This paper presents a much improved, highly accurate yet efficient crosstalk noise model, the 2- ¢ model, and applies it to noiseconstrained interconnect optimizations. Compared with previous crosstalk noise models of similar complexity, our 2- ¢ model takes into consideration many key parameters, such as coupling locations (near-driver or near-receiver), and the coarse distributed RC characteristics for victim net. Thus, it is very accurate (less than 6% error on average compared with HSPICE simulations). Moreover, our model provides simple closed-form expressions for both peak noise amplitude and noise width, so it is very useful for noise-aware layout optimizations. In particular, we demonstrate its effectiveness in two applications: (i) Optimization rule generation for noise reduction using various interconnect optimization techniques; (ii) Simultaneous wire spacing to multiple nets for noise constrained interconnect minimization. 1

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.

Net weighting is a key technique in large scale timing driven placement, which plays a crucial role for deep submicron physical synthesis and timing closure. A popular way to assign net weight is based on the slack of the nets, trying to minimize the worst negative slack (WNS) for the entire circuit. While WNS is an important optimization metric, another figure of merit (FOM), defined as the total slack difference compared to a certain slack threshold for all timing end points, is of equivalent importance to measure the overall timing closure result for highly complex modern ASIC and microprocessor designs. In this paper, we perform a comprehensive analysis of the slack and FOM sensitivities to the net weight, and propose a new net weighting scheme based on the slack and FOM sensitivities. Such sensitivity analysis implicitly takes potential physical synthesis effect into consideration. Experiment results on a set of industrial circuits are promising for both stand-alone timing driven placement and physical synthesis afterwards.

Recently, several algorithms for interconnect optimization via repeater insertion and wire sizing have appeared based on the Elmore delay model. Using the Devgan noise metric [6] a noiseaware repeater insertion technique has also been proposed recently. Recognizing the conservatism of these delay and noise models, we propose a moment-matching based technique to interconnect optimization that allows for much higher accuracy while preserving the hierarchical nature of Elmore-delay-based techniques. We also present a novel approach to noise computation that accurately captures the effect of several attackers in linear time with respect to the number of attackers and wire segments. Our practical experiments with industrial nets indicate that the corresponding reduction in error afforded by these more accurate models justifies this increase in runtime for aggressive designs which is our targeted domain. Our algorithm yields delay and noise estimates within 5% of circuit simulation results.

It has been shown recently that simultaneous shield insertion and net ordering (called SINO/R as only random shields are used) provides an area-efficient solution to reduce the RLC noise. In this paper, we first develop simple formulae with errors less than 10% to estimate the number of shields in the min-area SINO/R solution. In order to accommodate pre-routed P/G wires that also serve as shields, we then formulate two new SINO problems: SINO/SPR and SINO/UPG, and propose effective and efficient two-phase algorithms to solve them. Compared to the existing dense wiring fabric scheme, the resulting SINO/SPR and SINO/UPG schemes maintain the regularity of the P/G structure, have negligible penalty on noise and delay variation, and reduce the total routing area by up to 42% and 36%, respectively. Various estimation results developed in this paper can be readily used to guide global routing and high-level design decisions.

In deep submicron digital circuits capacitive couplings make delay of a switching signal highly dependent on its neighbors ’ switching times and switching directions. A long path may have a large number of coupling neighbors with difficult to determine interdependencies. Ignoring the mutual relationship among the signals may result in a very pessimistic estimation of circuit delay. In this paper, we apply efficient functional correlation analysis techniques to identify critical paths caused by crosstalk delay effects. We also discuss applications to static timing optimization. Experiments demonstrate efficacy of the proposed technique. 1.

Abstract- As gate delays decrease faster than wire delays for each technology generation, buffer insertion becomes a popular method to reduce the interconnect delay. Several modern buffer insertion algorithms (e.g., [7, 6, 15]) are based on van Ginneken’s dynamic programming paradigm [14]. However, van Ginneken’s original algorithm does not control buffering resources and tends to over-buffering, thereby wasting area and power. It has been a major open problem whether it is possible to optimize slack and at the same time minimize the buffer usage. This paper settles this open problem by showing that for arbitrary integer cost functions, the problem is NP-complete. We also extend the pre-buffer slack technique [12] to minimize the buffer cost. This technique can significantly reduce the running time and memory in buffer cost minimization problem. The experimental results show that our algorithm can speed up the running time up to 17 times and reduces the memory to 1/30 of traditional best know algorithm. Finally, we show how to efficiently deal with multiway merge in buffer insertion. I.

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

We present a method for incorporating crosstalk reduction criteria into global routing under an innovative power supply architecture, while considering the constraints imposed by limited routing and buffering resources. An iterative procedure is employed to route the signal wires, assign supply shields, and insert buffers so that both buffer/routing capacity and signal integrity goals are met. In each iteration, shield assignment and buffer insertion are considered simultaneously via a dynamic programming-like approach. Our noise calculations are based on Devgan’s noise metric, and our work shows, for the first time, that this metric shows good fidelity on average. Experimental results on testcases with up to about 10,000 nets point towards an asymptotic run time that increases linearly with the number of nets. Our algorithm achieves noise reduction improvements of up to 53% and 28%, respectively, compared to methods considering only buffer insertion, or only shield insertion after buffer planning. 1

Variations of power and ground levels affect VLSI circuit performance. Trends in device technology and in packaging have necessitated a revision in conventional delay models. In particular, simple scalable models are needed to predict delays in the presence of uncorrelated power and ground noise. In this paper, we analyze the effect of such noise on signal propagation through a buffer and present simple, closed-form formulas to estimate the corresponding change of delay. The model captures both positive (slowdown) and negative (speedup) delay changes. It is consistent with shortchannel MOSFET behavior, including carrier velocity saturation effects. An application shows that repeater chains using buffers instead of inherently faster inverters tend to have superior supply-level-induced jitter characteristics. The expressions can be used in any existing circuit performance optimization design flow or can be combined into any delay calculations as a correction factor.