Capturing Post-Silicon Variations Using a Representative Critical Path

In nanoscale technologies that experience large levels of process variation, post-silicon adaptation is an important step in circuit design. These adaptation techniques are often based on measurements of 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 three 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 all three approaches. For both our approach and the critical path replica method, it is essential to guard-band the prediction to ensure pessimism: on average our approach requires a guard band 31% smaller than for the critical path replica method.