High-dimensional statistical modeling and analysis of custom integrated circuits (invited paper)

Custom circuit designers have long favored manual equation-based approaches in early design stages, because it gives excellent insight and control over the design. However, this flow is threatened: as modern process nodes advance, process variation affects circuit performance more strongly, hurting the accuracy of existing equations. Because designers are typically not statistical modeling experts, it is difficult to adapt the equations to incorporate statistical variations. This paper presents a fast, deterministic technique to help designers revise equations to account for statistical variation. Specifically, the technique extracts compact equations of performance as a function of process variables, even for cases when there are thousands of possible variables and the equations are highly nonlinear. In fact, it provides a whole set of equations that trade off simplicity versus accuracy compared to SPICE. The technique is validated on a broad range of custom integrated circuit modeling problems.