Carbon Nanotube and Graphene Nanoribbon Interconnects

Debaprasad Das, Hafizur Rahaman

• Publisher: CRC Press
• Year: 2017
• Print ISBN:
  9781482239485
• eBook ISBN:
  9781351831086
• Topic: Technology & Engineering
• Subtopic: Electrical Engineering & Telecommunications
• Index: Technology & Engineering

An Alternative to Copper-Based Interconnect Technology

With an increase in demand for more circuit components on a single chip, there is a growing need for nanoelectronic devices and their interconnects (a physical connecting medium made of thin metal films between several electrical nodes in a semiconducting chip that transmit signals from one point to another without any distortion). Carbon Nanotube and Graphene Nanoribbon Interconnects explores two new important carbon nanomaterials, carbon nanotube (CNT) and graphene nanoribbon (GNR), and compares them with that of copper-based interconnects. These nanomaterials show almost 1,000 times more current-carrying capacity and significantly higher mean free path than copper. Due to their remarkable properties, CNT and GNR could soon replace traditional copper interconnects. Dedicated to proving their benefits, this book covers the basic theory of CNT and GNR, and provides a comprehensive analysis of the CNT- and GNR-based VLSI interconnects at nanometric dimensions.

Explore the Potential Applications of CNT and Graphene for VLSI Circuits

The book starts off with a brief introduction of carbon nanomaterials, discusses the latest research, and details the modeling and analysis of CNT and GNR interconnects. It also describes the electrical, thermal, and mechanical properties, and structural behavior of these materials. In addition, it chronicles the progression of these fundamental properties, explores possible engineering applications and growth technologies, and considers applications for CNT and GNR apart from their use in VLSI circuits.

Comprising eight chapters this text:

• Covers the basics of carbon nanotube and graphene nanoribbon
• Discusses the growth and characterization of carbon nanotube and graphene nanoribbon
• Presents the modeling of CNT and GNR as future VLSI interconnects
• Examines the applicability of CNT and GNR in terms of several analysis works
• Addresses the timing and frequency response of the CNT and GNR interconnects
• Explores the signal integrity analysis for CNT and GNR interconnects
• Models and analyzes the applicability of CNT and GNR as power interconnects
• Considers the future scope of CNT and GNR

Beneficial to VLSI designers working in this area, Carbon Nanotube and Graphene Nanoribbon Interconnects provides a complete understanding of carbon-based materials and interconnect technology, and equips the reader with sufficient knowledge about the future scope of research and development for this emerging topic.

1

Introduction to Allotropes of Carbon Nanomaterials

1.1 Introduction to Carbon Nanotube and Graphene Nanoribbon

Carbon nanotube (CNT) and graphene nanoribbon (GNR) are two new important carbon nanomaterials in the nanometer regime. Though CNT was discovered more than two decades ago, in 1991, by Japanese physicist Sumio Iijima, GNR was discovered more recently, in 2004, by Andre Geim and Konstantin Novoselov at the University of Manchester. Since their discovery, both of these carbon nanomaterials have gained a lot of importance due to their remarkable properties. Significant progress has been made in finding out the fundamental properties, exploring the possibility of engineering applications, and growth technologies. This chapter provides a brief description about CNT and GNR.

1.2 Graphene

A single layer of three-dimensional (3D) graphite forms a two-dimensional (2D) material called 2D graphite or a graphene layer. Graphene is an allotrope of carbon. Its structure is one-atom-thick planar sheets of sp²-bonded carbon atoms that are densely packed in a honeycomb crystal lattice [1]. The term graphene was coined as a combination of graphite and the suffix -ene [2]. Graphene is most easily visualized as an atomic-scale chicken net made of carbon atoms and their bonds (Figure 1.1).

The carbon–carbon bond length in graphene is 0.142 nm [3]. Graphene sheets stack to form graphite with an interplanar spacing of 0.335 nm [4]. Graphene is the basic structural element of some carbon allotropes including graphite, charcoal, CNTs, and fullerenes. The band theory of 2D graphite or a graphene layer was studied more than six decades ago, in 1947 by Wallace [5]. But until 2004, it was believed that 2D crystals were thermodynamically unstable and could not exist. However, the experimental discovery of graphene in 2004 flaunted common wisdom, and the Nobel Prize in physics for 2010 was awarded to Andre Geim and Konstantin Novoselov at the University of Manchester “for their groundbreaking experiments regarding the two-dimensional material graphene” [6].

FIGURE 1.1
Graphene sheet.

1.3 Graphene Nanoribbon

GNRs (also called nanographene ribbons) are strips of graphene with ultra-thin width (<50 nm). The theoretical study on electronic states of graphene ribbons was introduced as a theoretical model by Fujita et al. [7].

Depending on the orientation of carbon atoms on the edge of the graphene sheet, GNR is either armchair or zigzag (Figure 1.2). Zigzag GNR is always metallic, whereas armchair GNR can be either semiconducting or metallic depending on geometry (chirality). For interconnect applications, zigzag GNR is proposed due to its metallic property.

FIGURE 1.2
GNR with chirality (a) armchair and (b) zigzag.

1.4 Carbon Nanotube

CNT was discovered accidentally by Sumio Iijima in 1991. CNTs are basically rolled graphene sheets and show both semiconducting and metallic properties depending on their chirality. Although the semiconducting CNTs are being considered for nanoelectronic devices, the metallic CNTs are being considered for nanointerconnects. CNT can be either single-walled or multiwalled. The single-walled CNT (SWCNT) is a rolled graphene sheet, whereas the multiwalled CNT (MWCNT) is concentrically rolled graphene sheets. The diameter of SWCNTs varies from 0.7 to 5 nm, whereas that of the MWCNTs ranges from a few nanometers to tens of nanometers. Figure 1.3 shows a schematic of a graphene sheet.

FIGURE 1.3
(See color insert.) Schematic of a graphene sheet.

The characteristic of a CNT is determined by its chirality. Chirality [3] is defined by a vector given by

P→=na1→+ma2→⁢(1.1)

where:

a→1 and a→2 are the unit vectors of the hexagonal lattice

n, m are integers

The diameter of a CNT is determined by the pair (n, m) and is given by

d=γπn2+nm+m2⁢(1.2)

where γ is the length of unit vectors. The relation between γ and a_CC (carbon–carbon bond length) is given by

γ=3aCC⁢(1.3)

The value of a_CC is 0.142 nm.

The c...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Preface
• Acknowledgments
• Authors
• 1. Introduction to Allotropes of Carbon Nanomaterials
• 2. Growth of Carbon Nanotubes and Graphene Nanoribbon
• 3. Modeling of CNT and GNR Interconnects
• 4. Timing Analysis in CNT Interconnects
• 5. RF and Stability Analyses in CNT and GNR Interconnects
• 6. Signal Integrity in CNT and GNR Interconnects
• 7. Applicability of CNT and GNR as Power Interconnects
• 8. Future Applications of CNT and GNR
• References
• Index