Optimal planning for mesh-based power distribution

Robust power distribution within available routing area resources is critical to chip performance and reliability. Here, we propose a novel and efficient method for optimizing worst-case static IR-drop in hierarchical, uniform power distribution networks. Our results can be used for planning of hierarchical power distribution in early design stages, so that for a fixed total routing area the worst-case IR-drop on the power mesh is minimal, or for a given IR-drop tolerance the power mesh achieves the IR-drop specification with minimal routing area. Our contributions are as follows. (1) We derive a closed-form approximation for the worst-case IR-drop on a single-level power mesh. The formula shows that for a given total routing area, the worst-case IR-drop increases logarithmically with the number of metal lines on the mesh. (2) Based on the previous analysis and empirical studies, we propose a model for the worst-case static IR-drop on a two-level power mesh, and obtain an accurate empirical expression. (3) Using this expression, we present a novel approach to optimize the two-level mesh topology. (4) We extend our study to three-level power meshes, and find that a third, middle-level mesh helps to reduce IR-drop by only a relatively small extent (about 5%, according to our experiments).