Fast interval-valued statistical modeling of interconnect and effective capacitance

Correlated interval representations of range uncertainty offer an attractive solution to approximating computations on statistical quantities. The key idea is to use finite intervals to approximate the essential mass of a probability density function (pdf) as it moves through numerical operators; the resulting compact interval-valued solution can be easily interpreted as a statistical distribution and efficiently sampled. This paper first describes improved interval-valued algorithms for asymptotic wave evaluation (AWE)/passive reduced-order interconnect macromodeling algorithm (PRIMA) model order reduction for tree-structured interconnect circuits with correlated resistance, inductance, and capacitance (RLC) parameter variations. By moving to a much faster interval-valued linear solver based on path-tracing ideas, and making more optimal tradeoffs between interval- and scalar-valued computations, the delay statistics roughly 10 x faster than classical Monte Carlo (MC) simulation, with accuracy to within 5% can be extracted. This improved interval analysis strategy is further applied in order to build statistical effective capacitance (C-eff) models for variational interconnect, and show how to extract statistics of Ceff over 100x faster than classical MC simulation, with errors less than 4%.