A New Probability-based Method Of The Analysis Of The Integrity Of Power Grid

In an integrated circuit, all the devices get power supplies through Power/Ground network. As manufacturing technology moves forward and continued to scale to ever smaller dimensions, which makes analysis and verification of power grid integrity more important, and the resistance of the interconnect and wire can not be ignored any more. Because of the existence of this kind of resistance, when currents flow through P/G network, there are unavoidable voltage drop on it. This kind of voltage drop is called IR drop. IR drop is one of the four main problems we are faced with when we carry out analysis on the verification of power grid integrity. The three other problems are called ground bounce analysis, Ldi/dt from the pin inductance and EM analysis. This paper focuses on IR drop analysis, and the principle of ground bounce analysis is almost the same as it.Power grid integrity analysis is a global problem since that IR drop of the one part of the design is closely relative to the current drawn by the other parts. What's more, for a million-gate design, nodes in power grid are always more than one million. Therefore the bottleneck arises because of the size and traditional linear system can't deal with such a large network whether in speed or in memory. All the reasons above show that this kind of problem should be solved very effectively when we implement our design.With a thorough research on the structure of power grid, we put forward a new kind of approach to the IR drop problem. This approach is based on probability and statistics, which can give us an outlook of the probability distribution of IR drop. Power grid integrity analysis can be implemented in three steps. First, to model power grid as a linear system. Second, to consider block currents and voltages as random processes. Finally, to estimate the probability distribution of IR drop with the mean and variance of IR drop.The analysis was carried out on a number of grids, including the power grids of industrial processors and we can see that this approach is very effective. Theapproach also offers us useful information about which parts of the grid are most likely to go wrong and therefore we get to know that we should pay special attention to these parts when we are supposed to correct the power grid.