Interval-Valued Reduced-Order Statistical Interconnect Modeling

We show how advances in the handling of correlated interval representations of range uncertainty can be used to approximate the mass of a probability density function as it moves through numerical operations and, in particular, to predict the impact of statistical manufacturing variations on linear...

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Bibliographic Details
Published in:IEEE transactions on computer-aided design of integrated circuits and systems 2007-09, Vol.26 (9), p.1602-1613
Main Authors: Ma, J.D., Rutenbar, R.A.
Format: Article
Language:English
Subjects:
Affine arithmetic
Algorithms
Asymptotic properties
Circuit simulation
Correlation
Delay
Design automation
design-for-manufacturing
Gaussian distribution
Integrated circuit interconnections
interconnect simulation
Intervals
Materials handling
Mathematical models
numerical analysis
Predictive models
Reduction
RLC circuits
Sampling
Semiconductor device manufacture
statistical modeling
Timing
Virtual manufacturing
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Summary:We show how advances in the handling of correlated interval representations of range uncertainty can be used to approximate the mass of a probability density function as it moves through numerical operations and, in particular, to predict the impact of statistical manufacturing variations on linear interconnect. We represent correlated statistical variations in resistance-inductance-capacitance parameters as sets of correlated intervals and show how classical model-order reduction methods - asymptotic waveform evaluation and passive reduced-order interconnect macromodeling algorithm - can be retargeted to compute interval-valued, rather than scalar-valued, reductions. By applying a simple statistical interpretation and sampling to the resulting compact interval-valued model, we can efficiently estimate the impact of variations on the original circuit. Results show that the technique can predict mean delay and standard deviation with errors between 5% and 10% for correlated parameter variations up to 35%.
ISSN:0278-0070
1937-4151
DOI:10.1109/TCAD.2007.895577