Effective power network prototyping via statistical-based clustering and sequential linear programming

In this paper, we propose a framework that automatically generates a power network based on given placed design and verifies the power network by the commercial tool without IR and Electro-Migration (EM) violations. Our framework integrates synthesis, optimization and analysis of power network. A deterministic method is proposed to decide number and location of power stripes based on clustering analysis. After an initial power network is synthesized, we propose a sensitivity matrix Gs which is the correlation between updates in stripe resistance and nodal voltage. An optimization scheme based on Sequential Linear Programming (SLP) is applied to iteratively adjust power network to satisfy a given IR drop constraint. The proposed framework constantly updates voltage distribution in response to incremental change in power network. To accurately capture voltage distribution on a given chip, our power network models every existing power stripes and via resistances on each layer. Experimental result demonstrates that our power network analysis can accurately capture voltage distribution on a given chip and effectively minimize power network area. The proposed methodology is experimented on two real designs in TSMC 90nm and UMC 90nm technology respectively and achieves 9%–32% reduction in power network area, compared with the results from modern commercial PG synthesizer.