Explicit computation of performance as a function of process variation

Each manufactured chip is a little bit different, and designers want as many as possible of these chips to work. Process variation is a function of many variables, as the width, thickness, and inter-layer thickness can vary independently for each layer on a chip, as can temperature and voltage. Currently designers cope with this by picking a few subsets of these conditions, called process corners, and analyzing at these conditions. However, it's easy to show this approach is both too conservative (the specified conditions will seldom occur) and not conservative enough (it misses errors that can occur due to process variation). We present a unified theory of process variation that includes inter-chip variation, intra-chip deterministic variation (such as caused by proximity effects and metal density), and intra-chip statistical variation. Using this mechanism, we can explicitly compute performance as a function of process variation. This allows us to compute less pessimistic timing numbers and address yield optimization in the design process.