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.

Abstract—As the operating frequency increases to gigahertz and the rise time of a signal is less than or comparable to the time-of-flight delay of a wire, it is necessary to consider the transmission line behavior for delay computation. We present in this paper, an analytical formula for the delay computation under the transmission line model. Extensive simulations with SPICE show the high fidelity of the formula. Compared with previous works, our model leads to smaller average errors in delay estimation. Based on this formula, we show the property that the minimum delay for a transmission line with reflection occurs when the number of round trips is minimized (i.e., equals one). Besides, we show that the delay of a circuit path is a posynomial function in wire and buffer sizes, implying that a local optimum is equal to the global optimum. Thus, we can apply any efficient search algorithm such as the well-known gradient search procedure to compute the globally optimal solution. Experimental results show that simultaneous wire and buffer sizing is very effective for performance optimization under the transmission line model. Index Terms—Buffer sizing, delay model, inductance, interconnect, performance optimization, transmission line, wire sizing.

This paper presents a sensitivity-based wiresizing algorithm for interconnect delay optimization of lossy transmission line topology under MCM technologies. Our approach computes the maximum delay and its sensitivities with respect to the widths of wires in the topology via high order moments based on an exact moment matching model[6]. Compared with other approaches, it achieves analytical sensitivity computation and calculates higher order moments (sensitivities) recursively from lower order moments for tree network. It can yield optimal wiresizing solution for interconnect delay minimization. Experiments show that the delay estimation using high order moments is very accurate compared with SPICE simulation and our approach can reduce the maximum rising delay by over 60% with small penalty in routing area. Besides delay optimization, the final solution eliminates the overshooting of response waveform and is robust under parameter variations. 1 Introduction With the rapid increase o...

In this paper, an optimization scheme is proposed for interconnect design with wire width and series resistance being design variables. Due to the distributed nature of interconnects, poles of such systems are transcendental and infinite in number. First, a two-pole approximation is used to capture the system behavior. Lower-order moments are employed to obtain two approximate dominant poles. Then, the two parameters, damping ratio and natural undamped frequency, are expressed as functions of the two dominant poles. Since the output response is characterized by the two parameters, the parameters are used to define the objective function and constraints, which form a constrained multivariable nonlinear optimization problem. After that, the optimization problem is solved using gradient projection method. One advantage of our approach is the ability to explicitly control the maximum overshoot of the observation points. Two numerical examples are given.