Imperfection-Aware Design of CNFET Digital VLSI Circuits

Carbon nanotube field-effect transistor (CNFET) is one of the promising candidates as extensions to silicon CMOS devices. The CNFET, which is a 1-D structure with a near-ballistic transport capability, can potentially offer excellent device characteristics and order-of-magnitude better energy-delay product over standard CMOS devices. Significant challenges in CNT synthesis prevent CNFETs today from achieving such ideal benefits. CNT density variation and metallic CNTs are the dominant type of CNT variations/imperfections that cause performance variation, large static power consumption, and yield degradation. We present an imperfection-aware design technique for CNFET digital VLSI circuits by: 1) Analytical models that are developed to analyze and quantify the effects of CNT density variation on device characteristics, gate and system levels delays. The analytical models, which were validated by comparison to real experimental/simulation data, enables us to examine the space of CNFET combinational, sequential and memory cells circuits to minimize delay variations. Using these model, we drive CNFET processing and circuit design guidelines to manage/overcome CNT density variation. 2) Analytical models that are developed to analyze the effects of metallic CNTs on device characteristics, gate and system levels delay and power consumption. Using our presented analytical models, which are again validated by comparison with simulation data, it is shown that the static power dissipation is a more critical issue than the delay and the dynamic power of CNFET circuits in the presence of m-CNTs. 3) CNT density variation and metallic CNTs can result in functional failure of CNFET circuits. The complete and compact model for CNFET probability of failure that consider CNT density variation and m-CNTs is presented. This analytical model is applied to analyze the logical functional failures. The presented model is extended to predict opportunities and limitations of CNFET technology at todays Gigascale integration and beyond.\u2

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

Robust Circuit & Architecture Design in the Nanoscale Regime

Silicon based integrated circuit (IC) technology is approaching its physical limits. For sub 10nm technology nodes, the carbon nanotube (CNT) based field effect transistor has emerged as a promising device because of its excellent electronic properties. One of the major challenges faced by the CNT technology is the unwanted growth of metallic tubes. At present, there is no known CNT fabrication technology which allows the fabrication of 100% semiconducting CNTs. The presence of metallic tubes creates a short between the drain and source terminals of the transistor and has a detrimental impact on the delay, static power and yield of CNT based gates. This thesis will address the challenge of designing robust carbon nanotube based circuits in the presence of metallic tubes. For a small percentage of metallic tubes, circuit level solutions are proposed to increase the functional yield of CNT based gates in the presence of metallic tubes. Accurate analytical models with less than a 3% inaccuracy rate are developed to estimate the yield of CNT based circuit for a different percentage of metallic tubes and different drive strengths of logic gates. Moreover, a design methodology is developed for yield-aware carbon nanotube based circuits in the presence of metallic tubes using different CNFET transistor configurations. Architecture based on regular logic bricks with underlying hybrid CNFET configurations are developed which gives better trade-offs in terms of performance, power, and functional yield. In the case when the percentage of metallic tubes is large, the proposed circuit level techniques are not sufficient. Extra processing techniques must be applied to remove the metallic tubes. The tube removal techniques have trade-offs, as the removal process is not perfect and removes semiconducting tubes in addition to removing unwanted metallic tubes. As a result, stochastic removal of tubes from the drive and fanout gate(s) results in large variation in the performance of CNFET based gates and in the worst case open circuit gates. A Monte Carlo simulation engine is developed to estimate the impact of the removal of tubes on the performance and power of CNFET based logic gates. For a quick estimation of functional yield of logic gates, accurate analytical models are developed to estimate the functional yield of logic gates when a fraction of the tubes are removed. An efficient tube level redundancy (TLR) is proposed, resulting in a high functional yield of carbon nanotube based circuits with minimal overheads in terms of area and power when large fraction of tubes are removed. Furthermore, for applications where parallelism can be utilized we propose to increase the functional yield of the CNFET based circuits by increasing the logic depth of gates

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

Overcoming nanoscale variations through statistical error compensation

Increasingly severe parameter variations that are observed in advanced nanoscale technologies create great obstacles in designing high-performance, next-generation digital integrated circuits (ICs). Conventional design principles impose increased design margins in power supply, device sizing, and operating frequency, leading to overly conservative designs which prevent the realization of potential benefits from nanotechnology advances. In response, robust digital circuit design techniques have been developed to overcome processing non-idealities. Statistical error compensation (SEC) is a class of system-level, communication-inspired techniques for designing energy efficient and robust systems. In this thesis, stochastic sensor network on chip (SSNOC), a known SEC technique, is applied to a computational kernel implemented with carbon nanotube field-effect transistors (CNFETs). With the aid of a well developed CNFET delay distribution modeling method, circuit simulations show up to 90× improvement of the SSNOC-based design in the circuit yield over the conventional design. The results verify the robustness of an SEC-based design under CNFET-specific variations. The error resiliency of SEC allows CNFET circuits to operate with reduced design margins under relaxed processing requirements, while concurrently maintaining the desired application-level performance

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

New Logic Synthesis As Nanotechnology Enabler (invited paper)

Nanoelectronics comprises a variety of devices whose electrical properties are more complex as compared to CMOS, thus enabling new computational paradigms. The potentially large space for innovation has to be explored in the search for technologies that can support large-scale and high- performance circuit design. Within this space, we analyze a set of emerging technologies characterized by a similar computational abstraction at the design level, i.e., a binary comparator or a majority voter. We demonstrate that new logic synthesis techniques, natively supporting this abstraction, are the technology enablers. We describe models and data-structures for logic design using emerging technologies and we show results of applying new synthesis algorithms and tools. We conclude that new logic synthesis methods are required to both evaluate emerging technologies and to achieve the best results in terms of area, power and performance

Dense implementations of binary cellular nonlinear networks : from CMOS to nanotechnology

This thesis deals with the design and hardware realization of the cellular neural/nonlinear network (CNN)-type processors operating on data in the form of black and white (B/W) images. The ultimate goal is to achieve a very compact yet versatile cell structure that would allow for building a network with a very large spatial resolution. It is very important to be able to implement an array with a great number of cells on a single die. Not only it improves the computational power of the processor, but it might be the enabling factor for new applications as well. Larger resolution can be achieved in two ways. First, the cell functionality and operating principles can be tailored to improve the layout compactness. The other option is to use more advanced fabrication technology – either a newer, further downscaled CMOS process or one of the emerging nanotechnologies. It can be beneficial to realize an array processor as two separate parts – one dedicated for gray-scale and the other for B/W image processing, as their designs can be optimized. For instance, an implementation of a CNN dedicated for B/W image processing can be significantly simplified. When working with binary images only, all coefficients in the template matrix can also be reduced to binary values. In this thesis, such a binary programming scheme is presented as a means to reduce the cell size as well as to provide the circuits composed of emerging nanodevices with an efficient programmability. Digital programming can be very fast and robust, and leads to very compact coefficient circuits. A test structure of a binary-programmable CNN has been designed and implemented with standard 0.18 µm CMOS technology. A single cell occupies only 155 µm2, which corresponds to a cell density of 6451 cells per square millimeter. A variety of templates have been tested and the measured chip performance is discussed. Since the minimum feature size of modern CMOS devices has already entered the nanometer scale, and the limitations of further scaling are projected to be reached within the next decade or so, more and more interest and research activity is attracted by nanotechnology. Investigation of the quantum physics phenomena and development of new devices and circuit concepts, which would allow to overcome the CMOS limitations, is becoming an increasingly important science. A single-electron tunneling (SET) transistor is one of the most attractive nanodevices. While relying on the Coulomb interactions, these devices can be connected directly with a wire or through a coupling capacitance. To develop suitable structures for implementing the binary programming scheme with capacitive couplings, the CNN cell based on the floating gate MOSFET (FG-MOSFET) has been designed. This approach can be considered as a step towards a programmable cell implementation with nanodevices. Capacitively coupled CNN has been simulated and the presented results confirm the proper operation. Therefore, the same circuit strategies have also been applied to the CNN cell designed for SET technology. The cell has been simulated to work well with the binary programming scheme applied. This versatile structure can be implemented either as a pure SET design or as a SET-FET hybrid. In addition to the designs mentioned above, a number of promising nanodevices and emerging circuit architectures are introduced.reviewe

Memristors

This Edited Volume Memristors - Circuits and Applications of Memristor Devices is a collection of reviewed and relevant research chapters, offering a comprehensive overview of recent developments in the field of Engineering. The book comprises single chapters authored by various researchers and edited by an expert active in the physical sciences, engineering, and technology research areas. All chapters are complete in itself but united under a common research study topic. This publication aims at providing a thorough overview of the latest research efforts by international authors on physical sciences, engineering, and technology,and open new possible research paths for further novel developments