This paper presents a comprehensive survey of existing techniques for interconnect optimization during the VLSI physical design process, with emphasis on recent studies on interconnect design and optimization for high-performance VLSI circuit design under the deep submicron fabrication technologies. First, we present a number of interconnect delay models and driver/gate delay models of various degrees of accuracy and efficiency which are most useful to guide the circuit design and interconnect optimization process. Then, we classify the existing work on optimization of VLSI interconnect into the following three categories and discuss the results in each category in detail: (i) topology optimization for highperformance interconnects, including the algorithms for total wire length minimization, critical path length minimization, and delay minimization; (ii) device and interconnect sizing, including techniques for efficient driver, gate, and transistor sizing, optimal wire sizing, and simultaneous topology construction, buffer insertion, buffer and wire sizing; (iii) highperfbrmance clock routing, including abstract clock net topology generation and embedding, planar clock routing, buffer and wire sizing for clock nets, non-tree clock routing, and clock schedule optimization. For each method, we discuss its effectiveness, its advantages and limitations, as well as its computational efficiency. We group the related techniques according to either their optimization techniques or optimization objectives so that the reader can easily compare the quality and efficiency of different solutions.

Interconnect has become the dominating factor in determining circuit performance and reliability in deep submicron designs. In this embedded tutorial, we first discuss the trends and challenges of interconnect design as the technology feature size rapidly decreases towards below 0.1 micron. Then, we present commonly used interconnect models and a set of interconnect design and optimization techniques for improving interconnect performance and reliability. Finally, we present comparisons of different optimization techniques in terms of their efficiency and optimization results, and show the impact of these optimization techniques on interconnect performance in each technology generation from the 0.35µm to 0.07µm projected in the National Technology Roadmap for Semiconductors.

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In this paper, we formulated a new class of optimization problem, named the general CH-posynomial program, which is more general than the simple and bounded-variation CH-posynomial programs in [1]. We revealed the general dominance property so that an efficient and unified algorithm based on the local refinement (LR) operation can be used to optimize the simple, bounded-variation and general CH-posynomial programs. We applied the LR-based optimization algorithm to solve the device sizing problem using accurate table-based model, and the wire sizing and spacing problem with consideration of coupling between multiple nets. Both problems are solved in the context of simultaneous device and wire sizing optimization for deep submicron designs. Experiments show that our LR-based optimization algorithm is very effective and extremely efficient. Up to 16.5% delay reduction is observed when compared with previous work based on the simple device model [1], and up to 31% delay reduction and 100x speedup is observed when compared the global interconnect sizing and spacing work [2]. We believe that our general CH-posynomial formulation and LR-based algorithm can also be applied to other optimization problems in the CAD field.

As very large scale integrated (VLSI) circuits move into the era of deepsubmicron (DSM) technology and gigahertz frequency, the system performance has increasingly become dominated by the interconnect delay. This dissertation presents five related research topics on interconnect layout optimization, and interconnect extraction and modeling: the multi-source wire sizing (MSWS) problem, the simultaneous transistor and interconnect sizing (STIS) problem, the global interconnect sizing and spacing (GISS) problem, the interconnect capacitance extraction problem, and the interconnect inductance extraction problems. Given a routing tree with multiple sources, the MSWS problem determines the optimal widths of the wire segments such that the delay is minimized. We reveal several interesting properties for the optimal MSWS solution, of which the most important is the bundled refinement property. Based on this property, we propose a polynomial time algorithm, which uses iterative bundled refinement operations to compute lower and upper bounds of an optimal solution. Since the algorithm often achieves identical lower and upper bounds in experiments, the optimal solution is obtained simply by the bound computation. Furthermore, this algorithm can be used for single-source wire sizing problem and runs 100x xxi faster than previous methods. It has replaced previous single-source wire sizing methods in practice.

Field-programmable gate arrays (FPGAs) are used in a wide range of markets that have differing cost, performance and power consumption requirements. It would be advantageous if a single device family could serve these varied needs but the economics of catering to this wide distribution of market demands suggest more than one family is appropriate. Consequently, FPGA vendors have moved to provide a more diverse set of families that sit at different points in the areaspeed-power design space. In this work, our goal is to understand the circuit and architectural design attributes of an FPGA that enable tradeoffs between area and speed, and to determine the magnitude of the possible trade-offs. This will be useful for architects seeking to determine the number of device families in a suite of offerings, as well as the changes to make between families. We have found that varying both architecture and transistor sizing of an FPGA allows the effective area to change by a factor of 3.6 from largest to smallest and the speed to change by a factor of 2.6 from fastest to slowest. It is interesting to observe that the range of area and delay tradeoffs possible by varying only the transistor sizing of a single architecture is larger than the ranges observed in past architectural experiments. In addition to transistor size, we note that LUT size is one of the most useful parameters for trading off area and delay.

Successful timing analysis for high-speed integrated circuits requires accurate delay computation. However, full-custom circuits popular in today’s CPU designs make this difficult. A good circuitlevel static timing analysis tool should 1) consider both internally or externally specified input constraints; 2) handle a wide range of circuit structures; and 3) have a robust underlying framework that can be applied independent of the actual device model. In this paper, we present RESTA, a Robust and Extendable Symbolic Timing Analysis tool that aims to address these three goals. RESTA estimates the delay for all valid input assignments, while naturally handling input constraints. We start with a simple linear resistor model for transistors and from there apply various heuristics to improve the delay estimation for the circuits without altering the symbolic algorithms. Our worst-case delay estimates are within 10% of SPICE for over 90 % of the circuits we simulated.

The creation of an FPGA requires extensive transistor-level design. This is necessary for both the final design, and during architecture exploration, when many different logic and routing architectures are considered. For such explorations, it is not feasible to spend significant amounts of time on transistor-level design. This paper presents an automated transistor sizing tool for FPGA architecture exploration that uses a two-phased approach- a coarse rapid phase with simple modeling followed by refinement with much more accurate models. The output of the system is a design optimized towards a specific area-delay criterion. We compare the quality of our results to prior manual and partially automated approaches. Also, our tool has been used to produce hundreds of candidate architectures which we are releasing to support future high quality explorations.

This paper presents an overview of recent advances on modeling and layout optimization of devices and interconnects for high-performance VLSI circuit design under the deep submicron technology. First, we review a number of interconnect and driver/gate delay models, which are most useful to guide the layout optimization. Then, we summarize the available performance optimization techniques for VLSI device and interconnect layout, including driver and transistor sizing, transistor ordering, interconnecttopology optimization, optimal wire sizing, optimal buffer placement, and simultaneous topology construction, buffer insertion, buffer and wire sizing. The efficiency and impact of these techniques will be discussed in the tutorial.

A new and efficient procedure is proposed to evaluate the timing performance of VLSI circuits with circuit level accuracy. The efficiency is obtained by rapidly identifying the critical portions of the circuit at high hierarchical levels with rough delay models. These portions are then successively studied at more detailed levels for maximal accuracy. This procedure, implemented and applied to several circuits, is shown to significantly reduce the analysis time. 1 Introduction For some applications, the timing performance estimation time of a circuit is more important than the accuracy. For others, the accuracy cannot be sacrificed and there is a need for efficient and accurate timing analysis. This need increases with the complexity and speed of VLSI systems. Speed-up is usually achieved by sacrificing delay accuracy using abstract delay models, such as switch (e.g. [1, 2]) or block (e.g. [3]) level instead of circuit level (e.g. [4]). However, constraining timing analysis tools to l...