MCMM clock tree optimization based on slack redistribution using a reduced slack graph

Modern clock networks are required to operate in multiple corners and in multiple modes (MCMM). An initially constructed clock tree may contain different timing violations in different mode and corner combinations. Clock tree optimization (CTO) is employed to remove these timing violations. We propose a CTO framework based on slack redistribution using a reduced slack graph. The main idea is to reduce the MCMM problem to an equivalent single-corner single-mode (SCSM) problem using delay adjustment linearization. Using the equivalent SCSM problem, a linear program is solved to determine a set of delay adjustments to remove the timing violations. Next, the delay adjustments are realized using feasible delay adjustment ranges. The experimental results show that the proposed framework obtains average reductions of 84% and 83% in the total negative slack and the worst negative slack, respectively, at the expense of a 4% capacitive overhead.