Fast and Broadband Signal Integrity Analysis of Multiple Vias in Heterogeneous 3D IC and Die-Level Packaging by Using Generalized Foldy-Lax Scattering Method

Abstract

This dissertation proposal is concerned with the use of fast and broadband full-wave electromagnetic methods for modeling high speed interconnects (e.g, vertical vias and horizontal traces) and passive components (e.g, decoupling capacitors) for structures of PCB and packages, in 3D IC, Die-level packaging and SIW based devices, to effectively modeling the designs signal integrity (SI) and power integrity (PI) aspects. The main contributions finished in this thesis is to create a novel methodology, which hybridizes the Foldy-Lax multiple scattering equations based fast full wave method, method of moment (MoM) based 1D technology, modes decoupling based geometry decomposition and cavity modes expansions, to model and simulate the electromagnetic scattering effects for the irregular power/ground planes, multiple vias and traces, for fast and accurate analysis of link level simulation on multilayer electronic structures. For the modeling details, the interior massively-coupled multiple vias problem is modeled most-analytically by using the Foldy-Lax multiple scattering equations. The dyadic Green’s functions of the magnetic field are expressed in terms of waveguide modes in the vertical direction and vector cylindrical wave expansions or cavity modes expansions in the horizontal direction, combined with 2D MoM realized by 1D technology. For the incident field of the case of vias in the arbitrarily shaped antipad in finite large cavity/waveguide, the exciting and scattering field coefficients are calculated based on the transformation which converts surface integration of magnetic surface currents in antipad into 1D line integration of surface charges on the vias and on the ground plane. Geometry decomposition method is applied to model and integrate both the vertical and horizontal interconnects/traces in arbitrarily shaped power/ground planes. Moreover, a new form of multiple scattering equations is derived for solving coupling effects among mixed metallic/dielectric vias. The advantage of this kind of form has much better property for making inverse operation to obtain accurate results. All the proposed methods developed in this thesis have been verified by comparing the S parameters with the results from Ansoft’s HFSS, for various via configurations and via array sizes in high density layout in benchmark simulations. It is shown that the hybrid method is accurate mostly within 5% difference from results of HFSS and is about tens to hundreds of times faster than running HFSS up to 100GHz