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.

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.

This paper presents an efficient approach to perform global interconnect sizing and spacing (GISS) for multiple nets to minimize interconnect delays with consideration of coupling capacitance, in addition to area and fringing capacitances. We introduce the formulation of symmetric and asymmetric wire sizing and spacing. We prove two important results on the symmetric and asymmetric effective-fringing properties which leadtoavery effective bound computation algorithm to compute the upper and lower bounds of the optimal wire sizing and spacing solution for all nets under consideration. Our experiments show that in most cases the upper and lower bounds meet quickly after a few iterations and we actually obtain the optimal solution. To our knowledge, this is the first in-depth study of global wire sizing and spacing for multiple nets with consideration of coupling capacitance. Experimental results show that our GISS solutions lead to substantial delay reduction than existing single net wire-sizing solutions without consideration of coupling capacitance.

This paper presents a set of interconnect performance estimation models for design planning with consideration of various effective interconnect layout optimization techniques, including optimal wire sizing, simultaneous driver and wire sizing, and simultaneous buffer insertion/sizing and wire sizing. These models are extremely efficient, yet provide high degree of accuracy. They have been tested on a wide range of parameters and shown to have over 90% accuracy on average compared to running best-available interconnect layout optimization algorithms directly. As a result, these fast yet accurate models can be used efficiently during high-level design space exploration, interconnect-driven design planning/synthesis, and timing-driven placement to ensure design convergence for deep submicrometer designs.

In this paper, we study the simultaneous transistor and interconnect sizing (STIS) problem. We define a class of optimization problems as CH-posynomial programs and reveal a general dominance property for all CH-posynomial programs (Theorem 1). We show that the STIS problems under a number of transistor delay models are CH-posynomial programs and propose an efficient and near-optimal STIS algorithm based on the dominance property. When used to solve the simultaneous driver/buffer and wire sizing problem for real designs, it reduces the maximum delay by up to 17.7%, and more significantly, reduces the power consumption by a factor of 61.6%, when compared with the original designs. When used to solve the transistor sizing problem, it achieves a smooth area-delay trade-off. Moreover, the algorithm optimizes a clock net of 367 drivers/buffers and 59304m-long wire in 120 seconds, and a 32bit adder with 1,026 transistors in 66 seconds on a SPARC-5 workstation.

To achieve timing closure in a placed design, buffer insertion and driver sizing are two of the most effective transforms that can be applied. Since the driver sizing solution and the buffer insertion solution affect each other, sub-optimal solutions may result if these techniques are applied sequentially instead of simultaneously. We show how to simply extend van Ginneken’s buffer insertion algorithm to simultaneously incorporate driver sizing and introduce the idea of a delay penalty to encapsulate the effect of driver sizing on the previous stage. The delay penalty can be pre-computed efficiently via dynamic programming. Experimental results show that using driver sizing with a delay penalty function obtains designs with superior timing and area characteristics. 1

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 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.