Physical Parameter Based Model for Characteristic Impedance of SWCNT Interconnects and its Performance Analysis

Single walled carbon nanotubes (SWCNTs) have been identified as a possible replacement for copper interconnects due to their magnificent electrical and material properties. A series of performance predictions of these interconnects have been done in the last decade. Even then none of the literatures have been provided compact expression for characteristic impedance (Zo) in terms of physical parameters of SWCNT interconnects. A simplified representation of characteristic impedance and the analyze the transient behavior under different mismatch conditions will enable the chip designer to optimize the performance of total circuitry. These studies give an overview of safe amount of load mismatch that can be tolerated by different lengths of interconnects without causing any signal reliability issues. Keywords: SWCNTs, CNT Interconnects, characteristic impedance, transient response, frequency response, load mismatc

Electrical conductivity of carbon nanotubes grown inside a mesoporous anodic aluminium oxide membrane

Well-aligned, open-ended carbon nanotubes (CNTs), free of catalyst and other carbon products, were synthesized inside the pores of an anodic aluminium oxide (AO) template without using any metallic catalyst. The CNTs and the CNT/AO composites were characterized by scanning and transmission electron microscopy, thermogravimetric analysis, Raman spectroscopy and X-ray diffraction. Particular care was devoted to the reactor design, synthesis conditions, the catalytic role of the templating alumina surface and the preservation of the alumina structure. The transport properties (sorption, diffusion and permeability) to water vapor were evaluated for both the alumina template and the CNT/AO composite membrane. The measured effective electrical volume conductivity of the CNT/AO composite was found ranging from a few up to 10 kS/m, in line with the recent literature. The estimated averaged values of the CNTs-wall conductivity was around 50 kS/m

Performance assessment of multi-walled carbon nanotube interconnects using advanced polynomial chaos schemes

2019 Spring.Includes bibliographical references.With the continuous miniaturization in the latest VLSI technologies, manufacturing uncertainties at nanoscale processes and operations are unpredictable at the chip level, packaging level and at board levels of integrated systems. To overcome such issues, simulation solvers to model forward propagation of uncertainties or variations in random processes at the device level to the network response are required. Polynomial Chaos Expansion (PCE) of the random variables is the most common technique to model the unpredictability in the systems. Existing methods for uncertainty quantification have a major drawback that as the number of random variables in a system increases, its computational cost and time increases in a polynomial fashion. In order to alleviate the poor scalability of standard PC approaches, predictor-corrector polynomial chaos scheme and hyperbolic polynomial chaos expansion (HPCE) scheme are being proposed in this dissertation. In the predictor-corrector polynomial scheme, low-fidelity meta-model is generated using Equivalent Single Conductor (ESC) approximation model and then its accuracy is enhanced using low order multi-conductor circuit (MCC) model called a corrector model. In HPCE, sparser polynomial expansion is generated based on the hyperbolic criterion. These schemes result in an immense reduction in CPU cost and speed. This dissertation presents the novel approach to quantify the uncertainties in multi-walled carbon nano-tubes using these schemes. The accuracy and validation of these schemes are shown using various numerical examples

Novel methods to quantify aleatory and epistemic uncertainty in high speed networks

2017 Summer.Includes bibliographical references.With the sustained miniaturization of integrated circuits to sub-45 nm regime and the increasing packaging density, random process variations have been found to result in unpredictability in circuit performance. In existing literature, this unpredictability has been modeled by creating polynomial expansions of random variables. But the existing methods prove inefficient because as the number of random variables within a system increase, the time and computational cost increases in a near-polynomial fashion. In order to mitigate this poor scalability of conventional approaches, several techniques are presented, in this dissertation, to sparsify the polynomial expansion. The sparser polynomial expansion is created, by identifying the contribution of each random variable on the total response of the system. This sparsification is performed primarily using two different methods. It translates to immense savings, in the time required, and the memory cost of computing the expansion. One of the two methods presented is applied to aleatory variability problems while the second method is applied to problems involving epistemic uncertainty. The accuracy of the proposed approaches is validated through multiple numerical examples

Worst-Case Analysis of Electrical and Electronic Equipment via Affine Arithmetic

In the design and fabrication process of electronic equipment, there are many unkown parameters which significantly affect the product performance. Some uncertainties are due to manufacturing process fluctuations, while others due to the environment such as operating temperature, voltage, and various ambient aging stressors. It is desirable to consider these uncertainties to ensure product performance, improve yield, and reduce design cost. Since direct electromagnetic compatibility measurements impact on both cost and time-to-market, there has been a growing demand for the availability of tools enabling the simulation of electrical and electronic equipment with the inclusion of the effects of system uncertainties. In this framework, the assessment of device response is no longer regarded as deterministic but as a random process. It is traditionally analyzed using the Monte Carlo or other sampling-based methods. The drawback of the above methods is large number of required samples to converge, which are time-consuming for practical applications. As an alternative, the inherent worst-case approaches such as interval analysis directly provide an estimation of the true bounds of the responses. However, such approaches might provide unnecessarily strict margins, which are very unlikely to occur. A recent technique, affine arithmetic, advances the interval based methods by means of handling correlated intervals. However, it still leads to over-conservatism due to the inability of considering probability information. The objective of this thesis is to improve the accuracy of the affine arithmetic and broaden its application in frequency-domain analysis. We first extend the existing literature results to the efficient time-domain analysis of lumped circuits considering the uncertainties. Then we provide an extension of the basic affine arithmetic to the frequency-domain simulation of circuits. Classical tools for circuit analysis are used within a modified affine framework accounting for complex algebra and uncertainty interval partitioning for the accurate and efficient computation of the worst case bounds of the responses of both lumped and distributed circuits. The performance of the proposed approach is investigated through extensive simulations in several case studies. The simulation results are compared with the Monte Carlo method in terms of both simulation time and accuracy

Carbon Nanotube Interconnect Modeling for Very Large Scale Integrated Circuits

In this research, we have studied and analyzed the physical and electrical properties of carbon nanotubes. Based on the reported models for current transport behavior in non-ballistic CNT-FETs, we have built a dynamic model for non-ballistic CNT-FETs. We have also extended the surface potential model of a non-ballistic CNT-FET to a ballistic CNT-FET and developed a current transport model for ballistic CNT-FETs. We have studied the current transport in metallic carbon nanotubes. By considering the electron-electron interactions, we have modified two-dimensional fluid model for electron transport to build a semi-classical one-dimensional fluid model to describe the electron transport in carbon nanotubes, which is regarded as one-dimensional system. Besides its accuracy compared with two-dimensional fluid model and Lüttinger liquid theory, one-dimensional fluid model is simple in mathematical modeling and easier to extend for electronic transport modeling of multi-walled carbon nanotubes and single-walled carbon nanotube bundles as interconnections. Based on our reported one-dimensional fluid model, we have calculated the parameters of the transmission line model for the interconnection wires made of single-walled carbon nanotube, multi-walled carbon nanotube and single-walled carbon nanotube bundle. The parameters calculated from these models show close agreements with experiments and other proposed models. We have also implemented these models to study carbon nanotube for on-chip wire inductors and it application in design of LC voltage-controlled oscillators. By using these CNT-FET models and CNT interconnects models, we have studied the behavior of CNT based integrated circuits, such as the inverter, ring oscillator, energy recovery logic; and faults in CNT based circuits