Clock driver suffers from delay variation due to manufacturing and environmental variabilities as well as combinational cells. The delay variation causes clock skew and jitter, and varies both setup and hold timing margins. This paper presents a timing verification method that takes into consideration delay variation inside a clock network due to both manufacturing variability and dynamic power supply noise. We also discuss that setup and hold slack computation inherently involves a structural correlation problem due to common paths, and demonstrate that assigning individual random variables to upstream clock drivers provides a notable accuracy improvement in clock skew estimation with limited increase in computational cost. We applied the proposed method to industrial designs in 90 nm process. Experimental results show that dynamic delay variation reduces setup slack by over 500 ps and hold slack by 16.4 ps in test cases.

We propose an optimization method for power distribution network that explicitly deals with timing. We have found and focused on the facts that decoupling capacitance (decap) does not necessarily improve gate delay depending on the switching timing within a cycle and that power wire expansion may locally degrade the voltage. To resolve the above facts, we devised an efficient sensitivity calculation of timing to decap size and power wire width for guiding optimization. The proposed method, which is based on statistical noise modeling and timing analysis, accelerates sensitivity calculation with an approximation and adjoint sensitivity analysis. Experimental results show that decap allocation based on the sensitivity analysis efficiently minimizes the worst-case circuit delay within a given decap budget. Compared to the maximum decap placement, the delay improvement due to decap increases by 3.13% even while the total amount of decaps is reduced to 40%. The wire sizing with the proposed method also efficiently reduces required wire resource necessary to attain the same circuit delay by 11.5%.