11 research outputs found

    Algorithms for DFM in electronic design automation

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    As the dimension of features in integrated circuits (IC) keeps shrinking to fulfill Moore’s law, the manufacturing process has no choice but confronting the limit of physics at the expense of design flexibility. On the other hand, IC designs inevitably becomes more complex to meet the increasing demand of computational power. To close this gap, design for manufacturing (DFM) becomes the key to enable an easy and low-cost IC fabrication. Therefore, efficient electronic design automation (EDA) algorithms must be developed for DFM to address the design constraints and help the designers to better facilitate the manufacture process. As the core of manufacturing ICs, conventional lithography systems (193i) reach their limit for the 22 nm technology node and beyond. Consequently, several advanced lithography techniques are proposed, such as multiple patterning lithography (MPL), extreme ultra-violet lithography (EUV), electron beam (E-beam), and block copolymer directed self-assembly (DSA); however, DFM algorithms are essential for them to achieve better printability of a design. In this dissertation, we focus on analyzing the compatibility of designs and various advanced lithography techniques, and develop efficient algorithms to enable the manufacturing. We first explore E-Beam, one of the promising candidates for IC fabrication beyond the 10 nm technology node. To address its low throughput issue, the character projection technique has been proposed, and its stencil planning can be optimized with an awareness of overlapping characters. 2D stencil planning is proved NP-Hard. With the assumption of standard cells, the 2D problem can be partitioned into 1D row ordering subproblems; however, it is also considered hard, and no efficient optimal solution has been provided so far. We propose a polynomial time optimal algorithm to solve the 1D row ordering problem, which serves as the major subroutine for the entire stencil planning problem. Technical proofs and experimental results verify that our algorithm is efficient and indeed optimal. As the most popular and practical lithography technique, MPL utilizes multiple exposures to print a single layout and thus allows placement of features within the minimum distance. Therefore, a feasible decomposition of the layout is a must to adopt MPL, and it is usually formulated as a graph k-coloring problem, which is computationally difficult for k > 2. We study the k-colorability of rectangular and diagonal grid graphs as induced subgraphs of a rectangular or diagonal grid respectively, since it has direct applications in printing contact/via layouts. It remains an open question on how hard it is to color grid graphs due to their regularity and sparsity. In this dissertation, we conduct a complete analysis of the k-coloring problems on rectangular and diagonal grid graphs, and particularly the NP-completeness of 3-coloring on a diagonal grid graph is proved. In practice, we propose an exact 3-coloring algorithm for those graphs and conduct experiments to verify its performance and effectiveness. Besides, we also develop an efficient algorithm for model based MPL, because it is more expensive but accurate than the rule based decomposition. As one of the alternative lithography techniques, block copolymer directed self-assembly (DSA) is studied. It has emerged as a low-cost, high- throughput option in the pursuit of alternatives to traditional optical lithography. However, issues of defectivity have hampered DSA’s viability for large-scale patterning. Recent studies have shown the copolymer fill level to be a crucial factor in defectivity, as template overfill can result in malformed DSA structures and poor LCDU after etching. For this reason, the use of sub-DSA resolution assist features (SDRAFs) as a method of evening out template density has been demonstrated. In this dissertation, we propose an algorithm to place SDRAFs in random logic contact/via layouts. By adopting this SDRAF placement scheme, we can significantly improve the density unevenness and the resources used are also optimized. We also apply our knowledge in coloring grid graphs to the problem of group-and-coloring in DSA-MPL hybrid lithography. We derive a solution to group-3-coloring and prove the NP-completeness of grouping-2-coloring

    Micro-Resonators: The Quest for Superior Performance

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    Microelectromechanical resonators are no longer solely a subject of research in university and government labs; they have found a variety of applications at industrial scale, where their market is predicted to grow steadily. Nevertheless, many barriers to enhance their performance and further spread their application remain to be overcome. In this Special Issue, we will focus our attention to some of the persistent challenges of micro-/nano-resonators such as nonlinearity, temperature stability, acceleration sensitivity, limits of quality factor, and failure modes that require a more in-depth understanding of the physics of vibration at small scale. The goal is to seek innovative solutions that take advantage of unique material properties and original designs to push the performance of micro-resonators beyond what is conventionally achievable. Contributions from academia discussing less-known characteristics of micro-resonators and from industry depicting the challenges of large-scale implementation of resonators are encouraged with the hopes of further stimulating the growth of this field, which is rich with fascinating physics and challenging problems

    Generalized averaged Gaussian quadrature and applications

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    A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

    MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

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    Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

    Layout decomposition for triple patterning lithography

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    Nowadays the semiconductor industry is continuing to advance the limits of physics as the feature size of the chip keeps shrinking. Products of the 22 nm technology node are already available on the market, and there are many ongoing research studies for the 14/10 nm technology nodes and beyond. Due to the physical limitations, the traditional 193 nm immersion lithography is facing huge challenges in fabricating such tiny features. Several types of next-generation lithography techniques have been discussed for years, such as {\em extreme ultra-violet} (EUV) lithography, {\em E-beam direct write}, and {\em block copolymer directed self-assembly} (DSA). However, the source power for EUV is still an unresolved issue. The low throughput of E-beam makes it impractical for massive productions. DSA is still under calibration in research labs and is not ready for massive industrial deployment. Traditionally features are fabricated under single litho exposure. As feature size becomes smaller and smaller, single exposure is no longer adequate in satisfying the quality requirements. {\em Double patterning lithography} (DPL) utilizes two litho exposures to manufacture features on the same layer. Features are assigned to two masks, with each mask going through a separate litho exposure. With one more mask, the effective pitch is doubled, thus greatly enhancing the printing resolution. Therefore, DPL has been widely recognized as a feasible lithography solution in the sub-22 nm technology node. However, as the technology continues to scale down to 14/10 nm and beyond, DPL begins to show its limitations as it introduces a high number of stitches, which increases the manufacturing cost and potentially leads to functional errors of the circuits. {\em Triple pattering lithography} (TPL) uses three masks to print the features on the same layer, which further enhances the printing resolution. It is a natural extension for DPL with three masks available, and it is one of the most promising solutions for the 14/10 nm technology node and beyond. In this thesis, TPL decomposition for standard-cell-based designs is extensively studied. We proposed a polynomial time triple patterning decomposition algorithm which guarantees finding a TPL decomposition if one exists. For complex designs with stitch candidates, our algorithm is able to find a solution with the optimal number of stitches. For standard-cell-based designs, there are additional coloring constraints where the same type of cell should be fabricated following the same pattern. We proposed an algorithm that is guaranteed to find a solution when one exists. The framework of the algorithm is also extended to pattern-based TPL decompositions, where the cost of a decomposition can be minimized given a library of different patterns. The polynomial time TPL algorithm is further optimized in terms of runtime and memory while keeping the solution quality unaffected. We also studied the TPL aware detailed placement problem, where our approach is guaranteed to find a legal detailed placement satisfying TPL coloring constraints as well as minimizing the {\em half-perimeter wire length} (HPWL). Finally, we studied the problem of performance variations due to mask misalignment in {\em multiple patterning decompositions} (MPL). For advanced technology nodes, process variations (mainly mask misalignment) have significant influences on the quality of fabricated circuits, and often lead to unexpected power/timing degenerations. Mask misalignment would complicate the way of simulating timing closure if engineers do not understand the underlying effects of mask misalignment, which only exists in multiple patterning decompositions. We mathematically proved the worst-case scenarios of coupling capacitance incurred by mask misalignment in MPL decompositions. A graph model is proposed which is guaranteed to compute the tight upper bound on the worst-case coupling capacitance of any MPL decompositions for a given layout

    A highly-efficient row-structure stencil planning approach for e-beam lithography with overlapped characters

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    Street Furniture and the Nation State: A Global Process

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    In the popular imagination, street furniture has traditionally been understood as evoking a sense of national or local identity. From Paris’ metro entrances, DDR lampposts in Berlin, and London’s york stone pavements, the designed environment has been able to contribute to the unique qualities of a place. In some instances this was deliberate. In postwar Britain for instance, the Council of Industrial Design – a state-funded design organization - often appeared to measure the quality of street furniture on the basis of its national characteristics. On other occasions, the relationship between such objects and identity emerged accidentally. In Britain during the 1980s, for example, the replacement of Gilbert Scott's red telephone box with an alternative BT model provoked considerable debate. For many people, this act was not just a Conservative attack on nationalization and state-ownership, but also on the very fabric of British identity. This understanding of street furniture has retained its currency for many years, and cities across the world have used street furniture to provide a sense of visual coherency for neighbourhoods in need of new identities, strengthening their character and improving the public's relationship to them. In this way, street furniture has been employed as a cipher for the narrative of regeneration, in which - as a means of altering the identity of a space - street furniture can project a new face upon the street. Increasingly however, advertising companies are able to lever themselves into the street furniture market by offering to provide the service to the local authorities for free in return for advertising space. In offering this service, global companies like JC Decaux, Wall and Clear Channel command a huge amount of commercial power within the city. The excessive homogenization of street furniture coupled with the overwhelming presence of advertising which is increasingly sanctioned by local authorities keen to reduce costs, has resulted in the perception of poorer quality streets. Thus, the irony of regeneration is that by seeking to promote the unique identity of a city, many places often end up looking more and more alike. This paper will examine recent developments in the process by which the street is furnished and the agents responsible. It will specifically look at how these changes have affected the relationship between street furniture and identity, and equally the effect this process has had on understandings of national design histories. Clearly, evaluating contemporary street furniture through the lens of the nation-state is of very little value, since the international differences between street furniture are considerably less marked than they used to be. This extraordinary aesthetic convergence is partly linked to economies of scale - after all, just how many different kinds of bus stop can Europe afford to have? Yet it also reflects some of the challenges posed by globalization and privatization of public space. This paper will reflect upon that process, and how these bigger narratives increasingly affect the landscape of the street

    GSI Scientific Report 2013

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