Numerically stable Green function for modeling and analysis of substrate coupling in integrated circuits
The couplings via realistic lossy substrates can be modeled as frequency-dependent coupling parameters. The fast extraction at multiple frequencies can be accomplished in two sequent steps. The first is to extract the coupling resistance using a direct boundary element method (DBEM). The second is to revise the resistance into the parameter at the frequency in an exact and rapid way. The first step is time-consuming, while it runs only one time; the second repeats at each frequency, but is much easier. For more frequency calculation, this method is more advanced. Numerical experiments illustrate that this method has high accuracy, and it can be hundreds of times faster than an advanced Green's function based method. Substrates with arbitrary doping profiles can also be easily handled, which is partly verified by experiment.