Interconnect transient simulation in the presence of layout and routing uncertainty

A methodology is presented for the calculation of the transient transmission-line response of package-level or board-level interconnects in the presence of layout and routing uncertainty. The proposed methodology makes use of the generalized polynomial chaos framework and advances in sparse stochastic collocation for interpolation and sampling in the probability space defined by the random variables that describe routing uncertainty. In this manner, a modeling framework is established that facilitates the computation of the statistics of the transient response and its post-processing for the purpose of assessing the impact of interconnect layout and routing uncertainty on signal distortion and crosstalk.