Development of a floating random-walk algorithm for solving Maxwell's equations in complex IC-interconnect structures

A floating random-walk algorithm for Maxwell's equations has been developed in this thesis with a view to electromagnetic analysis of IC interconnect structures at high frequencies. This thesis accomplishes its two major objectives. In the first half of the thesis, an iterative-perturbation-theory based floating random-walk algorithm has been developed for the Maxwell-Helmholtz equation, subject to Dirichlet boundary conditions in materially inhomogeneous problem domains. Existing random-walk literature contains algorithms capable of solving the Helmholtz equation only in homogeneous structures and hence our algorithm is the first, significant step towards electromagnetic analysis of interconnect structures. A skin-effect type problem has been solved in a single circular conductor using this algorithm. In the second half of this thesis, an entirely new floating random-walk algorithm has been developed for solving the Helmholtz equation at multi-wavelength length scales, subject to Dirichlet-Neumann boundary conditions. This algorithm is the first attempt to solve the Helmholtz equation beyond sub-quarter wavelength length scales. Though this work is currently in the developmental stage, the initial results have been most encouraging, and this algorithm shows excellent promise for future interconnect analysis.