An efficient, fully nonlinear, variability-aware non-monte-carlo yield estimation procedure with applications to SRAM cells and ring oscillators

Abstract — Failures and yield problems due to parameter vari-ations have become a significant issue for sub-90-nm technologies. As a result, CAD algorithms and tools that provide designers the ability to estimate the effects of variability quickly and accurately are being urgently sought. The need for such tools is particularly acute for static RAM (SRAM) cells and integrated oscillators, for such circuits require expensive and high-accuracy simulation during design. We present a novel technique for fast computation of parametric yield. The technique is based on efficient, adaptive geometric calculation of probabilistic hypervolumes subtended by the boundary separating pass/fail regions in parameter space. A key feature of the method is that it is far more efficient than Monte-Carlo, while at the same time achieving better accuracy in typical applications. The method works equally well with parameters specified as corners, or with full statistical distributions; importantly, it scales well when many parameters are varied. We apply the method to an SRAM cell and a ring oscillator and provide extensive comparisons against full Monte-Carlo, demonstrating speedups of 100-1000×. I

Process variability in sub-16nm bulk CMOS technology

The document is part of deliverable D3.6 of the TRAMS Project (EU FP7 248789), of public nature, and shows and justifies the levels of variability used in the research project for sub-18nm bulk CMOS technologies.Postprint (published version

Variability-Aware Parametric Yield Estimation for Analog/Mixed-Signal Circuits: Concepts, Algorithms, and Challenges

The undesired uncertainties in circuit performance can lead to analog/mixed-signal circuit failures and yield loss at nanoscale. As such, it has become extremely critical for high precision analog/RF circuits such as phase-locked loop (PLL) and custom/mixed-signal circuits such as SRAM arrays, which both have tight operating margin due to lower power supply and higher operating frequency. Many performance-domain techniques have become available in past few decades: the Monte Carlo (MC) method repeatedly draws samples, runs simulations, and evaluates the yield rate, which can be easily applied to high-dimensional problems. However, it is extremely time consuming. IS can reduce the number of samples required to achieve a desired accuracy, especially in the case where the failure region is small for rare failure events. However, it is always challenging to obtain an optimal sampling distribution or shift vector efficiently

Surrogate based Optimization and Verification of Analog and Mixed Signal Circuits

Nonlinear Analog and Mixed Signal (AMS) circuits are very complex and expensive to design and verify. Deeper technology scaling has made these designs susceptible to noise and process variations which presents a growing concern due to the degradation in the circuit performances and risks of design failures. In fact, due to process parameters, AMS circuits like phase locked loops may present chaotic behavior that can be confused with noisy behavior. To design and verify circuits, current industrial designs rely heavily on simulation based verification and knowledge based optimization techniques. However, such techniques lack mathematical rigor necessary to catch up with the growing design constraints besides being computationally intractable. Given all aforementioned barriers, new techniques are needed to ensure that circuits are robust and optimized despite process variations and possible chaotic behavior. In this thesis, we develop a methodology for optimization and verification of AMS circuits advancing three frontiers in the variability-aware design flow. The first frontier is a robust circuit sizing methodology wherein a multi-level circuit optimization approach is proposed. The optimization is conducted in two phases. First, a global sizing phase powered by a regional sensitivity analysis to quickly scout the feasible design space that reduces the optimization search. Second, nominal sizing step based on space mapping of two AMS circuits models at different levels of abstraction is developed for the sake of breaking the re-design loop without performance penalties. The second frontier concerns a dynamics verification scheme of the circuit behavior (i.e., study the chaotic vs. stochastic circuit behavior). It is based on a surrogate generation approach and a statistical proof by contradiction technique using Gaussian Kernel measure in the state space domain. The last frontier focus on quantitative verification approaches to predict parametric yield for both a single and multiple circuit performance constraints. The single performance approach is based on a combination of geometrical intertwined reachability analysis and a non-parametric statistical verification scheme. On the other hand, the multiple performances approach involves process parameter reduction, state space based pattern matching, and multiple hypothesis testing procedures. The performance of the proposed methodology is demonstrated on several benchmark analog and mixed signal circuits. The optimization approach greatly improves computational efficiency while locating a comparable/better design point than other approaches. Moreover, great improvements were achieved using our verification methods with many orders of speedup compared to existing techniques