The objective of this dissertation is to develop electrical modeling and co-simulation methodologies for signal and power integrity of package and board applications. The dissertation includes 1) the application of the finite element method to the optimization for decoupling capacitor selection and placement on a power delivery network (PDN), 2) the development of a PDN modeling method effective for multidimensional and multilayer geometries, 3) the analysis and modeling of return path discontinuities (RPDs), and 4) the implementation of the absorbing boundary condition for PDN modeling. The optimization technique for selection and placement of decoupling capacitors uses a genetic algorithm (GA) and the multilayer finite element method (MFEM), a PDN modeling method using FEM. The GA is customized for the decoupling problem to enhance the convergence speed of the optimization. The mathematical modifications necessary for the incorporation of the capacitor model into MFEM is also presented. The main contribution of this dissertation is the development of a new modeling method, the multilayer triangular element method (MTEM), for power/ground planes of a PDN. MTEM creates a surface mesh on each plane-pair using dual graphs; a non-uniform triangular mesh (Delaunay triangulation) and its orthogonal counterpart (Voronoi diagram), to which electromagnetic and equivalent circuit concepts are applied. The non-uniform triangulation is especially efficient for discretizing multidimensional and irregular geometries which are common in package and board PDNs. Moreover, MTEM generates a sparse, banded, and symmetric system matrix, which enables efficient computations. For a given plane-pair, MTEM extracts an equivalent circuit that is consistent with the physics-based planar-circuit model of a plane-pair. Thus, the values of the lumped elements can be simply calculated from the physical parameters, such as material properties and mesh geometries of each unit-cell. Consequently, the modeling of MTEM is flexible and easy to modify for further extensions, such as the incorporation of external circuits, e.g. decoupling capacitors and vertical interconnects. Power and ground planes provide paths for the return current of signal traces. Typically, planes have discontinuities such as via holes, plane cutouts, and split planes that disturb flow of signal return currents. At the discontinuity, return currents have to detour or switch to different layers, causing signal and power integrity problems. Therefore, a separate analysis of signal interconnects will neglect the significant coupling with a PDN, and the result will not be reliable. In this dissertation, the co-simulation of the signal and power integrity is presented focusing on the modeling of RPDs created by split planes, apertures, and vias. Plane resonance is one of the main sources of power integrity problems in package and board PDNs. A number of techniques have been developed and published in literature to reduce or prevent the resonance of a plane-pair. One of the techniques is to surround plane-pair edges with absorbing material that effectively damps the outgoing parallel-plate wave and minimizes the reflection. To model this behavior, the boundary condition of MTEM needs to be changed from its original form, the open-circuit boundary condition. In this dissertation, the application of the 1st order absorbing boundary condition to MTEM is presented.

Mixed signal system-on-package (SoP) technology is a key enabler for increasing functional integration, especially in mobile and wireless systems. Due to the presence of multiple dissimilar modules, each having unique power supply requirements, the design of the power distribution network (PDN) becomes critical. Typically, this PDN is designed as alternating layers of power and ground planes with signal interconnects routed in between or on top of the planes. The goal for the simulation of multi-layer power/ground planes, is the following: Given a stack-up and other geometrical information, it is required to find the network parameters (S/Y/Z) between port locations. Commercial packages have extremely complicated stack-ups, and the trend to increasing integration at the package level only points to increasing complexity. It is computationally intractable to solve these problems using these existing methods. The approach proposed in this thesis for obtaining the response of the PDN is the multi-layer finite difference method (M-FDM). A surface mesh / finite difference based approach is developed, which leads to a system matrix that is sparse and banded, and can be solved efficiently. The contributions of this research are the following: 1. The development of a PDN modeler for multi-layer packages and boards called the the multi-layer finite difference method. 2. The enhancement of M-FDM using multi-port connection networks to include the effect of fringe fields and gap coupling. 3. An adaptive triangular mesh based scheme called the multi-layer finite element method (MFEM) to address the limitations of M-FDM 4. The use of modal decomposition for the co-simulation of signal nets with the PDN. 5. The use of a robust GA-based optimizer for the selection and placement of decoupling capacitors in multi-layer geometries. 6. Implementation of these methods in a tool called MSDT 1.

Ce travail de recherche intitulé " Contribution à la modélisation de l'Intégrité des Alimentations dans les System-in-Package", effectué chez NXP semi-conducteurs, se propose d'étudier l'intégrité des alimentations et des signaux dans un système complexe tel que le System-in-Package(SiP), les System-on-Chip(SoC) ou autres (PoP,...). C'est-à-dire la générations de perturbations électromagnétiques conduites dues à l'activité d'un système complexe sur son environnement d'intégration. Un bilan de puissance statique et dynamique permet de considérer l’influence de l’activité des fonctions numériques sur le système SiP. L’activité dynamique est représentée sous forme de profils canoniques caractérisés par la technologie de conception des fonctions logiques. Cette représentation en base tient compte du cadencement multi fréquentiel (ou multi-harmonique) du système. Un logiciel a été développé permettant d'extraire un profil d'activité numérique définit suivant la géométrie de la fonction, sa technologie et ses fréquences d'activation. Les fonctions analogiques et le réseau passif d'interconnexions sont modélisés au travers de fonctions de transfert et validés par une approche expérimentale (domaine fréquentiel et temporel) et en simulation. Cette analyse a permis de souligner les potentialités de la modélisation BBS (Broad Band Spice Model). Ceci a permis une modélisation multi-port globale de l'environnement d'intégration modélisé depuis le PCB jusqu’aux fonctions actives (PCB-Boitier-interconnexions-circuits). Les modèles extraits sont utilisables dans un environnement SPICE où l’ensemble du système est modélisé dans un environnement unique. La CO-MODÉLISATION et la CO-SIMULATION GLOBALES permettent la proposition de règles de conception et l’optimisation du découplage souligné par le potentiel du substrat de report PICS (Passive Integrating Component Substrate). / This thesis, performed in NXP Semiconductors, presents an analysis on POWER INTEGRITY and SIGNAL INTEGRITY in complex systems (System-in-Package SiP, System-on-Chip SoC, PoP, etc). This subject takes in account the propagation and its effects of conducted electromagnetic interferences due to digital activities in power distribution network. A statement of static and dynamic power consumption allows to consider effects of digital activities through a multi-clock and multi harmonic model based on technologies, clocks and geometries of a dedicated functions, blocks or dices. A global distributed CO-SIMULATION/CO-MODELISATION methodology for concurrent/simultaneous analysis of passif distribution network have been successfully applied to a full complex system. An original "power signature" concept is used to model high speed digital modules temporal and spatial distribution of their power switching activity for analog-mixed-digital co-simulations. Analysis of coupling effects at systems level have been studied through access ports with and without active SiP modules. The measured coupling is validated with predicted simulation results based on electromagnetic simulations and broad band SPICE extractions. Correlations are validated between observed spurs in presence of SiP active modules and the behavioral response (transfer function) of the active die multiport, and multi-port de-embedding analysis. The full model of complex system, available in SPICE environnement, allows to analyse propagation and its effects of conducted electromagnetic interferences on dices, functions and system of the SiP. Thanks to this work, it will possible to supply new design rules and optimize of decoupling capacities values. A dedicated software was elaborated to generate a quick digital activity model easy-to-implement in SPICE environment.