Synthesizing a representative critical path for post-silicon delay prediction

Several approaches to post-silicon adaptation require feedback from a replica of the nominal critical path, whose variations are intended to reflect those of the entire circuit after manufacturing. For realistic circuits, where the number of critical paths can be large, the notion of using a single critical path is too simplistic. This paper overcomes this problem by introducing the idea of synthesizing a representative critical path (RCP), which captures these complexities of the variations. We first prove that the requirement on the RCP is that it should be highly correlated with the circuit delay. Next, we present two novel algorithms to automatically build the RCP. Our experimental results demonstrate that over a number of samples of manufactured circuits, the delay of the RCP captures the worst case delay of the manufactured circuit. The average prediction error of all circuits is shown to be below 2.8% for both approaches. For both our approach and the critical path replica method, it is essential to guard-band the prediction to ensure pessimism: our approach requires a guard band 30% smaller than for the critical path replica method.