In an early design stage of LSI designing, finding out the proper parameters for power planning is important from the viewpoint of cost minimization. In this paper, we present simple analytical formulas which are used to obtain the initial parameters close to the proper power distribution networks in the early design stage. The formulas for estimating static and pseudo-dynamic voltage drops (IR-drops) are derived by the response surface method (RSM). By making the formulas once, they can be used for the general power planning for the power-grid style in any process technology.

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.