Enhancing 3-D Random Walk Capacitance Solver with Analytic Surface Green's Functions of Transition Cubes

The complicated dielectric profile under advanced process technologies challenges the accuracy of floating random walk (FRW) based capacitance extraction, as the latter pre-computes the surface Green's functions for a finite set of multi-dielectric transition cubes and makes approximations of transition cubes during the FRW process. In this work, we derive analytic surface Green's functions for transition cubes with arbitrary stratified dielectrics and propose a fast algorithm named AGF to compute them. A capacitance solver named FRW-AGF is then proposed to incorporate AGF into the FRW process to accurately model realistic transition cubes. Experimental results show that the proposed AGF is over 100× faster than the state-of-the-art, and FRW-AGF largely improves the accuracy of RWCap4 [3, 16] (making all errors to golden values below 5%) without degrading computational speed and parallel scalability.