The high-density integrated circuit (IC) gives rise to geometrically complex multiscale chip-package structures whose electromagnetic performance is difficult to predict. This motivates this dissertation to work on an efficient full-wave transient solver that is capable of capturing all the electromagnetic behaviors of such structures with high accuracy and reduced computational complexity compared to the existing methods. In this work, the unconditionally stable Laguerre-FDTD method is adopted as the core algorithm for the transient full-wave solver. As part of this research, skin-effect is rigorously incorporated into the solver which avoids dense meshing inside conductor structures and significantly increases computational efficiency. Moreover, as an alternative to typical planar interconnects for next generation high-speed ICs, substrate integrated waveguide, is investigated. Conductor surface roughness is efficiently modeled to accurately capture its high-frequency loss behavior. To further improve the computational performance of chip-package co-simulation, a novel transient non-conformal domain decomposition method has been proposed. Large-scale chip-package structure can be efficiently simulated by decomposing the computational domain into subdomains with independent meshing strategy. Numerical results demonstrate the capability, accuracy and efficiency of the proposed methods.

Three-dimensional (3-D) system integration is believed to be a promising technology and has gained tremendous momentum in the semiconductor industry recently. The Silicon interposer is the key enabler for the 3-D systems, and is expected to have high input/output counts, fine wiring lines and many TSVs. Modeling and design of the silicon interposer can be challenging and is becoming a critical task. This dissertation mainly focuses on developing an efficient modeling approach for silicon interposers in 3-D systems. The developed numerical methods can be classified as several categories. 1. The investigation of the coupling effects in large TSV arrays in silicon interposers. The importance of coupling between TSVs for low resistivity silicon substrates is quantified both in frequency and time domains. This has been compared with high resistivity silicon substrates. 2. The development of an electromagnetic modeling approach for non-uniform TSVs. To model the complex TSV structures, an approach for modeling conical TSVs is proposed first. Later a hybrid modeling method which combines the conical TSV modeling method and cylindrical modeling method is proposed to model the non-uniform TSV structures. 3. The development of a hybrid modeling approach for power delivery networks (PDN) with through-silicon vias (TSVs). The proposed approach extends multi-layer finite difference method (M-FDM) to include TSVs by extracting their parasitic behavior using an integral equation based solver. 4. The development of an efficient approach for modeling signal paths with TSVs in silicon interposers. The proposed method utilizes the 3-D finite-difference frequency-domain (FDFD) method to model the redistribution layer (RDL) transmission lines. A new formulation on incorporating multiport networks into the 3-D FDFD formulation is presented to include the parasitic effects of TSV arrays in the system matrix. 5. The development of a 3-D FDFD non-conformal domain decomposition method. The proposed method allows modeling individual domains independently using the FDFD method with non-matching meshing grids at interfaces. This non-conformal domain decomposition method is applied to model interconnections in silicon interposer.

The continuous miniaturization of electronic systems using the three-dimensional (3D) integration technique has brought in new challenges for the computer-aided design and modeling of 3D integrated circuits (ICs) and systems. The major challenges for the modeling and analysis of 3D integrated systems mainly stem from four aspects: (a) the interaction between the electrical and thermal domains in an integrated system, (b) the increasing modeling complexity arising from 3D systems requires the development of multiscale techniques for the modeling and analysis of DC voltage drop, thermal gradients, and electromagnetic behaviors, (c) efficient modeling of microfluidic cooling, and (d) the demand of performing fast thermal simulation with varying design parameters. Addressing these challenges for the electrical/thermal modeling and analysis of 3D systems necessitates the development of novel numerical modeling methods. This dissertation mainly focuses on developing efficient electrical and thermal numerical modeling and co-simulation methods for 3D integrated systems. The developed numerical methods can be classified into three categories. The first category aims to investigate the interaction between electrical and thermal characteristics for power delivery networks (PDNs) in steady state and the thermal effect on characteristics of through-silicon via (TSV) arrays at high frequencies. The steady-state electrical-thermal interaction for PDNs is addressed by developing a voltage drop-thermal co-simulation method while the thermal effect on TSV characteristics is studied by proposing a thermal-electrical analysis approach for TSV arrays. The second category of numerical methods focuses on developing multiscale modeling approaches for the voltage drop and thermal analysis. A multiscale modeling method based on the finite-element non-conformal domain decomposition technique has been developed for the voltage drop and thermal analysis of 3D systems. The proposed method allows the modeling of a 3D multiscale system using independent mesh grids in sub-domains. As a result, the system unknowns can be greatly reduced. In addition, to improve the simulation efficiency, the cascadic multigrid solving approach has been adopted for the voltage drop-thermal co-simulation with a large number of unknowns. The focus of the last category is to develop fast thermal simulation methods using compact models and model order reduction (MOR). To overcome the computational cost using the computational fluid dynamics simulation, a finite-volume compact thermal model has been developed for the microchannel-based fluidic cooling. This compact thermal model enables the fast thermal simulation of 3D ICs with a large number of microchannels for early-stage design. In addition, a system-level thermal modeling method using domain decomposition and model order reduction is developed for both the steady-state and transient thermal analysis. The proposed approach can efficiently support thermal modeling with varying design parameters without using parameterized MOR techniques.