3D substrate modeling; from a first order electrical analysis, towards some possible signal fluctuations consideration, for radio frequency circuits

• From any point source, we calculate the impedance spreading into the bulk.
• Method: Green kernels, over or into a multi-layered substrate.
• Opening for an investigation on a transfer impedance method for 3D noise.

3D Si integration seems a right way to go and compete with Moore׳s law (more than Moore versus more Moore). However, it is still a long way to go.In 2010, the question was: why 3D? Today, the questions are: when 3D? and how 3D? The 3D chip stacking is considered known to overcome conventional 2D-IC issues, using in-depth contacts or some trough silicon via for signal transmission. First of all, from any source, we calculate the staggered impedance. For this, our approach is, at least, twofold: a compact Green kernel, or transmission line model, over or into a multi-layered substrate, is derived by solving Poisson׳s equation analytically. The discrete cosine transform 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. Thus, it permits to extract impedances between any two embedded contacts, real or virtual; this is original, up to our knowledge.We investigate our models on both analytical and numerical methods, like finite elements-based simulations. This extended model enables one to extract substrate impedance and parasitic elements between any two points embedded into the substrate. They are fully compatible with SPICE-like solvers and should allow an investigation in depth of the impact of buried contacts on circuit performance.This work should be an opening for an in depth study on the transfer impedance method concept applied to tridimensional calculations of noise,