A floating random-walk algorithm based on iterative perturbation theory: Solution of the 2D, vector-potential Maxwell-Helmholtz equation

At present multi-GHz operating frequencies, the electrical properties of high-end, multilevel IC interconnects must be described with Maxwell's equations. We have developed an entirely new floating random-walk (RW) algorithm to solve the 2D time-harmonic Maxwell-Helmholtz equation. The algorithm requires no numerical mesh, thus consuming, a minimum of computational memory-even in complicated problem domains, such as those encountered in IC interconnects. The major theoretical challenge of deriving an analytical Green's functions in arbitrary heterogeneous problem domains has been successfully resolved by means of an accurate approximation: iterative perturbation theory. Initial numerical verification of the algorithm has been achieved for the case of a "skin-effect" problem within a uniform circular conductor cross section, and also for a heterogeneous "split-conductor" problem, where one segment of a square domain is conducting material, while the other segment is insulating. As an example of electrical parameter extraction using this algorithm, we have extracted the frequency-dependent impedance of the uniform circular cross-section previously mentioned. Excellent agreement has been obtained between the analytical and RW solutions, supporting the theoretical formulation presented here.