Full Wave Modeling of Substrate Doping Effects and Nonideal Conductors in Integrated Circuit Interconnects

On-chip interconnects form complex networks composed of coupled metal lines on oxide and substrate layers. Substrate parasitic effects (substrate currents and propagation loss) are becoming limiting factors to the performance of modern high-speed digital and analog integrated circuits (ICs). Signals traveling along the metal-insulator-silicon-metal (MISM) structure (a fundamental on-chip interconnect unit) will have different attenuation and dispersion when changing operation frequencies and substrate doping densities. These are categorized into three fundamental propagation modes: the slow-wave mode, the dielectric quasi-TEM mode, and the skin-effect mode (Hasegawa et al., 1971). In high-speed radio frequency (RF) circuits, interconnects are likely to operate in the skin-effect mode. In this mode, the nonideal substrate functions as a current return path of the signal, located very close to the oxide layer. Accurate modeling of interconnects in this mode is difficult, because the Courant's stability condition limits most explicit time-domain full-wave Maxwell solvers. To overcome this problem, we apply the alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method (Namiki, 1999) to solve Maxwell's equations. In spite of the conductor loss, we have found considerable substrate current and loss, which depend on the substrate doping and operation frequency