Analytical and Numerical Model Confrontation for Transfer Impedance Extraction in Three-Dimensional Radio Frequency Circuits

Abstract

3D chip stacking is considered known to overcome conventional 2D-IC issues, using through silicon vias to ensure vertical signal transmission. From any point source, embedded or not, we calculate the impedance spread out; our ultimate goal will to study substrate noise via impedance field method. For this, our approach is twofold: a compact Green function or a Transmission Line Model over a multi-layered substrate is derived by solving Poisson’s equation analytically. The Discrete Cosine Transform (DCT) and its variations are used for rapid evaluation. Using this technique, the substrate coupling and loss in IC’s can be analyzed. We implement our algorithm in MATLAB; it permits to extract impedances between any pair of embedded contacts. Comparisons are performed using finite element methods