E xp ert 1
In p u t 1 In p u t 2 In p u t 3
L oca l E xp ert 2
In p u t 1 In p u t 2 In p u t 3
G atin g N e tw ork
MANN Probabilistic Weight Update
Training is by back-propagation of error Update of LE weights posed as a max likelihood
problem Initially gating net outputs mixture of LE outputs As learning progresses, gate net tends to select
one LE for each region of input space Learning rule - gate net learns by matching prior
and posterior probabilities that LE was responsible for current output vector
Interconnect Building Blocks - Wirecells
(a) Parallel Pair (PP)
(b) L-Shaped Pair (LP)
© 4-ConductorParallel Pair
(d) 4-Conductor L-Shaped PairFig 2 Wirecells
Wirecell Circuit Extraction
Electrically characterise 3D conducting structures via 3-step process :
EM FieldEM FieldSimulationSimulation
Circuit Circuit ParameterParameterExtractionExtraction
FEMFEMFiniteFiniteElementElementMethodMethod
Parameterized MANN Models
In p u t 1 In p u t 2 In p u t 3
N eu ra l N etw ork O u tp u ts
Wirecell
For each interconnect wirecell Generate Monte Carlo Database for Training
and Testing MANN Store final MANN model in library
(a) Parallel Pair (PP)
(b) L-Shaped Pair (LP)
© 4-ConductorParallel Pair
(d) 4-Conductor L-Shaped PairFig 2 Wirecells
Standard Wirecells
WirecellsChipInterconnect
(a) Parallel Pair (PP)
(b) L-Shaped Pair (LP)
© 4-ConductorParallel Pair
(d) 4-Conductor L-Shaped PairFig 2 Wirecells
MANN-Based Standard Wirecell Approach
MANNWirecellModels
ChipInterconnect
In p u t 1 In p u t 2 In p u t 3
N eu ra l N e tw ork O u tp u ts
In p u t 1 In p u t 2 In p u t 3
N eu ra l N e two rk O u tp u ts
In p u t 1 In p u t 2 In p u t 3
N eu ra l N e tw ork O u tp u ts
In p u t 1 In p u t 2 In p u t 3
N eu ra l N e tw ork O u tp u ts
Advantages of MANN-Based Approach
Simultaneous modelling of several non-correlated interconnect variables
Can handle 3D systems of multiple conductors
Computationally efficient due to wirecell re-usability
Results for some CMOS Circuits
Ring Oscillator Operational
Transconductance Amplifier
Combinational Logic Circuit
Ring Oscillator Circuit
Ring Oscillator Results
Ring Osc Layout showing isocouples
Operational Transconductance Amp
OTA DC Transfer Characteristic
Effect of Crosstalk on DC Gain
OTA Isocouples: Contours of Equi-coupling
CMOS COMB LOGIC
Crosstalk in Comb Logic Circuit
Conclusions & Future Research
Efficient method presented for MANN-based standard cell approach to interconnect delay & crosstalk prediction
Contours of equi-coupling - isocouples - derived to guide layout
Future research - develop reverse neural net mapping for automated crosstalk minimization by manipulation of interconnect geometry and material properties
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