Session 4A: Variability Issues in Timing

4A-1 (Time: 10:15 - 10:40

Title Statistical Gate Delay Model for Multiple Input Switching
Author *Takayuki Fukuoka, Akira Tsuchiya, Hidetoshi Onodera (Kyoto Univ., Japan)
Abstract In this paper, we propose a calculation method of gate delay for SSTA (Statistical Static Timing Analysis) considering MIS (Multiple Input Switching). Most SSTA approaches assume a single input switching model and ignore the effect of MIS on gate delay. MIS occurs when multiple inputs of a gate switch nearly simultaneously. Thus, ignoring MIS causes error in MAX operation in SSTA. We propose a statistical gate delay model considering MIS. We verify the proposed method by SPICE based Monte Carlo simulations and experimental results show that the proposed method improves the error due to ignoring MIS.

4A-2 (Time: 10:40 - 11:05)

Title Non-Gaussian Statistical Timing Models of Die-to-Die and Within-Die Parameter Variations for Full Chip Analysis
Author *Katsumi Homma, Izumi Nitta, Toshiyuki Shibuya (Fujitsu Labs., Japan)
Abstract Statistical Timing Analysis (SSTA) is a method that calculates circuit delay statistically with process parameter variations, die-to-die (D2D) and within-die (WID) variations. In this paper, we model that WID parameter variations are for each cell and line in a chip and D2D variations are governed by one variation on a chip. We propose a new method of computing a full chip delay distribution considering both D2D and WID parameter variations. Experimental results show that the proposed method is more accurate than previous methods on actual chip designs.

4A-3 (Time: 11:05 - 11:30)

Title Non-Gaussian Statistical Timing Analysis Using Second-Order Polynomial Fitting
Author Lerong Cheng (Univ. of California, Los Angeles, USA), *Jinjun Xiong (IBM, USA), Lei He (Univ. of California, Los Angeles, USA)
Abstract In the nanometer manufacturing region, process variation causes significant uncertainty for circuit performance verification. Statistical static timing analysis (SSTA) is thus developed to estimate timing distribution under process variation. However, most of the existing SSTA techniques have difficulty in handling the non-Gaussian variation distribution and non-linear dependency of delay on variation sources. To solve such a problem, in this paper, we first propose a new method to approximate the max operation of two non-Gaussian random variables through second-order polynomial fitting. We then present new non-Gaussian SSTA algorithms under two types of variational delay models: quadratic model and semi-quadratic model (i.e., quadratic model without crossing terms). All atomic operations (such as max and sum) of our algorithms are performed by closed-form formulas, hence they scale well for large designs. Experimental results show that compared to the Monte-Carlo simulation, our approach predicts the mean, standard deviation, and skewness within 1%, 1%, and 5% error, respectively. Our approach is more accurate and also 20x faster than the most recent method for non-Gaussian and nonlinear SSTA.
No Slides

4A-4 (Time: 11:30 - 11:55)

Title A Capacitive Boosted Buffer Technique for High-Speed Process-Variation-Tolerant Interconnect in UDVS Application
Author Saihua Lin, *Yu Wang, Rong Luo, Huazhong Yang (Tsinghua Univ., China)
Abstract In this paper, we propose a new capacitive boosted buffer technique that can be used in high speed interconnect for ultra-dynamic voltage scaling (UDVS) application with the process variation effect mitigated. The circuit is simple and fully compatible with digital CMOS technology. Implemented in a standard 0.18 µm CMOS technology, the circuit is shown applicable for both sub-threshold circuit and above threshold circuit without the problem of short current. Simulation results demonstrate the conclusion that the proposed new buffer is more robust to load, process, voltage, and temperature (PVT) variations. When applied to a simple H-tree clock network, the proposed buffer can reduce the skew by 5.5Õ when compared to that of the traditional buffer.
No Slides

4A-5 (Time: 11:55 - 12:20)

Title Static Timing: Back to Our Roots
Author Ruiming Chen, Lizheng Zhang, Vladimir Zolotov, Chandu Visweswariah, *Jinjun Xiong (IBM, USA)
Abstract Existing static timing methodologies apply various techniques to address increasingly larger process variations. The techniques include multi-corner timing, on-chip variation (OCV) derating coefficients, and path-based common path pessimism removal (CPPR) procedures. These techniques, however, destroy the benefits of linear run-time and incrementality possessed by classical static timing. The major contribution of this work is an efficient statistical timing methodology with comprehensive modeling of process variations, while at the same time retaining those key benefits. Our methodology is compatible with existing characterization methods and scales well to large chip designs. To achieve this goal, three techniques are developed: (1) building the statistical delay model based on existing multi-corner library characterization; (2) modeling spatial correlation in a scalable manner; and (3) avoiding the time-consuming CPPR procedure by removing common path pessimism in the clock network by an incremental block-based technique. Experimental results on industrial 90 nm ASIC designs show that the proposed timing methodology correctly handles all types of process variation, achieves high correlation with traditional multi-corner timing with more than 4 x speedup, and is a vehicle for pessimism reduction.
No Slides
Last Updated on: January 31, 2008