We introduce a time-domain method to simulate the digital signal propagation along on-chip interconnects by solving Maxwell's equations with the Alternating-Direction-Implicit (ADI) method. With this method, we are able to resolve the large scale (i.e. on-chip electromagnetic wave propagation) and fine scale (i.e. skin depth and substrate current) structure in the same simulation, and the simulation time step is not limited by the Courant condition. The simulations allow us to calculate in detail parasitic current flow inside the substrate; propagation losses; skin-depth; and dispersion of digital signals on non-ideal interconnects. We have found considerable substrate currents and losses that depend on the substrate doping.