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Abstract-We develop a method to estimate the variation of leakage current due to both intra-die and inter-die gate length process variability. We derive an analytical expression to estimate the probability density function (PDF) of the leakage current for stacked devices found in CMOS gates. These distributions of individual gate leakage currents are then combined to obtain the mean and variance of the leakage current for an entire circuit. We also present an approach to account for both the inter-and intra-die gate length variations to ensure that the circuit leakage PDF correctly models both types of variation. The proposed methods were implemented and tested on a number of benchmark circuits. Comparison to Monte Carlo simulation validates the accuracy of the proposed method and demonstrates the efficiency of the proposed analysis method. Comparison with traditional deterministic leakage current analysis demonstrates the need for statistical methods for leakage current analysis.

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Abstracttiming analysis tools to replace standard deterministic static timing analyzers whereas [8,27] develop approaches for the statistical estimation of leakage power considering within-die and across-die variations.Increasing levels of process variability in sub-100nm CMOS design has become a critical concern for performance and power constraint designs. In this paper, we propose a new statistically aware Dual-Vt and sizing optimization that considers both the variability in performance and leakage of a design. While extensive work has been performed in the past on statistical analysis methods, circuit optimization is still largely performed using deterministic methods. We show in this paper that deterministic optimization quickly looses effectiveness for stringent performance and leakage constraints in designs with significant variability. We then propose a statistically aware dual-Vt and sizing algorithm where both delay constraints and sensitivity computations are performed in a statistical manner. We demonstrate that using this statistically aware optimization, leakage power can be reduced by 15-35% compared to traditional deterministic analysis. The improvements increase for strict delay constraints making statistical optimization especially important for high performance designs.However, very little work has been done on using statistical approaches to perform circuit optimization. Previous work [9,10] uses joint probability density functions (PDFs) of the circuit performance metrics and poses the yield optimization problem as a maximization of a higher dimensional integral which are estimated using Monte Carlo simulations. However, these methods are difficult to apply in modern applications due to their high runtime and memory requirements with increases in statistical parameters. Recent approaches to counter the impact of process variation have generally been limited to post-fabrication techniques. Forward and reverse body-biasing have been shown to improve yield and result in tighter distributions of circuit performance [11]. Reference [12] compares the approaches of adaptive body-bias and adaptive power supply to counter process variability. In [13], a simple circuit structure is used to automatically generate the ideal body-bias which is a function of process parameters and is ideal for a localized portion of the die. Alternatively, [14] proposes an optimization method to counter the effects of process variations. However this approach does not actually use statistical analysis but instead employs a heuristic to prevent a buildup of critical timing paths during the optimization.Categories and Subject Descriptors: B.6.3 Performance Analysis and Design Aids General Terms: Algorithms, performance, reliability Keywords: Leakage, variability, optimization Thus, we see that although a large amount of work is aimed towards countering the effects of process variations, there is only limited effort thus far in developing optimization approaches that consider these effects making intelligent decisions bas...