With the rapid developments in very large-scale integration (VLSI) technology, design and computer-aided design (CAD) techniques, at both the chip and package level, the operating frequencies are fast reaching the vicinity of gigahertz and switching times are getting to the subnanosecond levels. The ever increasing quest for high-speed applications is placing higher demands on interconnect performance and highlighted the previously negligible effects of interconnects such as ringing, signal delay, distortion, reflections, and crosstalk. In this review paper various high-speed interconnect effects are briefly discussed. In addition, recent advances in transmission line macromodeling techniques are presented. Also, simulation of high-speed interconnects using model-reduction-based algorithms is discussed in detail.

/pdf/simulation-of-high-speed-interconnects-4k5dt3lsur.pdf

Simulation of high-speed interconnects

http://users.ece.gatech.edu/limsk/www/pdfs/integration97.pdf

Performance optimization of VLSI interconnect layout

In this work, a finite difference formulation is used to simulate large networks. The method makes use or introduces reactive latency in all branches and nodes of a circuit to generate update algorithms for the voltage and current quantities. A criterion is established that guarantees the stability of the algorithm for specified choices of the time step. Because of its linear numerical complexity, several orders of magnitude in speedup over matrix-based methods are obtained. Nonlinear networks can also be simulated by the formulation. Several comparisons are made with standard simulators in order to evaluate the accuracy and efficiency of the algorithm. In all cases that satisfy the stability criterion, good agreements with established techniques are obtained.

Latency insertion method (LIM) for the fast transient simulation of large networks

In this paper, we study the interconnect layout optimization problem under a higher-order RLC model to optimize not just delay, but also waveform for RLC circuits with non-monotone signal response. We propose a unified approach that considers topology optimization, wiresizing optimization, and waveform optimization simultaneously. Our algorithm considers a large class of routing topologies, ranging from shortest-path Steiner trees to bounded-radius Steiner trees and Steiner routings. We construct a set of required-arrival-time Steiner trees or RATS-trees, providing a smooth trade-off among signal delay, waveform, and routing area. Using a new incremental moment computation algorithm, we interleave topology construction with moment computation to facilitate accurate delay calculation and evaluation of waveform quality. Experimental results show that our algorithm is able to construct a set of topologies providing a smooth trade-off among signal delay, signal settling time, voltage overshoot, and routing cost.

/pdf/interconnect-design-for-deep-submicron-ics-1wpzzxlew8.pdf

Interconnect design for deep submicron ICs

As the integrated circuits (ICs) are scaled into nanometer dimensions and operate in gigahertz frequencies, interconnects have become critical in determining system performance and reliability. This paper presents the ongoing research effort at UCLA in developing an interconnect-centric design flow, including interconnect planning, interconnect synthesis, and interconnect layout, which allows interconnect design and optimization to be properly considered at every level of the design process. Efficient interconnecter performance estimation models and tools at various levels are also developed to support such an interconnect-centric design flow.

An interconnect-centric design flow for nanometer technologies

In this paper, we introduce a general method of interconnect simulation based on distributed circuits. The algorithm is very efficient and consists of two main steps. In the first step, each distributed line is modeled by a finite order system with passivity preservation and multipoint moment matching of its input admittance/impedance matrix. In the second step, an Arnoldi-based congruence transform is applied to the network to form its reduced order model. The main feature of the algorithm is in its first step, where a passive multipoint moment matching model of a distributed line can be generated without any discretization of the line. We provide an integrated-congruence transform which can be directly applied to the partial differential equations of a distributed line and generate a passive finite order system as its model. We also provide an algorithm based on the L/sup 2/ Hilbert space theory so that exact moment matching at multiple points can be obtained, We demonstrate the accuracy of our method with examples and show the advantage of ours over conventional ones based on lumped circuit models.

Passive multipoint moment matching model order reduction algorithm on multiport distributed interconnect networks

Model-order reduction is a key technique to do fast simulation of interconnect networks. Among many model-order reduction algorithms, those based on projection methods work quite well. In this paper, we review the projection-based algorithms in two categories. The first one is the coefficient matching algorithms. We generalize the Krylov subspace method on moment matching at a single point, to multipoint moment-matching methods with matching points located anywhere in the closed right-hand side (RHS) of the complex plane, and we provide algorithms matching the coefficients of series expansion-based on orthonormal polynomials and generalized orthonormal basis functions in Hilbert and Hardy space. The second category belongs to the grammian-based algorithms, where we provide efficient algorithm for the computation of grammians and new approximate grammian-based approaches. We summarize some important properties of projection-based algorithms so that they may be used more flexibly.

On projection-based algorithms for model-order reduction of interconnects

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. 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 over-shoot of response waveform and is robust under parameter variations.

A sensitivity-based wiresizing approach to interconnect optimization of lossy transmission line topologies

In today's deep submicrometer technology the coupling capacitances among individual on-chip RC trees have an essential effect on the signal delay and crosstalk, and the interconnects should be modeled as coupled RC trees. In this paper we provide simple exact explicit formulas for the Elmore delay and higher order voltage moments and a linear order recursive algorithm for the voltage moment computation for lumped and distributed coupled RC trees. By using the formulas and algorithms, the moment-matching method can be efficiently implemented to deal with delay and crosstalk estimation, model order reduction, and optimal design of interconnects. As an application of the algorithm, we provide a new efficient and accurate model for crosstalk estimation in coupled RC trees. Simulation results show it works better than existing methods.

Moment computation of lumped and distributed coupled RC trees with application to delay and crosstalk estimation

We provide a multipoint moment matching model for multiport distributed interconnect networks. We introduce a new concept: integrated congruence transform which can be applied to the partial differential equations of a distributed line and generate a passive finite order system as its model. Moreover, we also provide an efficient algorithm based on the L/sup 2/ Hilbert space theory so that exact moment matching at multiple points can be obtained.

/pdf/multipoint-moment-matching-model-for-multiport-distributed-4bfew5j9ca.pdf

Qingjian Yu

Papers

Passive multipoint moment matching model order reduction algorithm on multiport distributed interconnect networks

On projection-based algorithms for model-order reduction of interconnects

A sensitivity-based wiresizing approach to interconnect optimization of lossy transmission line topologies

Moment computation of lumped and distributed coupled RC trees with application to delay and crosstalk estimation

Multipoint moment matching model for multiport distributed interconnect networks