Stochastic power/ground supply voltage prediction and optimization via analytical placement

Increasingly significant power/ground (P/G) supply voltage degradation in nanometer VLSI designs leads to system performance degradation and even malfunction, which requires stochastic analysis and optimization techniques. We represent the supply voltage degradation at a P/G node as a function of the supply currents and the effective resistance of a P/G supply network and propose an efficient stochastic system-level P/G supply voltage prediction method, which computes P/G supply network effective resistances in a random walk process. We further propose to reduce P/G supply voltage degradation via placement of supply current sources, and integrate P/G supply voltage degradation reduction with conventional placement objectives in an analytical placement framework. Our experimental results show that the proposed stochastic P/G supply network prediction method achieves 10×-100× speedup compared with traditional SPICE simulation, and the proposed P/G supply voltage degradation aware placement achieves an average of 20.9% (11.7%) reduction on maximum (average) supply voltage degradation with only 4.3 % wirelength increase.