Power Distribution Network Optimization for Timing Improvement with Statistical Noise Model and Timing Analysis

Takashi ENAMI
Takashi SATO

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E95-A    No.12    pp.2261-2271
Publication Date: 2012/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E95.A.2261
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on VLSI Design and CAD Algorithms)
Category: Device and Circuit Modeling and Analysis
power distribution network,  decoupling capacitance,  timing analysis,  statistical static timing analysis,  decap insertion,  wire sizing,  

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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%.