Electrical recommendations and formulas for metal fill in radio-frequency integrated circuits

With increasing transistor operating frequencies, interconnects and passive devices are becoming performance limiters in integrated circuit (IC) designs. To combat this, the interconnect layers above the active silicon are trending toward low-κ dielectrics and Cu metallization. The use of these new materials has popularized chemical mechanical polishing (CMP) to planarize the several interconnect layers. Unfortunately, the mechanical trade-offs of CMP require metal pattern density uniformity and additional dummy metal shapes fill in regions of low density. These metal fills act as parasitics that increase the capacitances in interconnects and passive devices – hindering their performance. This work analyzes and optimizes the parasitic capacitive impact of rectangular metal fills on key passive components. Our systematic analysis of fills below a metal-insulator-metal (MIM) capacitor reveals an optimal design: large, square fills with lengths roughly 40% of MIM capacitors plate length. We fabricated such a MIM capacitor in a 250nm process showing a reduction in the substrate capacitance by half (compared to default tiling). Fill’s impact on interconnects, such as transmission lines, is also investigated. A detailed study of schemes that use grounded fills as shielding between interconnects informs an optimal grounding strategy. The strategy provides maximal isolation while minimizing capacitive loading. In fact, compared to no fills the addition of our metal fill shield increases loading by 58% while providing 58dB more isolation between example interconnects fabricated in a 130nm process. The capacitive impact of adding metal fills is found to be more significant as process dimensions shrink. In a 65nm process the inter-level dielectric constant is 3.5, but the addition of 50% density fills causes the effective dielectric constant to be 5.5. A semi-empirical, closed-form formula is developed to calculate this effective dielectric constant. The formula is accurate to within <1% for a wide range of metal fill densities, sizes, aspect ratios, and process dimensions. This is a significant improvement over state-of-the-art formulas which are found to be accurate to within ~10%. Our high accuracy is maintained when applied to multiple layers with and without staggering. Moreover, we successfully apply the formula to calculating ground/substrate capacitances of MIM capacitors, microstrip transmission lines, and a spiral inductor. This may speed up the calculation by hundredfold or even thousandfold. Results are compared to fabricated MIM capacitors and microstrips. Calculations and measurements match to within <5% for the capacitors and <2% for the microstrips

Field solver technologies for variation-aware interconnect parasitic extraction

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 207-213).Advances in integrated circuit manufacturing technologies have enabled high density onchip integration by constantly scaling down the device and interconnect feature size. As a consequence of the ongoing technology scaling (from 45nm to 32nm, 22nm and beyond), geometrical variabilities induced by the uncertainties in the manufacturing processes are becoming more significant. Indeed, the dimensions and shapes of the manufactured devices and interconnect structures may vary by up to 40% from their design intent. The effect of such variabilities on the electrical characteristics of both devices and interconnects must be accurately evaluated and accounted for during the design phase. In the last few years, there have been several attempts to develop variation-aware extraction algorithms, i.e. algorithms that evaluate the effect of geometrical variabilities on the electrical characteristics of devices and interconnects. However, most algorithms remain computationally very expensive. In this thesis the focus is on variation-aware interconnect parasitic extraction. In the first part of the thesis several discretization-based variation-aware solver techniques are developed. The first technique is a stochastic model reduction algorithm (SMOR) The SMOR guarantees that the statistical moments computed from the reduced model are the same as those of the full model. The SMOR works best for problems in which the desired electrical property is contained in an easily defined subspace.(cont.) The second technique is the combined Neumann Hermite expansion (CNHE). The CNHE combines the advantages of both the standard Neumann expansion and the standard stochastic Galerkin method to produce a very efficient extraction algorithm. The CNHE works best in problems for which the desired electrical property (e.g. impedance) is accurately expanded in terms of a low order multivariate Hermite expansion. The third technique is the stochastic dominant singular vectors method (SDSV). The SDSV uses stochastic optimization in order to sequentially determine an optimal reduced subspace, in which the solution can be accurately represented. The SDSV works best for large dimensional problems, since its complexity is almost independent of the size of the parameter space. In the second part of the thesis, several novel discretization-free variation aware extraction techniques for both resistance and capacitance extraction are developed. First we present a variation-aware floating random walk (FRW) to extract the capacitance/resistance in the presence of non-topological (edge-defined) variations. The complexity of such algorithm is almost independent of the number of varying parameters. Then we introduce the Hierarchical FRW to extract the capacitance/resistance of a very large number of topologically different structures, which are all constructed from the same set of building blocks. The complexity of such algorithm is almost independent of the total number of structures. All the proposed techniques are applied to a variety of examples, showing orders of magnitude reduction in the computational time compared to the standard approaches. In addition, we solve very large dimensional examples that are intractable when using standard approaches.by Tarek Ali El-Moselhy.Ph.D

Advanced analog layout design automation in compliance with density uniformity

To fabricate a reliable integrated circuit chip, foundries follow specific design rules and layout processing techniques. One of the parameters, which affect circuit performance and final electronic product quality, is the variation of thickness for each semiconductor layer within the fabricated chips. The thickness is closely dependent on the density of geometric features on that layer. Therefore, to ensure consistent thickness, foundries normally have to seriously control distribution of the feature density on each layer by using post-processing operations. In this research, the methods of controlling feature density distribution on different layers of an analog layout during the process of layout migration from an old technology to a new one or updated design specifications in the same technology have been investigated. We aim to achieve density-uniformity-aware layout retargeting for facilitating manufacturing process in the advanced technologies. This can offer an advantage right to the design stage for the designers to evaluate the effects of applying density uniformity to their drafted layouts, which are otherwise usually done by the foundries at the final manufacturing stage without considering circuit performance. Layout modification for density uniformity includes component position change and size modification, which may induce crosstalk noise caused by extra parasitic capacitance. To effectively control this effect, we have also investigated and proposed a simple yet accurate analytic method to model the parasitic capacitance on multi-layer VLSI chips. Supported by this capacitance modeling research, a unique methodology to deal with density-uniformity-aware analog layout retargeting with the capability of parasitic capacitance control has been presented. The proposed operations include layout geometry position rearrangement, interconnect size modification, and extra dummy fill insertion for enhancing layout density uniformity. All of these operations are holistically coordinated by a linear programming optimization scheme. The experimental results demonstrate the efficacy of the proposed methodology compared to the popular digital solutions in terms of minimum density variation and acute parasitic capacitance control

Modeling and characterization of on-chip interconnects, inductors and transformers

Ph.DNUS-SUPELEC JOINT PH.D. PROGRAMM

トランジスタ・アレイ方式に基づくアナログレイアウトにおける密度最適化

In integrated circuit design of advanced technology nodes, layout density uniformity significantly influences the manufacturability due to the CMP variability. In analog design, especially, designers are suffering from passing the density checking since there are few useful tools. To tackle this issue, we focus on a transistor-array(TA)-style analog layout, and propose a density optimization algorithm consistent with complicated design rules. Based on TA-style, we introduce a density-aware layout format to explicitly control the layout pattern density, and provide the mathematical optimization approach. Hence, a design flow incorporating our density optimization can drastically reduce the design time with fewer iterations. In a design case of an OPAMP layout in a 65nm CMOS process, the result demonstrates that the proposed approach achieves more than 48× speed-up compared with conventional manual layout, meanwhile, it shows a good circuit performance in the post-layout simulation.北九州市立大

Characterization and design of CMOS components for microwave and millimeter wave applications

Ph.DDOCTOR OF PHILOSOPH

Studies on physical interconnect technologies in advanced SoC designs

制度:新 ; 文部省報告番号:甲1992号 ; 学位の種類:博士(工学) ; 授与年月日:2005/3/15 ; 早大学位記番号:新392

Efficient numerical methods for capacitance extraction based on boundary element method

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

Miniaturized Transistors, Volume II

In this book, we aim to address the ever-advancing progress in microelectronic device scaling. Complementary Metal-Oxide-Semiconductor (CMOS) devices continue to endure miniaturization, irrespective of the seeming physical limitations, helped by advancing fabrication techniques. We observe that miniaturization does not always refer to the latest technology node for digital transistors. Rather, by applying novel materials and device geometries, a significant reduction in the size of microelectronic devices for a broad set of applications can be achieved. The achievements made in the scaling of devices for applications beyond digital logic (e.g., high power, optoelectronics, and sensors) are taking the forefront in microelectronic miniaturization. Furthermore, all these achievements are assisted by improvements in the simulation and modeling of the involved materials and device structures. In particular, process and device technology computer-aided design (TCAD) has become indispensable in the design cycle of novel devices and technologies. It is our sincere hope that the results provided in this Special Issue prove useful to scientists and engineers who find themselves at the forefront of this rapidly evolving and broadening field. Now, more than ever, it is essential to look for solutions to find the next disrupting technologies which will allow for transistor miniaturization well beyond silicon’s physical limits and the current state-of-the-art. This requires a broad attack, including studies of novel and innovative designs as well as emerging materials which are becoming more application-specific than ever before

Miniaturized Transistors

What is the future of CMOS? Sustaining increased transistor densities along the path of Moore's Law has become increasingly challenging with limited power budgets, interconnect bandwidths, and fabrication capabilities. In the last decade alone, transistors have undergone significant design makeovers; from planar transistors of ten years ago, technological advancements have accelerated to today's FinFETs, which hardly resemble their bulky ancestors. FinFETs could potentially take us to the 5-nm node, but what comes after it? From gate-all-around devices to single electron transistors and two-dimensional semiconductors, a torrent of research is being carried out in order to design the next transistor generation, engineer the optimal materials, improve the fabrication technology, and properly model future devices. We invite insight from investigators and scientists in the field to showcase their work in this Special Issue with research papers, short communications, and review articles that focus on trends in micro- and nanotechnology from fundamental research to applications