RC delay metrics for performance optimization

TLDR

The Elmore RC delay metric is widely used for performance optimization because it is simple, fast, and reasonably accurate, whereas more accurate methods are computationally intensive or hard to implement, and the Elmore model ignores resistive shielding effects. The authors propose two new RC delay metrics, D2M and ECM, to combine the accuracy of advanced methods with the simplicity and speed of the Elmore metric. D2M computes delay using two moments of the impulse response for high accuracy at the far end of RC lines, while ECM models downstream capacitance as an effective capacitance to capture resistive shielding effects. ECM, though less accurate than D2M, delivers consistent performance and is suitable for optimization because of its Elmore-like recursive construction.

Abstract

For performance optimization tasks such as floorplanning, placement, buffer insertion, wire sizing, and global routing, the Elmore resistance-capacitance (RC) delay metric remains popular due to its simple closed form expression, fast computation speed, and fidelity with respect to simulation. More accurate delay computation methods are typically central processing unit intensive and/or difficult to implement. To bridge this gap between accuracy and efficiency/simplicity, we propose two new RC delay metrics called delay via two moments (D2M) and effective capacitance metric (ECM), which are virtually as simple and fast as the Elmore metric, but more accurate. D2M uses two moments of the impulse response in a simple formula that has high accuracy at the far end of RC lines. ECM captures resistive shielding effects by modeling the downstream capacitance by an "effective capacitance." In contrast, the Elmore metric models this as a lumped capacitance, thereby ignoring resistive shielding. Although not as accurate as D2M, ECM yields consistent performance and may be well-suited to optimization due to its Elmore-like recursive construction.