Device-parameter estimation sensors inside a chip are gaining its importance as the post-fabrication tuning is becoming of a practical use. In estimation of variational parameters using on-chip sensors, it is often assumed that the outputs of variation sensors are not affected by random variations. However, random variations can deteriorate the accuracy of the estimation result. In this paper, we propose a device-parameter estimation method with on-chip variation sensors explicitly considering random variability. The proposed method derives the global variation parameters and the standard deviation of the random variability using the maximum likelihood estimation. We experimentally verified that the proposed method improves the accuracy of device-parameter estimation by 11.1 to 73.4% compared to the conventional method that neglects random variations.

Statistical timing analysis for manufacturing variability requires modeling of spatially-correlated variation. Common grid-based modeling for spatially-correlated variability involves a trade-off between accuracy and computational cost, especially for PCA (principal component analysis). This paper proposes to spatially interpolate variation coefficients for improving accuracy instead of fining spatial grids. Experimental results show that the spatial interpolation realizes a continuous expression of spatial correlation, and reduces the maximum error of timing estimates that originates from sparse spatial grids For attaining the same accuracy, the proposed interpolation reduced CPU time for PCA by 97.7% in a test case.

As the integrated circuit technology has undergone continuous downscaling to improve the LSI performance and reduce chip size, design for manufacturability (DFM) and design for yield (DFY) have become very important. As one of the DFM/DFY methods, a redundant via insertion technique uses as many vias as possible to connect the metal wires between different layers. In this paper, we focus on redundant vias and propose an effective redundant via insertion method for practical use to address the manufacturing variability and reliability concerns. First, the results of statistical analysis for via resistance and via capacitance in some real physical layouts are shown, and the impact on circuit delay of the resistance variation of vias caused by manufacturing variability is clarified. Then, the valuation functions of delay variation, electro-migration (EM), and stress-migration (SM) are defined and a practical method concerning redundant via insertion is proposed. Experimental results show that LSI with redundant vias inserted by our method robust against manufacturing variability and reliability problems.

This paper discusses clock skew due to manufacturing variability and environmental change. In clock tree design, transition time constraint is an important design parameter that controls clock skew and power dissipation. In this paper, we evaluate clock skew under several variability models, and demonstrate relationship among clock skew, transition time constraint and power dissipation. Experimental results show that constraint of small transition time reduces clock skew under manufacturing and supply voltage variabilities, whereas there is an optimum constraint value for temperature gradient. Our experiments in a 0.18 µm technology indicate that clock skew is minimized when clock buffer is sized such that the ratio of output and input capacitance is four.