An interval-valued computation methodology for statistical retrofitting of existing circuit and technology CAD tools

As semiconductor technology advances into nanoscale, accommodating manufacturing variations has become an important design issue. Correlated affine interval representations of range uncertainty offer an attractive solution to approximating computations on statistical quantities. The key idea is to use finite affine 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 dissertation proposes a general and flexible interval-valued computation methodology for statistical "retrofitting" of existing circuit and technology computer-aided design (CAD) tools to accommodate semiconductor manufacturing variations. Starting from the original affine model, we develop a template-based affine interval model to bring statistics into affine arithmetic, with accuracy and efficiency empirically verified. Then we investigate various issues and solutions associated with deploying the affine model in interval-valued statistical algorithms. We demonstrate in the circuit CAD domain how to re-target classical interconnect analysis algorithms---asymptotic waveform evaluation (AWE), passive reduced-order interconnect macromodeling algorithm (PRIMA), and their path-tracing based formulation: Rapid Interconnect Circuit Evaluation (RICE)---to statistical model order reductions and distributions. We further apply this methodology to statistical modeling of chemical-mechanical polishing (CMP) step in the domain of technology CAD for manufacturability. Compared with straightforward Monte Carlo simulation, various statistical circuit and technology CAD tools achieve 10X-100X speedup with accuracy to within 1-10%. Overall, the proposed interval-valued computation methodology provides a viable alternative for quickly and effectively developing statistical CAD tools to handle increasing manufacturing variations.