| The ongoing scaling of high-end digital ICs has increased the number of devices on a chip. Consequently, interconnect wiring density has also risen considerably. This inevitably results in massive electromagnetic coupling among neighboring wires, directly limiting circuit performance. Furthermore, on-chip, low-resistance (Cu) power- and clock-distribution networks give rise to inductance effects, particularly as clock frequency increases along with integration density. Impulse-response (IR) moments derived from an appropriate RLC interconnect model can be a computationally efficient means of analysis for the design of massively coupled digital ICs. This, we consider the primary subject of the Thesis.;In recent times, researchers have been seeking novel materials for future high-performance IC interconnects. One prime candidate, today, is the carbon nanotube (CNT) bundle. It can be adequately described with a distributed lumped-element electrical network. This suggests that an efficient IR moment-extraction algorithm would facilitate predictive electrical analysis of both conventional and non-conventional interconnects.;In this Thesis, as a preliminary theoretical investigation, we estimate a so-called "Granularity Metric" to evaluate digital-circuit nodal density in hypothetical CNT-bundle interconnects. Nodal density has a direct impact on the true circuit complexity of IC interconnects. Thus, our preliminary investigation will drive our main Thesis objective, which we will present later.;In deducing the Granularity Metric, we employed the well-known complex wave-propagation constant. We defined four hypothetical CNT bundles with various cross-sectional dimensions, all operating under a 10GHz clock, with 10ps edge resolution. The results indicated that no nodal discretization was needed for 50nmx 50nm and 500nmx 500nm wires. For 5micromx 5microm and 50micromx 50microm wires, the Granularity Metric was on the order of 1mm to 10mm. For better accuracy, we subsequently included skin effect, kinetic inductance, and return-path resistance as part of a second, more refined calculation. This refined analysis confirmed our previous 1mm to 10mm Granularity Metric.;We now turn to the principal focus of the Thesis. We have created, for the first time, a stochastic algorithm for arbitrary-order IR moment extraction in RLC IC-interconnect networks. To maintain full parallelism, our algorithm stochastically estimates the underlying s-domain IR circuit equation solution by means of Cramer's Rule. The algorithm, as we have devised it, computes the IR solution for only the orders of s we require. By expanding the Cramer Numerator-to-Denominator ratio in powers of s, we establish a simple mathematical connection to any desired IR moment.;Our algorithm was preliminarily tested with 3-, 5- and 10-stage RLC coupled-line interconnect networks. IR moments were determined for both active- and passive-line outputs, and were compared to exact analytical values. An error of less than 0.1% was obtained for moments up to tenth order, at 1G stochastic samples.;In conclusion, we believe an algorithm similar to the one we have discovered here may become a viable alternative for future, high-end digital IC CAD. |
