Process variation is becoming a primal concern in timing closure of LSI (Large Scale Integrated Circuit) with the progress of process technology scaling. To overcome this problem, SSTA (Statistical Static Timing Analysis) has been intensively studied since it is expected to be one of the most efficient ways for performance estimation. In this paper, we study variation of output transition-time. We firstly clarify that the transition-time variation can not be expressed accurately by a conventional first-order sensitivity-based approach in the case that the input transition-time is slow and the output load is small. We secondly reveal quadratic dependence of the output transition-time to operating margin in voltage. We finally propose a procedure through which the estimation of output transition-time becomes continuously accurate in wide range of input transition-time and output load combinations.

This paper evaluates impact of self-heating in wire interconnection on signal propagation delay in an upcoming 32 nm process technology, using practical physical parameters. This paper examines a 64-bit data transmission model as one of the most heating cases. Experimental results show that the maximum wire temperature increase due to the self-heating appears in the case where the ratio of interconnect delay becomes largest compared to the driver delay. However, even in the most significant case which induces the maximum temperature rise of 11.0, the corresponding increase in the wire resistance is 1.99% and the resulting delay increase is only 1.15%, as for the assumed 32 nm process. A part of the impact reduction of wire self-heating on timing comes from the size-effect of nano-scale wires.

This paper discusses how to cope with dynamic power supply noise in FF timing estimation. We first review the dependence of setup and hold times on supply voltage, and point out that setup time is more sensitive to supply voltage than hold time, and hold time at nominal voltage is reasonably pessimistic. We thus propose a procedure to estimate setup time and clock-to-Q delay taking into account given voltage drop waveforms using an equivalent DC voltage approach. Experimental results show that the proposed procedure estimates setup time and clock-to-Q delay fluctuations well with 5% and 3% errors on average.

Leakage current is an important qualitative metric of LSI (Large Scale Integrated circuit). In this paper, we focus on reduction of leakage current variation under the process variation. Firstly, we derive a set of quadratic equations to evaluate delay and leakage current under the process variation. Using these equations, we discuss the cases of varying leakage current without degrading delay distribution and propose a procedure to reduce the leakage current variations. From the experiments, we show the proposed method effectively reduces the leakage current variation up to 50% at 90 percentile point of the distribution compared with the conventional design approach.

A method to derive design rules for SSO (Simultaneous Switching Outputs) considering jitter constraint on LSI outputs is proposed. Since conventional design rules do not consider delay change caused by SSO, timing errors have sometimes occurred in output signals especially for a high-speed memory interface which allows very small jitter. A design rule derived by the proposed method includes delay change characteristics of output buffers to consider the jitter constraint. The rule also gives mapping from the jitter constraint to constraint on design parameters such as effective power/ground inductance, number of SSO and drivability of buffers.

This paper presents a gate delay estimation method that takes into account dynamic power supply noise. We review STA based on static IR-drop analysis and a conventional method for dynamic noise waveform, and reveal their limitations and problems that originate from circuit structures and higher delay sensitivity to voltage in advanced technologies. We then propose a gate delay computation that overcomes the problems with iterative computations and consideration of input voltage drop. Evaluation results with various circuits and noise injection timings show that the proposed method estimates path delay fluctuation well within 1% error on average.

With the recent advance of process technology shrinking, process parameter variation has become one of the major issues in SoC designs, especially for timing convergence. Recently, Statistical Static Timing Analysis (SSTA) has been proposed as a promising solution to consider the process parameter variation but it has not been widely used yet. For estimating the delay yield, designers have to know and understand the accuracy of SSTA. However, the accuracy has not been thoroughly studied from a practical point of view. This paper proposes two metrics to measure the pessimism/optimism of SSTA; the first corresponds to yield estimation error, and the second examines delay estimation error. We apply the metrics for a problem which has been widely discussed in SSTA community, that is, normal-distribution approximation of max operation. We also apply the proposed metrics for benchmark circuits and discuss about a potential problem originating from normal-distribution approximation. Our metrics indicate that the appropriateness of the approximation depends on not only given input distributions but also the target yield of the product, which is an important message for SSTA users.