Prediction of interconnect pattern density distribution: derivation, validation, and applications

A rigorous derivation of the interconnect pattern density distribution for random logic networks is presented using the Bernoulli probability distribution. The derived analytical model provides a statistical interconnect pattern density distribution for a given wiring layer. Sampling window size, average wire length, wiring width and spacing, gate pitch, and wiring utilization are the input parameters.Monte-Carlo simulations agree with the results of the model. Comparison to product data shows that the model also successfully predicts the metal pattern density distribution of actual random logic networks.Several possible applications of the interconnect pattern density prediction are proposed. Among the applications of the model are: quantitative study of interconnect pattern density, statistical interconnect reference circuit for more realistic capacitance estimation, and assessing the impact of metal pattern density variation on system performance.