A clustering technique for fast electrothermal analysis of on-chip power distribution networks

This paper presents an equivalent self-consistent electrothermal circuit model for power integrity analysis of large on-chip power distribution networks. Two coupled circuits are used to co-simulate the electrical and thermal behavior of the power grid. After a steady-state analysis, the order of the circuit is strongly reduced by means of a node clustering technique. The obtained low-order circuit allows a cost-effective complete power integrity analysis, including dynamic analysis and evaluation of time-domain features like voltage droop. As a case-study, a 45-nm chip power grid is analyzed: the full circuit for the electrothermal model with 4 million nodes is reduced by a factor of about 3500x, with a relative error on the solution below few percent.