Jeffrey Dyck

3-Sigma Verification and Design

This chapter explores how to efficiently design circuits accounting for statistical process variation, with target yields of two to three sigma (95–99.86 %). This yield range is appropriate for typical analog, RF, and I/O circuits. This chapter reviews various design flows to handle statistical process variations, and compares these flows in terms of speed and accuracy. It shows how a sigma-driven corner flow has excellent speed and accuracy characteristics. It then describes the key algorithms needed to enable the sigma-driven corner flow, namely sigma-driven corner extraction and confidence-based statistical verification. Some enabling technologies include Monte Carlo, Optimal Spread Sampling, confidence intervals, and 3σ corner extraction.

Variation-Aware Design

Previous chapters focused on the analysis of a fixed design, and corner extraction and verification in particular. Complementary to those chapters, this chapter focuses on changing the design. Specifically, it explores three different methodologies for changing device sizings, given accurate corners. First, it explores manual sizing and the advantages and disadvantages of a manual approach. Second, it explores automated sizing and its associated advantages and disadvantages. Finally, this chapter introduces a new idea that integrates manual and automated design techniques. This integrated approach incorporates the benefits of both manual and automated design, providing fast and thorough design exploration while allowing the designer to maintain full control over the design and providing more insight than ever.

Fast PVT Verification and Design

This chapter explores how to design circuits under PVT variation effects, as opposed to statistical process variation effects. Process, voltage, and temperature (PVT) variations are taken into account by individually varying P, V, and T over their allowable ranges and analyzing the subsequent combinations or so-called PVT corners. In modern designs, there can be hundreds or thousands of PVT corners. This chapter reviews design flows to handle PVT variations, and compares them in terms of relative speed and accuracy. It introduces a “Fast PVT” flow and shows how that flow has excellent speed and accuracy characteristics. It describes the Fast PVT algorithm, which is designed to quickly extract the most relevant PVT corners. These corners can be used within a fast and accurate iterative design loop. Furthermore, Fast PVT reliably verifies designs, on average 5x faster than the method of testing all corners on a suite of benchmark circuits. This chapter concludes with design examples based on the production use of Fast PVT technology by industrial circuit designers.

A Pictorial Primer on Probabilities

This chapter aims to build intuition about probability density functions (PDFs), Monte Carlo sampling, and yield estimation. It has an emphasis on graphical analysis as opposed to equations. Such intuition will help in many design scenarios, when one is observing actual PDF data in the form of scatterplots, histograms, and normal quantile (NQ) plots.