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

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