Nanofabrication and its Application in Renewable Energy

Gang Zhang, Navin Manjooran, Gang Zhang, Navin Manjooran

• Publisher: Royal Society of Chemistry
• Year: 2014
• ISBN:
  9781782621317
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Nanotechnology & MEMS
• Index: Technology & Engineering

Nanoscale materials and structures have attracted great attention in recent years because of their unique physical and chemical properties and potential use in energy transport and conversion. This book puts the subject into context by first looking at current synthesis methods for nanomaterials, from the bottom-up and top-down methods, followed by enhanced energy conversion efficiency at the nanoscale and then specific applications e.g. photovoltaic cells and nanogenerators. This authoritative and comprehensive book will be of interest to both the existing scientific community in this field, as well as for new people who wish to enter it.

CHAPTER 1

Fabrication Techniques of Graphene Nanostructures

XINRAN WANG* AND YI SHI

National Laboratory of Solid State Microstructures and School of Electronic Science and Engineering, Nanjing University, Nanjing 210093, P. R. China
*Email: [email protected]

1.1 Introduction to Graphene

Carbon is one of the most studied elements in the periodic table. The versatility of chemical bonds enables many carbon allotropes. In three-dimensional bulk form, carbon can exist as diamonds and graphite, which comprise of sp³ and sp² covalent bonds, respectively. In the 1980s and 1990s, another two types of carbon allotropes, the zero-dimensional fullerene¹ and one-dimensional carbon nanotubes,² were discovered (Figure 1.1(a)).³ These nanomaterials, with fascinating physical and chemical properties, have driven an enormous amount of research in many areas.⁴ However, the two-dimensional counterpart of carbon allotrope was still missing until 2004, when a single layer of graphite, or graphene, was successfully isolated on a substrate.⁵ In this section, we give a brief introduction to graphene. We do not intend to derive the properties of graphene from the lattice and band structures. Readers who are interested in those aspects are encouraged to read the excellent reviews that are available.^6,7

Figure 1.1 (a) Schematic drawing of the relationship between graphene and other carbon materials. Graphene is a 2D building material for carbon materials of all other dimensions. It can be wrapped up into 0D buckyballs, rolled into 1D nanotubes or stacked into 3D graphite. Adapted from Ref. 3. The lattice structure of graphene with the yellow region as the unit cell. (b) (Left) Hexagonal crystal structure of graphene with lattice parameters a₁ and a₂ and inequivalent atomic positions A and B of the diatomic basis shown in red and blue. (Right) Reciprocal lattice and Brillouin zone with reciprocal lattice parameters b₁ and b₂, showing Dirac points K and K′ at the Brillouin zone corners, as well as M, the midpoint of the BZ edge and Γ, the center of the Brillouin zone. Adapted from Ref. 90. (c) (Left) Electronic band structure of graphene. (Right) Enlargement of the band structure near the Dirac cone.
Adapted from Ref. 91.

1.1.1 Lattice and Band Structure

Graphene is composed of a honeycomb lattice of carbon atoms (Figures 1.1(b) and 1.2). Structurally, graphene is related to many carbon allotropes. For example, carbon nanotubes can be formed by rolling graphene along certain axes, and graphite can be formed by stacking graphene vertically³ (Figure 1.1(a)). The structure can be seen as a triangular lattice with two equivalent atoms in each unit cell. The unit vectors

, where a=1.42Å is the carbon–carbon distance (Figure 1.1(b)). The reciprocal lattice is also triangular, with unit vectors

. The shape of the Brillouin zone is rotated 90° compared to the lattice unit cell. In each Brillouin zone, there are two inequivalent corners, K and K′, called Dirac points. This is related to the presence of a pseudospin degree of freedom or two independent sublattices in graphene.^6,7

Figure 1.2 Lattice structure of graphene under (a) TEM and (b) STM showing the hexagonal lattice.
Adapted from Refs. 92 and 93.

The tight-binding band structure of graphene was calculated in 1947 by Wallace,⁸ which can be described by eqn (1).

(1)

here E_F is the Fermi energy, t is the nearest neighbor hopping integral. The±signs represent conduction and valance bands respectively. Figure 1(c) is the plot near the first Brillouin zone. The band structure of graphene is drastically different from that of conventional semiconductors. The most remarkable feature is the linear dispersion relation near the Dirac points, which resembles ultrarelativistic particles and can be described by the massless Dirac equation.^6,7 Therefore, the electrons in graphene are often called massless Dirac fermions. This can be seen quantitatively by expanding eqn (1) near the Dirac points to give eqn (2).

E(k)=±hν_Fk (2)

where v_F=3ta/2h is the graphene Fermi velocity. Take t=2.5 eV, v_F≈10⁸ cm s⁻¹, about 1/300 of the speed of light.⁶ Due to the unique dispersion relation, the density of states of graphene is linear with energy and vanishes at the Dirac points. This is again in contrast to conventional 2D materials with a constant density of states. The unique band structure of graphene has led to many intriguing phenomena like half integer quantum Hall effect,^9,10 Klein tunneling,¹¹ and electron focusing.¹²

1.1.2 Properties and Potential Applications

Graphene has many unique electrical, optical, mechanical properties and potential applications, which make it one of the most studied materials in the past ten years. Below we summarize some of the physical properties and potential applications of graphene, many of which require the fabrication of nanostructures, which will be discussed later in the chapter.

1. High carrier mobility
Electrons in graphene have well-defined chirality, which is related to the two component pseudospin degree of freedom. Such chirality prevents intervalley backscattering and therefore leads to intrinsically high mobility.⁶ Another advantage of graphene, compared to III-V semiconductors,¹³ is that the electron and hole mobility are equally high, due to the symmetric band structure. Theories have predicted that the phonon limited mobility can be as high as 2×10⁵ cm² Vs⁻¹ at a carrier concentration of 10¹² cm⁻².¹⁴ A similar mobility value has already been measured experimentally.^15,16
The ultrahigh mobility makes graphene a potential candidate in electronic applications, including radio frequency and logic transistors.^3,17–19 Although the absence of a bandgap places a major obstacle for logic applications, many ways of opening a bandgap have been proposed and tested, which will be the focus of discussion in this chapter.

2. Conductive and transparent
Due to the absence of backscattering, the resistivity of pristine graphene is expected to be ≈1×10⁻⁶ Ωcm, which is lower than the most conductive metal, silver, at room temperature.²⁰ Optically, graphene is quite transparent over the visible spectra, absorbing 2.3% of the light. However, considering that graphene only has one atomic layer, such absorption is quite dramatic. The absorption is expressed by a simple formula πα, where α≈1/137 is the fine-structure constant.²¹ Such an optical feature originates from the unique conical band structure of graphene near the Dirac points.
With a combination of high conductivity and transparency, graphene is expected to find applications in transparent conducting films.¹⁷ As a possible candidate to replace the increasingly costly indium tin oxide (ITO) based films, graphene is made entirely of carbon. Another advantage is the extreme mechanical strength and flexibility.²² Potential near term applications include touch screen display, e-paper and organic light-emitting diodes.¹⁷

3. Wide-band and tunable optical absorption
Graphene has a tunable optical absorption. Since the density of states is vanishing at the Dirac points, the Fermi energy can be tuned by carrier density (normally through electrostatic gating). The Pauli blockade ensures that optical absorption is only possible for energy greater than 2E_F.²³ Therefore, graphene is expected to respond to wide-band signals spanning microwave to ultraviolet, including the commonly used fiber-optic communication band at 1.55 μm. Combined with the superior carrier mobility, possible applications include ultrafast photodetectors, modulators, terahertz wave detectors and tunable fiber mode-locked lasers.^17,24

4. Large specific surface area
Since every atom of graphene is on its surface, graphene has one of the largest specific surface areas among all materials, 2630 m² g⁻¹. Therefore graphene is expected to have applications in sensors: it has been shown that detection of single molecule is possible with graphene.²⁵ Combined with high conductivity and transparency, graphene also has great potential in energy related applications. For example, supercapacitor electrodes require large conductivity for high specific power and large surface area for high specific energy. Chemically exfoliated graphene is shown to possess both properties and have superior capacitance.^26,27 Another example is lithium ion batteries. Since (chemically-reduced) graphene has a higher conductivity and can accommodate more strain than many cathode materi...

Table of contents

• Cover
• Title
• Copyright
• Preface
• Contents
• Author Biographies
• Chapter 1 Fabrication Techniques of Graphene Nanostructures
• Chapter 2 Nanophotonic Light Trapping Theory for Photovoltaics
• Chapter 3 Micro/nano Fabrication Technologies for Vibration-Based Energy Harvester
• Chapter 4 Thermal and Thermoelectric Properties of Nanomaterials
• Chapter 5 Nanotubes for Energy Storage
• Chapter 6 Measurements of Photovoltaic Cells
• Subject Index