Statistical Analysis Model of Nano-CMOS Variability with Intra-die Correlation Due to Proximity

The intrinsic variability of nano-scale integrated (IC) technology must be taken into account when analyzing circuit designs to predict likely yield. Monte Carlo (MC) and quasi-MC (QMC) based statistical techniques aim to do this by analysing many randomized copies of the circuit. The randomization must model many forms of variability that are to be expected in nano-CMOS technology which include 'atomistic' effects without intra-die correlation and also effects with intra-die correlation due to the proximity of neighbouring devices. The means of randomizing parameters with intra-die correlation as predicted by an 'exponential' model of proximity effects, is demonstrated. Examples are presented to show that the effects of intra-die correlation on statistical performance distribution and failure yield prediction can be significant, and that ignoring this correlation can give pessimistic estimates of yield.