Statistical skew modeling for general clock distribution networks in presence of process variations

Clock skew modeling is important in the performance evaluation and prediction of clock distribution networks. This paper addresses the problem of statistical skew modeling for general clock distribution networks in the presence of process variations. The only available statistical skew model is not suitable for modeling the clock skews of general clock distribution networks in which clock paths are not identical. The old model is also too conservative for estimating the clock skew of a well-balanced clock network that has identical but strongly correlated clock paths (for instance, a well-balanced H-tree). In order to provide a more accurate and more general statistical skew model for general clock distributions, we propose a new approach to estimating the mean values and variances of both clock skews and the maximal clock delay of general clock distribution networks. Based on the new approach, a closed-form model is also obtained for well-balanced H-tree clock distribution networks. The paths delay correlation caused by the overlapped parts of path lengths is considered in the new approach, so the mean values and the variances of both clock skews and the maximal clock delay are accurately estimated for general clock distribution networks. This enables an accurate estimate of yields of both clock skew and maximal clock delay to be made for a general clock distribution network.