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We study the minimum-cost bounded-skew routing tree problem under the pathlength (linear) and Elmore delay models. This problem captures several engineering tradeoffs in the design of routing topologies with controlled skew. Our bounded-skew routing algorithm, called the BST/DME algorithm, extends the DME algorithm for exact zero-skew trees via the concept of a merging region. For a prescribed topology, BST/DME constructs a bounded-skew tree (BST) in two phases: (i) a bottom-up phase to construct a binary tree of merging regions which represent the loci of possible embedding points of the internal nodes, and (ii) a top-down phase to determine the exact locations of the internal nodes. We present two approaches to construct the merging regions: (i) the Boundary Merging and Embedding (BME) method which utilizes merging points that are restricted to the boundaries of merging regions, and (ii) the Interior Merging and Embedding (IME) algorithm which employs a sampling strategy and a dynamic programming-based selection technique to consider merging points that are interior to, as well as on the boundary of, the merging regions. When the topology is not prescribed, we propose a new Greedy-BST/DME algorithm which combines the merging region computation with topology generation. The Greedy-BST/DME algorithm very closely matches the best known heuristics for the zero-skew case and for the unbounded-skew case (i.e., the Steiner minimal tree problem). Experimental results show that our BST algorithms can produce a set of routing solutions with smooth skew and wirelength tradeoffs.

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I. INTERCONNECT TRENDS AND CHALLENGESThe driving force behind the impressive advancement of the VLSI circuit technology has been the rapid scaling of the feature size, i.e., the minimum dimension of the transistor. Table I lists the main characteristics of each technology generation in the NTRS. Such rapid scaling has two profound impacts. First, it enables much higher degree of on-chip integration. The number of transistors per chip will increase by more than 2 per generation to reach 800 millions in the© ¢ m technology. Second, it implies that the circuit performance will be increasingly determined by the interconnect performance. The interconnect design will play the most critical role in achieving the projected clock frequencies in the NTRS. This paper presents the trends and challenges of interconnect design in current and future technologies and discusses the available solutions.In order to better understand the significance of interconnect design in the future technology generations, we performed a number of experiments based on the interconnect parameters provided in the NTRS as shown in the bold face in Table II global interconnects, we also derived the interconnect parameters for the M4 layer,c which are also shown in Table II. Furthermore, we derived a set of device parameters as shown in Table III based on the data on processes and device in the NTRS. Using these sets of parameters, we carried out extensive simulations using HSPICE to quantitatively measure the interconnect performance and reliability in future technology generations and obtained the following results:(1) Interconnect delay is clearly the dominating factor in determincWe assume that the minimum width and spacing of M4 is 2.5 times those of M1. The aspect ratios 7 6 8 and 7 6 A @ are used to determine the metal thickness and the dielectric thickness for all layers. For M1, we assume that the substrate and M2 are the ground planes; and for M4, we assume that M3 and M5 are the ground planes. The total capacitance, including the area capacitance, fringing capacitance, and coupling capacitance components, are obtained using the 3D field solver FastCap [2]. Based on these assumptions, our capacitance values for M1 closely match those given in the NTRS.

Many current designs contain a large number of standard cells intermixed with larger macro blocks. The range of size in these "mixed block" designs complicates the placement process considerably; traditional methods produce results that are far from satisfactory.In this paper we extend the traditional recursive bisection standard cell placement tool Feng Shui to directly consider mixed block designs. On a set of recent benchmarks, the new version obtains placements with wire lengths substantially lower than other current tools. Compared to Feng Shui 2.4, the placements of a Capo-based approach have 29% higher wire lengths, while the placements of mPG are 26% higher. Run times of our tool are also lower, and the general approach is scalable.

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In this article, we propose new approaches for solving the useful-skew tree (UST) routing problem [Xi and Dai 1997]: clock routing subject to general skew constraints. The clock layout synthesis engine of our UST algorithms is based on the deferred-merge embedding (DME) paradigm for the zero-skew tree (ZST) [Edahiro 1992;Chao et al. 1992] and bounded-skew tree (BST) [Cong and Koh 1995;Huang et al. 1995;Kahng and Tsao 1997;Cong et al. 1998] routings; hence, the names UST/DME and Greedy-UST/DME for our UST algorithms. Our novel contribution is that we simultaneously perform skew scheduling and tree routing so that each local skew range is incrementally refined to a skew value that minimizes the wirelength increase during the bottomup merging phase of DME. As a result, not only is the skew schedule feasible, but also the wirelength increase is minimized at each merging step of clock tree construction. The experimental results show very encouraging improvement over the previous BST/DME algorithm on three ISCAS89 benchmarks under general skew constraints in terms of total routing wirelength.