A high-capacity electromagnetic solution, layered finite element method, is proposed for high-frequency modeling of large-scale three-dimensional on-chip circuits. In this method, first, the matrix system of the original 3-D problem is reduced to that of 2-D layers. Second, the matrix system of 2-D layers is further reduced to that of a single layer. Third, an algorithm of logarithmic complexity is proposed to further speed up the analysis. In addition, an excitation and extraction technique is developed to limit the field unknowns needed for the final circuit extraction to a single layer only, as well as keep the right-hand side intact during the matrix reduction process. The entire procedure is numerically rigorous without making any theoretical approximation. The computational complexity only involves solving a single layer irrespective of the original problem size. Hence, the proposed method is equipped with a high capacity to solve large-scale IC problems. The proposed method was used to simulate a set of large-scale interconnect structures that were fabricated on a test chip using conventional Si processing techniques. Excellent agreement with the measured data has been observed from dc to 50 GHz.Index Terms-Electromagnetics, finite element method, high capacity, high frequency, on-chip circuits, three dimension.
The decreasing dimensions of IC devices is rendering the heat diffusion equation highly inaccurate for simulations of electrostatic discharge (ESD) phenomena. As dimensions of the heated region in the device are reduced far below 200 nm, neglecting the ballistic, sub-continuum nature of phonon conduction in the silicon lattice can strongly underpredict the temperature rise. This work integrates the phonon Boltzmann Transport Equation (BTE) in deep sub-micron silicon devices and presents a general methodology for solving the BTE. The approach developed is applicable to both Si and SO1 devices and predicts temperature rises consistent with failure voltage measurements for practical devices.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.