Yield-driven clock skew scheduling was previously formulated as a minimum cost-to-time ratio cycle problem, by assuming that variational path delays are in Gaussian distributions. However in today's nanometer technology, process variations show growing impacts on this assumption, as variational delays with non-Gaussian distributions have been observed on these paths. In this paper, we propose a novel yield-driven clock skew scheduling method for arbitrary distributions of critical path delays. Firstly, a general problem formulation is proposed. By integrating the cumulative distribution function (CDF) of critical path delays, the formulation is able to handle path delays with any distributions. It also generalizes the previous formulations on yield-driven clock skew scheduling and indicates their statistical interpretations. Generalized Howard algorithm is derived for finding the critical cycles of the underlying timing constraint graphs. Moreover, an effective algorithm based on minimum balancing is proposed for the overall yield improvement. Experimental results on ISCAS89 benchmarks show that, compared with two representative existing methods, our method remarkably improves the yield by 10.25% on average (up to 14.66%).

In this paper, a spectral domain method named the SDF (Spectral Density Fitting) method for intra-die spatial correlation function extraction is presented. Based on theoretical analysis of random field, the spectral density, as the spectral domain counterpart of correlation function, is employed to estimate the parameters of the correlation function effectively in the spectral domain. Compared with the existing extraction algorithm in the original spatial domain, the SDF method can obtain the same quality of results in the spectral domain. In actual measurement process, the unavoidable measurement error with arbitrary frequency components would greatly confound the extraction results. A filtering technique is further developed to diminish the high frequency components of the measurement error and recover the data from noise contamination for parameter estimation. Experimental results have shown that the SDF method is practical and stable.