Fault Modeling of Graphene Nanoribbon FET Logic Circuits

[EN] Due to the increasing defect rates in highly scaled complementary metal-oxide-semiconductor (CMOS) devices, and the emergence of alternative nanotechnology devices, reliability challenges are of growing importance. Understanding and controlling the fault mechanisms associated with new materials and structures for both transistors and interconnection is a key issue in novel nanodevices. The graphene nanoribbon field-effect transistor (GNR FET) has revealed itself as a promising technology to design emerging research logic circuits, because of its outstanding potential speed and power properties. This work presents a study of fault causes, mechanisms, and models at the device level, as well as their impact on logic circuits based on GNR FETs. From a literature review of fault causes and mechanisms, fault propagation was analyzed, and fault models were derived for device and logic circuit levels. This study may be helpful for the prevention of faults in the design process of graphene nanodevices. In addition, it can help in the design and evaluation of defect- and fault-tolerant nanoarchitectures based on graphene circuits. Results are compared with other emerging devices, such as carbon nanotube (CNT) FET and nanowire (NW) FET.This work was supported in part by the Spanish Government under the research project TIN2016-81075-R and by Primeros Proyectos de Investigacion (PAID-06-18), Vicerrectorado de Investigacion, Innovacion y Transferencia de la Universitat Politecnica de Valencia (UPV), under the project 200190032.Gil Tomás, DA.; Gracia-Morán, J.; Saiz-Adalid, L.; Gil, P. (2019). Fault Modeling of Graphene Nanoribbon FET Logic Circuits. Electronics. 8(8):1-18. https://doi.org/10.3390/electronics8080851S11888International Technology Roadmap for Semiconductors (ITRS) 2013http://www.itrs2.net/2013-itrs.htmlSchuegraf, K., Abraham, M. C., Brand, A., Naik, M., & Thakur, R. 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Variability and reliability analysis of carbon nanotube technology in the presence of manufacturing imperfections

In 1925, Lilienfeld patented the basic principle of field effect transistor (FET). Thirty-four years later, Kahng and Atalla invented the MOSFET. Since that time, it has become the most widely used type of transistor in Integrated Circuits (ICs) and then the most important device in the electronics industry. Progress in the field for at least the last 40 years has followed an exponential behavior in accordance with Moore¿s Law. That is, in order to achieve higher densities and performance at lower power consumption, MOS devices have been scaled down. But this aggressive scaling down of the physical dimensions of MOSFETs has required the introduction of a wide variety of innovative factors to ensure that they could still be properly manufactured. Transistors have expe- rienced an amazing journey in the last 10 years starting with strained channel CMOS transistors at 90nm, carrying on the introduction of the high-k/metal-gate silicon CMOS transistors at 45nm until the use of the multiple-gate transistor architectures at 22nm and at recently achieved 14nm technology node. But, what technology will be able to produce sub-10nm transistors? Different novel materials and devices are being investigated. As an extension and enhancement to current MOSFETs some promising devices are n-type III-V and p-type Germanium FETs, Nanowire and Tunnel FETs, Graphene FETs and Carbon Nanotube FETs. Also, non-conventional FETs and other charge-based information carrier devices and alternative information processing devices are being studied. This thesis is focused on carbon nanotube technology as a possible option for sub-10nm transistors. In recent years, carbon nanotubes (CNTs) have been attracting considerable attention in the field of nanotechnology. They are considered to be a promising substitute for silicon channel because of their small size, unusual geometry (1D structure), and extraordinary electronic properties, including excellent carrier mobility and quasi-ballistic transport. In the same way, carbon nanotube field-effect transistors (CNFETs) could be potential substitutes for MOSFETs. Ideal CNFETs (meaning all CNTs in the transistor behave as semiconductors, have the same diameter and doping level, and are aligned and well-positioned) are predicted to be 5x faster than silicon CMOS, while consuming the same power. However, nowadays CNFETs are also affected by manufacturing variability, and several significant challenges must be overcome before these benefits can be achieved. Certain CNFET manufacturing imperfections, such as CNT diameter and doping variations, mispositioned and misaligned CNTs, high metal-CNT contact resistance, the presence of metallic CNTs (m-CNTs), and CNT density variations, can affect CNFET performance and reliability and must be addressed. The main objective of this thesis is to analyze the impact of the current CNFET manufacturing challenges on multi-channel CNFET performance from the point of view of variability and reliability and at different levels, device and circuit level. Assuming that CNFETs are not ideal or non-homogeneous because of today CNFET manufacturing imperfections, we propose a methodology of analysis that based on a CNFET ideal compact model is able to simulate heterogeneous or non-ideal CNFETs; that is, transistors with different number of tubes that have different diameters, are not uniformly spaced, have different source/drain doping levels, and, most importantly, are made up not only of semiconducting CNTs but also metallic ones. This method will allow us to analyze how CNT-specific variations affect CNFET device characteristics and parameters and CNFET digital circuit performance. Furthermore, we also derive a CNFET failure model and propose an alternative technique based on fault-tolerant architectures to deal with the presence of m-CNTs, one of the main causes of failure in CNFET circuits

Novel Library of Logic Gates with Ambipolar CNTFETs: Opportunities for Multi-Level Logic Synthesis

This paper exploits the unique in-field controllability of the device polarity of ambipolar carbon nanotube field effect transistors (CNTFETs) to design a technology library with higher expressive power than conventional CMOS libraries. Based on generalized NOR-NAND-AOI-OAI primitives, the proposed library of static ambipolar CNTFET gates efficiently implements XOR functions, provides full-swing outputs, and is extensible to alternate forms with area-performance tradeoffs. Since the design of the gates can be regularized, the ability to functionalize them in-field opens opportunities for novel regular fabrics based on ambipolar CNTFETs. Technology mapping of several multi-level logic benchmarks — including multipliers, adders, and linear circuits — indicates that on average, it is possible to reduce both the number of gates and area by ∼ 38% while also improving performance by 6.9×

Performance analysis of fault-tolerant nanoelectronic memories

Performance growth in microelectronics, as described by Moore’s law, is steadily approaching its limits. Nanoscale technologies are increasingly being explored as a practical solution to sustaining and possibly surpassing current performance trends of microelectronics. This work presents an in-depth analysis of the impact on performance, of incorporating reliability schemes into the architecture of a crossbar molecular switch nanomemory and demultiplexer. Nanoelectronics are currently in their early stages, and so fabrication and design methodologies are still in the process of being studied and developed. The building blocks of nanotechnology are fabricated using bottom-up processes, which leave them highly susceptible to defects. Hence, it is very important that defect and fault-tolerant schemes be incorporated into the design of nanotechnology related devices. In this dissertation, we focus on the study of a novel and promising class of computer chip memories called crossbar molecular switch memories and their demultiplexer addressing units. A major part of this work was the design of a defect and fault tolerance scheme we called the Multi-Switch Junction (MSJ) scheme. The MSJ scheme takes advantage of the regular array geometry of the crossbar nanomemory to create multiple switches in the fabric of the crossbar nanomemory for the storage of a single bit. Implementing defect and fault tolerant schemes come at a performance cost to the crossbar nanomemory; the challenge becomes achieving a balance between device reliability and performance. We have studied the reliability induced performance penalties as they relate to the time (delay) it takes to access a bit, and the amount of power dissipated by the process. Also, MSJ was compared to the banking and error correction coding fault tolerant schemes. Studies were also conducted to ascertain the potential benefits of integrating our MSJ scheme with the banking scheme. Trade-off analysis between access time delay, power dissipation and reliability is outlined and presented in this work. Results show the MSJ scheme increases the reliability of the crossbar nanomemory and demultiplexer. Simulation results also indicated that MSJ works very well for smaller nanomemory array sizes, with reliabilities of 100% for molecular switch failure rates in the 10% or less range

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

Training Single Walled Carbon Nanotube based Materials to perform computation

This thesis illustrates the use of Single Walled Carbon Nanotube based materials for the solution of various computational problems by using the process of computer controlled evolution. The study aims to explore and identify three dimensions of a form of unconventional computing called, `Evolution-in-materio'. First, it focuses on identifying suitable materials for computation. Second, it explores suitable methods, i.e. optimisation and evolutionary algorithms to train these materials to perform computation. And third, it aims to identify suitable computational problems to test with these materials. Different carbon based materials, mainly single walled carbon nano-tubes with their varying concentrations in polymers have been studied to be trained for different computational problems using the principal of `evolution-in-materio'. The conductive property of the materials is used to train these materials to perform some meaningful computation. The training process is formulated as an optimisation problem with hardware in loop. It involves the application of an external stimuli (voltages) on the material which brings changes in its electrical properties. In order to train the material for a specific computational problem, a large number of configuration signals need to be tested to find the one that transforms the incident signal in such a way that a meaningful computation can be extracted from the material. An evolutionary algorithm is used to identify this configuration data and using a hardware platform, this data is transformed into incident signals. Depending on the computational problem, the specific voltages signals when applied at specific points on to the material, as identified by an evolutionary algorithm, can make the material behave as a Logic gate, a tone discriminator or a data classifier. The problem is implemented on two types of hardware platforms, one a more simple implementation using mbed ( a micro- controller) and other is a purpose-built platform for `Evolution-in-materio" called Mecobo. The results of this study showed that the single walled carbon nanotube composites can be trained to perform simple computational tasks (such as tone discriminator, AND, OR logic gates and a Half adder circuit), as well as complex computational problems such as Full Adder circuit and various binary and multiple class machine learning problems. The study has also identified the suitability of using evolutionary algorithms such as Particle Swarm Optimisation algorithm (PSO) and Differential evolution for finding solutions of complex computational problems such as complex logic gates and various machine learning classification problems. The implementation of classification problem with the carbon nanotube based materials also identified the role of a classifier. It has been found that K-nearest neighbour method and its variant kNN ball tree algorithm are more suitable to train carbon nanotube based materials for different classification problems. The study of varying concentrations of single walled carbon nanotubes in fixed polymer ratio for the solution of different computational problems provided an indication of the link between single walled carbon nanotubes concentration and ability to solve computational problem. The materials used in this study showed stability in the results for all the considered computational problems. These material systems can compliment the current electronic technology and can be used to create a new type of low energy and low cost electronic devices. This offers a promising new direction for evolutionary computation

Cutting Edge Nanotechnology

The main purpose of this book is to describe important issues in various types of devices ranging from conventional transistors (opening chapters of the book) to molecular electronic devices whose fabrication and operation is discussed in the last few chapters of the book. As such, this book can serve as a guide for identifications of important areas of research in micro, nano and molecular electronics. We deeply acknowledge valuable contributions that each of the authors made in writing these excellent chapters

Appropriateness of Imperfect CNFET Based Circuits for Error Resilient Computing Systems

With superior device performance consistently reported in extremely scaled dimensions, low dimensional materials (LDMs), including Carbon Nanotube Field Effect Transistor (CNFET) based technology, have shown the potential to outperform silicon for future transistors in advanced technology nodes. Studies have also demonstrated orders of magnitude improvement in energy efficiency possible with LDMs, in comparison to silicon at competing technology nodes. However, the current fabrication processes for these materials suffer from process imperfections and still appear to be inadequate to compete with silicon for the mainstream high volume manufacturing. Among the LDMs, CNFETs are the most widely studied and closest to high volume manufacturing. Recent works have shown a significant increase in the complexity of CNFET based systems, including demonstration of a 16-bit microprocessor. However, the design of such systems has involved significantly wider-than-usual transistors and avoidance of certain logic combinations. The resulting complexity of several thousand transistors in such systems is still far from the requirements of high-performance general-purpose computing systems having billions of transistors. With the current progress of the process to fabricate CNFETs, their introduction in mainstream manufacturing is expected to take several more years. For an earlier technology adoption, CNFETs appear to be suited for error-resilient computing systems where errors during computation can be tolerated to a certain degree. Such systems relax the need for precise circuits and a perfect process while leveraging the potential energy benefits of CNFET technology in comparison to conventional Si technology. In this thesis, we explore the potential applications using an imperfect CNFET process for error-resilient computing systems, including the impact of the process imperfections at the system level and methods to improve it. The current most widely adopted fabrication process for CNFETs (separation and placement of solution-based CNTs) still suffers from process imperfections, mainly from open CNTs due to missing of CNTs (in trenches connecting source and drain of CNFET). A fair evaluation of the performance of CNFET based circuits should thus take into consideration the effect of open CNTs, resulting in reduced drive currents. At the circuit level, this leads to failures in meeting 1) the minimum frequency requirement (due to an increase in critical path delay), and 2) the noise suppression requirement. We present a methodology to accurately capture the effect of open CNT imperfection in the state-of-the-art CNFET model, for circuit-level performance evaluation (both delay and glitch vulnerability) of CNFET based circuits using SPICE. A Monte Carlo simulation framework is also provided to investigate the statistical effect of open CNT imperfection on circuit-level performance. We introduce essential metrics to evaluate glitch vulnerability and also provide an effective link between glitch vulnerability and circuit topology. The past few years have observed significant growth of interest in approximate computing for a wide range of applications, including signal processing, data mining, machine learning, image, video processing, etc. In such applications, the result quality is not compromised appreciably, even in the presence of few errors during computation. The ability to tolerate few errors during computation relaxes the need to have precise circuits. Thus the approximate circuits can be designed, with lesser nodes, reduced stages, and reduced capacitance at few nodes. Consequently, the approximate circuits could reduce critical path delays and enhanced noise suppression in comparison to precise circuits. We present a systematic methodology utilizing Reduced Ordered Binary Decision Diagrams (ROBDD) for generating approximate circuits by taking an example of 16-bit parallel prefix CNFET adder. The approximate adder generated using the proposed algorithm has ~ 5x reduction in the average number of nodes failing glitch criteria (along paths to primary output) and 43.4% lesser Energy Delay Product (EDP) even at high open CNT imperfection, in comparison to the ideal case of no open CNT imperfection, at a mean relative error of 3.3%. The recent boom of deep learning has been made possible by VLSI technology advancement resulting in hardware systems, which can support deep learning algorithms. These hardware systems intend to satisfy the high-energy efficiency requirement of such algorithms. The hardware supporting such algorithms adopts neuromorphic-computing architectures with significantly less energy compared to traditional Von Neumann architectures. Deep Neural Networks (DNNs) belonging to deep learning domain find its use in a wide range of applications such as image classification, speech recognition, etc. Recent hardware systems have demonstrated the implementation of complex neural networks at significantly less power. However, the complexity of applications and depths of DNNs are expected to drastically increase in the future, imposing a demanding requirement in terms of scalability and energy efficiency of hardware technology. CNFET technology can be an excellent alternative to meet the aggressive energy efficiency requirement for future DNNs. However, degradation in circuit-level performance due to open CNT imperfection can result in timing failure, thus distorting the shape of non-linear activation function, leading to a significant degradation in classification accuracy. We present a framework to obtain sigmoid activation function considering the effect of open CNT imperfection. A digital neuron is explored to generate the sigmoid activation function, which deviates from the ideal case under imperfect process and reduced time period (increased clock frequency). The inherent error resilience of DNNs, on the other hand, can be utilized to mitigate the impact of imperfect process and maintain the shape of the activation function. We use pruning of synaptic weights, which, combined with the proposed approximate neuron, significantly reduces the chance of timing failures and helps to maintain the activation function shape even at high process imperfection and higher clock frequencies. We also provide a framework to obtain classification accuracy of Deep Belief Networks (class of DNNs based on unsupervised learning) using the activation functions obtained from SPICE simulations. By using both approximate neurons and pruning of synaptic weights, we achieve excellent system accuracy (only < 0.5% accuracy drop) with 25% improvement in speed, significant EDP advantage (56.7% less) even at high process imperfection, in comparison to a base configuration of the precise neuron and no pruning with the ideal process, at no area penalty. In conclusion, this thesis provides directions for the potential applicability of CNFET based technology for error-resilient computing systems. For this purpose, we present methodologies, which provide approaches to assess and design CNFET based circuits, considering process imperfections. We accomplish a DBN framework for digit recognition, considering activation functions from SPICE simulations incorporating process imperfections. We demonstrate the effectiveness of using approximate neuron and synaptic weight pruning to mitigate the impact of high process imperfection on system accuracy