Modeling and simulation of silicon interposers for 3-d integrated systems
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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.