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.

This paper considers simultaneous gate and wire sizing for general VLSI circuits under the Elmore delay model. We present a fast and exact algorithm which can minimize total area subject to maximum delay bound. The algorithm can be easily modified to give exact algorithms for optimizing several other objectives (e.g. minimizing maximum delay or minimizing total area subject to arrival time specifications at all inputs and outputs). No previous algorithm for simultaneous gate and wire sizing can guarantee exact solutions for general circuits. Our algorithm is an iterative one with a guarantee on convergence to global optimal solutions. It is based on Lagrangian relaxation and "one-gate/wire-at-a-time" local optimizations, and is extremely economical and fast. For example, we can optimize a circuit with 13824 gates and wires in about 13 minutes using under 12 MB memory on an IBM RS/6000 workstation. 1 Introduction Since the invention of integrated circuits almost 40 years ago, gate si...

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.

As the IC devices is scaled into nanometer dimen- sions and operates in giga-hertz frequencies, interconnect design and optimization have become critical in determining the system performance and reliability.

In this paper we formulate three classes of optimization problems: the simple, monotonically-constrained, and bounded CH-programs. We reveal the dominance property under the local refinement (LR) operation for the simple CH-program, as well as the general dominance property under the pseudo-LR operation for the monotonically-constrained CH-program and the extended-LR operation for the bounded CH-program. These properties enable a very efficient polynomial-time algorithm, using different types of LR operations to compute tight lower and upper bounds of the exact solution to any CH-program. We show that the algorithm is capable of solving many layout optimization problems in deep submicron IC and/or high-performance MCM/PCB designs. In particular, we apply...

In this paper, we study the simultaneous transistor and interconnect sizing (STIS) problem. Our contributions include: (1) We formulated the STIS problem using a distributed RC circuit model which models the waveformdependent transistor resistances, the distributed nature of the interconnects and the transistor-interconnect interactions. (2) We showed a general dominance property for a large class of posynomial functions (Theorems 1 and 2) and developed efficient algorithms based on recursive local refinement or bundled refinement for optimizing such functions. Although our intended application is to develop optimal algorithms for the STIS problem under a wide range of transistor and interconnect models, it also has direct applications to many other optimization problems in VLSI CAD and other domains. (3) Based on the general dominance property, we developed efficient and optimal algorithms for the STIS problem, which are much more efficient than the mathematical programming based methods such as the convex-programming based transistor-sizing and superior to the sensitivity-based heuristics used in many transistor or interconnect sizing works in terms of both global convergence and optimality. The preliminary experiments for both transistor sizing and simultaneous transistor and interconnect sizing are reported. To our knowledge, this is the first in-depth study of the simultaneous transistor and interconnect sizing problem. 1 1

In this paper we formulate three classes of optimization problems: the simple, monotonically constrained, and bounded Cong-He (CH)-programs. We reveal the dominance property under the local refinement (LR) operation for the simple CH-program, as well as the general dominance property under the pseudo-LR operation for the monotonically constrained CH-program and the extended-LR operation for the bounded CH-program. These properties enable a very efficient polynomial-time algorithm, using different types of LR operations to compute tight lower and upper bounds of the exact solution to any CH-program. We show that the algorithm is capable of solving many layout optimization problems in deep submicron iterative circuit and/or high-performance multichip module (MCM) and printed circuit board (PCB) designs. In particular, we apply the algorithm to the simultaneous transistor and interconnect sizing problem, and to the global interconnect sizing and spacing problem considering the coupling cap...

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.

We present a subjective review of custom cell generation methods in the context of future advances in state-of-the-art digital circuit synthesis. In particular, we describe three opportunities for coupling circuit optimization operations with the library development process. These operations include electrical optimization, technology mapping, and cell level place and route. 1.# Introduction Several methods have been developed in recent years for the automatic generation of cell libraries. This effort has been largely motivated by a need for alternatives to manual layout thereby reducing library development costs and time to market. The most common approaches are layout generators, re-compaction of existing libraries, and automatic cell synthesis. Procedural layout generators, which are either languagebased or interfaced with a symbolic layout system, are a means of capturing the layout design in a somewhat designrule independent fashion. This is useful in reducing the layout creati...

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.