Fast and accurate solvers for capacitance extraction are needed by the VLSI industry in order to achieve good design quality in feasible time. With the development of technology, this demand is increasing dramatically. Three-dimensional capacitance extraction algorithms are desired due to their high accuracy. However, the present 3D algorithms are slow and thus their application is limited. In this dissertation, we present several novel techniques to significantly speed up capacitance extraction algorithms based on boundary element methods (BEM) and to compute the capacitance extraction in the presence of floating dummy conductors. We propose the PHiCap algorithm, which is based on a hierarchical refinement algorithm and the wavelet transform. Unlike traditional algorithms which result in dense linear systems, PHiCap converts the coefficient matrix in capacitance extraction problems to a sparse linear system. PHiCap solves the sparse linear system iteratively, with much faster convergence, using an efficient preconditioning technique. We also propose a variant of PHiCap in which the capacitances are solved for directly from a very small linear system. This small system is derived from the original large linear system by reordering the wavelet basis functions and computing an approximate LU factorization. We named the algorithm RedCap. To our knowledge, RedCap is the first capacitance extraction algorithm based on BEM that uses a direct method to solve a reduced linear system. In the presence of floating dummy conductors, the equivalent capacitances among regular conductors are required. For floating dummy conductors, the potential is unknown and the total charge is zero. We embed these requirements into the extraction linear system. Thus, the equivalent capacitance matrix is solved directly. The number of system solves needed is equal to the number of regular conductors. Based on a sensitivity analysis, we propose the selective coefficient enhancement method for increasing the accuracy of selected coupling or self-capacitances with only a small increase in the overall computation time. This method is desirable for applications, such as crosstalk and signal integrity analysis, where the coupling capacitances between some conductors needs high accuracy. We also propose the variable order multipole method which enhances the overall accuracy without raising the overall multipole expansion order. Finally, we apply the multigrid method to capacitance extraction to solve the linear system faster. We present experimental results to show that the techniques are significantly more efficient in comparison to existing techniques.

In order to correctly perform circuit simulation, it is crucial that parasitic capacitances near devices are accurately extracted and are consistent with the SPICE models. Although 3D device simulation can be used to extract such parasitics, it is expensive and does not consider the effects of nearby interconnect and devices in a layout. Conventional rule-based layout parasitic extraction (LPE) tools which are used for interconnect extraction are inaccurate in modeling 3D effects near devices. In this thesis, we propose a methodology which combines 3D field solver based extraction with the ability to exclude specific parasitics from among the parameters in the SPICE model. We use this methodology to extract parasitics due to fringing fields and sidewall capacitances in MOSFETs, bipolar transistors and FinFETs in advanced process nodes. We analyze the importance of considering layout and process variables in device extraction by comparing with standard SPICE models. The results are validated by circuit simulation using predictive technology models and test chips. We also demonstrate the versatility of this flow by modeling the capacitance contributions of the raised gate profile in nanoscale FinFETs.

A new full-wave surface impedance integral equation method is presented for three-dimensional arbitrary-shaped interconnect parasitic extraction in layered media. Various new ways of applying voltage and current excitations for electromagnetic-circuit simulation are introduced. A new algorithm is proposed for matrix formation of electromagnetic-circuit simulation, low frequency solution and layered media so that it can be easily integrated to a Rao-Wilton-Glisson based method of moment code. Two mixed potential integral equation forms of the electric field integral equation are adapted along with the Michalski-Mosig formulations for layered kernels to model electromagnetic interactions of interconnects in layered media over a conducting substrate. The layered kernels are computed directly for controllable accuracy. The proposed methods are validated against existing methods for both electromagnetic and electromagnetic-circuit problems.

In this thesis, we present a new continuously variable high frequency standing wave oscillator and demonstrate its use in generating the phase locked clock signal of a digital IC. The ring based standing wave resonant oscillator is implemented with a plurality of wires connected in a mobius configuration, with a cross coupled inverter pair connected across the wires. The oscillation frequency can be modulated by coarse and fine tuning. Coarse modification is achieved by altering the number of wires in the ring that participate in the oscillation, by driving a digital word to a set of passgates which are connected to each wire in the ring. Fine tuning of the oscillation frequency is achieved by varying the body bias voltage of both the PMOS transistors in the cross coupled inverter pair which sustains the oscillations in the resonant ring. We validated our PLL design in a 90nm process technology. 3D parasitic RLCs for our oscillator ring were extracted with skin effect accounted for. Our PLL provides a frequency locking range from 6 GHz to 9 GHz, with a center frequency of 7.5 GHz. The oscillator alone consumes about 25 mW of power, and the complete PLL consumes a power of 28.5 mW. The observed jitter of the PLL is 2.56 percent. These numbers are significant improvements over the prior art in standing wave based PLLs.

Field-programmable analog arrays (FPAA) are integrated circuits with a collection of analog building blocks connected through a wire and switch fabric to achieve reconfigurability similar to the FPGAs of the digital domain. Like FPGAs, FPAAs can help reduce the time and money costs of the integrated circuit design cycle and make analog design much easier. In recent years, several types of FPAAs have been developed. Among these, FPAAs that use floating-gate transistors as programming elements have shown great potential in scalability because of the simplicity they provide in configuring the chip. Existing tools for programming FPAAs tend to be device specific and aimed at specific tasks such as filter design. To move FPAAs to the next step, more powerful and generic placement and routing tools are necessary. This thesis presents a placement and routing tool for large-scale floating-gate-based FPAAs. A topology independent routing resource graph (RRG) was used to model the FPAA routing topology, which enables generic description of any FPAA architecture with arbitrary connectivity including possible FPGA support in the future as well. So far, different FPAA architectures have been specified and routed successfully. The tool is already in use in classes and workshops for analog circuit and system design. Efficient ways to describe circuits and user constraints were developed to allow easy integration with other tools. Analog circuit performance was optimized by taking into account the routing parasitic effects on interconnects under various device-related constraints. Parasitic modeling allows simulation and evaluation of circuits routed on FPAA. Finally, a methodology was developed to explore the optimum architecture for a set of circuit classes by evaluating the efficiency of different architectures for each circuit class.

Continued technology scaling together with the integration of disparate technologies in a single chip means that device performance continues to outstrip interconnect and packaging capabilities, and hence there exist many difficult engineering challenges, most notably in power management, noise isolation, and intra and inter-chip communication. Significant research effort spanning many decades has been expended on traditional VLSI integration technologies, encompassing process, circuit and architectural issues to tackle these problems. Recently however, three- dimensional (3-D) integration has emerged as a leading contender in the challenge to meet performance, heterogeneous integration, cost, and size demands through this decade and beyond. Through silicon via (TSV) based 3-D wafer-level integration is an emerging vertical interconnect methodology that is used to route the signal and power supply links through all chips in the stack vertically. Delay and signal integrity (SI) calculation for signal propagation through TSVs is a critical analysis step in the physical design of such systems. In order to reduce design time and mirror well established practices, it is desirable to carry this out in two stages, with the physical structures being modelled by parasitic parameters in equivalent circuits, and subsequent analysis of the equivalent circuits for the desired metric. This thesis addresses both these issues. Parasitic parameter extraction is carried out using a field solver to explore trends in typical technologies to gain an insight into the variation of resistive, capacitive and inductive parasitics including coupling effects. A set of novel closed-form equations are proposed for TSV parasitics in terms of physical dimensions and material properties, allowing the electrical modelling of TSV bundles without the need for computationally expensive field-solvers. Suitable equivalent circuits including capacitive and inductive coupling are derived, and comparisons with field solver provided values are used to show the accuracy of the proposed parasitic parameter models for the purpose of performance and SI analysis. The deep submicron era saw the interconnection delay rather than the gate delay become the major bottleneck in modern digital design. The nature of this problem in 3-D circuits is studied in detail in this thesis. The ubiquitous technique of repeater insertion for reducing propagation delay and signal degradation is examined for TSVs, and suitable strategies and analysis techniques are proposed. Further, a minimal power smart repeater suitable for global on-chip interconnects, which has the potential to reduce power consumption by as much as 20% with respect to a traditional inverter is proposed. A modeling and analysis methodology is also proposed, that makes the smart repeater easier to amalgamate in CAD flows at different levels of hierarchy from initial signal planning to detailed place and route when compared to alternatives proposed in the literature. Finally, the topic of system-level performance estimation for massively integrated systems is discussed. As designers are presented with an extra spatial dimension in 3-D integration, the complexity of the layout and the architectural trade-offs also increase. Therefore, to obtain a true improvement in performance, a very careful analysis using detailed models at different hierarchical levels is crucial. This thesis presents a cohesive analysis of the technological, cost, and performance trade-offs for digital and mixed-mode systems, outlining the choices available at different points in the design and their ramifications / QC 20100916