Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
PRIMO: probability interpretation of moments for delay calculation
DAC '98 Proceedings of the 35th annual Design Automation Conference
h-gamma: an RC delay metric based on a gamma distribution approximation of the homogeneous response
Proceedings of the 1998 IEEE/ACM international conference on Computer-aided design
Model order-reduction of RC(L) interconnect including variational analysis
Proceedings of the 36th annual ACM/IEEE Design Automation Conference
PERI: a technique for extending delay and slew metrics to ramp inputs
Proceedings of the 8th ACM/IEEE international workshop on Timing issues in the specification and synthesis of digital systems
A delay metric for RC circuits based on the Weibull distribution
Proceedings of the 2002 IEEE/ACM international conference on Computer-aided design
Variational delay metrics for interconnect timing analysis
Proceedings of the 41st annual Design Automation Conference
Stochastic analysis of interconnect performance in the presence of process variations
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
RC delay metrics for performance optimization
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Closed-form delay and slew metrics made easy
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Statistical model order reduction for interconnect circuits considering spatial correlations
Proceedings of the conference on Design, automation and test in Europe
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For statistical timing analysis and physical design optimization, interconnect delay metrics that model the delay as a function of the metal process variations are very important. Accurate linear or at most second order delay models in terms of the process variables are necessary to efficiently propagate uncertainty in the state-of-the-art VLSI designs with millions of transistors and on chip interconnects. In this paper1, we develop a method to extend the traditional moment based delay analysis of interconnects to consider the impact of Gaussian metal process variations and obtain mean-square optimal linear delay models for interconnects. We consider linear models for the variations in the conductance and capacitance of interconnects and represent the moments (m_0, m_1, m_2) of the interconnect impulse response as a first order orthogonal polynomial series expansion in the process variables^2. We obtain the coefficients of the expansion by using the Galerkin residual error minimization method on the recursive equations that relate the interconnect moments (m_0, m_1, m_2). We compare the accuracy of our approach against SPICE based Monte Carlo simulations and demonstrate a good match.