Variation-Aware Custom IC Design for High Sigma White Paper

High-sigma IC designs such as memory and standard cell design are inherently difficult to create and verify. High-Sigma Monte Carlo (HSMC) is a high-sigma verification technology that is fast, accurate, scalable, and verifiable, and is made usable through its implementation in a high-quality commercial product. HSMC can be used both to improve feedback within the iterative design loop, as well as for comprehensive verification of high-sigma designs. This paper presents example results for representative high-sigma designs, revealing some of the key traits that make the HSMC technology effective.

High-sigma IC components can tolerate only a few defects in hundreds of millions or billions of instances. Common examples of high-sigma components are bit cells or sense amps in memory designs, and replicated digital standard cells. Some products, such as automotive or medical equipment parts, also have high-sigma requirements, even though they are not replicated.

High-sigma parts are inherently difficult to design and verify because it is difficult to measure the effects of variation on high-sigma designs quickly and accurately. When there are only a few defects in a very large number of samples, Monte Carlo (MC) sampling requires a prohibitive amount of time to run in order to obtain accurate information in the extreme tail of the distribution where the defects occur. Other methods, such as extrapolating results from a smaller number of MC samples or importance sampling, all have other drawbacks, such as long runtimes, poor accuracy, or that they are only effective for trivial examples and do not scale to the needs of production designs.

The result is that the actual sigma of high-sigma designs is often unknown, and additional margin must be added to compensate for this uncertainty. This in turn sacrifices power, performance, and area. Still, some designs may fail to meet their high-sigma goals, resulting in poor yields and expensive re-spins.

What is required is a fast, accurate, scalable, verifiable, and usable tool for measuring high-sigma designs.

This white paper covers:
1. Introduction
2. Review of High Sigma Approaches
3. High Sigma Monte Carlo (HSMC) method
4. Results: HSMC vs MC in finding failures
5. Results: HSMC vs. Extrapolated MC
6. HSMC Discussion

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