Fast and efficient parametric modeling of contact-to-substratecoupling

This paper presents two rapid and yet accurate modeling methods for substrate coupling between a device contact and a substrate backplane. We discuss effects of physical parameters and geometrical characteristics of the contact and the substrate on the proposed models. We also derive model expressions for extraction of circuit-model elements of the substrate. Both methods are efficient for speed, memory usage, and adaptable to computer-aided design (CAD) tools for optimization tasks. The accuracy of both methods, the parametric modeling method and the microstrip line approximation method, is validated by comparing with the rigorous simulation data obtained from IE3D. Using the new models, we record a much higher speedup factor and extremely lower memory requirements compared to other published methods. The modeling methods are extended to two-layer structures and the models are applied to spiral inductors for verification purposes. In our research, we have validated the models over a wide range of frequencies up to 20 GHz.