Basics of Graphene

The graphene structure, single layer of carbon atoms arranged in a hexagonal 2-D lattice, is actually predicted as early as 1947 by Wallace at the time the word “graphene”

was not even existed. However, the existence is questioned by scientists because they believe that the atoms cannot form thermodynamically stable two-dimensional structure in ambient. At 2004, the group led by A. K. Geim and K. S. Novoselov has finally fabricate monolayer graphene using mechanical exfoliation method form highly oriented pyrolytic graphite (HOPG) [2], proving that monolayer graphene does exist in nature. The pioneering result has let Geim and Novoselov to win the Nobel Prize in

2010.

The word “graphene” is a combination of “graphite” and the suffix “–ene.”

Two-dimensional honeycomb crystal lattice in which one carbon atom forms each vertex composes graphene. In this hexagonal two-dimensional structure, each carbon

atom consists of three sp² orbital hybridization. The carbon atom bonds with each other

-bond with the angle of 120^o (Fig. 1-2) [3]. The lattice constant is 2.46 Å and the

carbon-carbon bond length is 1.42 Å .

Graphene has a unique band structure. As we can see in Fig. 1-2 (b) [3], 2s, 2px and

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Fig. 1-2. (a) Hexagonal structure of graphene. The unit cell is shaded with standard unit cell vectors aG and bG. (b) Carbon-carbon bonding in graphene with the in-plane σ

bonds and the π orbitals. (Fig. taken from J. Hass [3])

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2py constitutes sp² orbital hybridization among four valence electrons of carbon (2s¹p³)

forming a covalent bond (-bond) with an angle of 120^oC while 2pz makes up the π-bond with adjacent carbon atom, enabling the electrons to hop and become

moving-free. The adjacent π-bonds hybridize together to form the π-band (valence band) and π^∗-bands (conduction band) according to the calculation using tight bonding

approximation model for monolayer graphene [4]. The conduction band and valence band meets at the edge of first Brillouin zone. At this point the density of state (DOS) is zero and is named charge neutrality point (CNP) or Dirac point (Fig. 1-3). Thus, graphene is a zero band gap semiconductor material in its nature.

There are several fabrication methods of graphene such as the mechanical exfoliation, epitaxial growth, the reduction from graphene oxides and the chemical vapor deposition (CVD). Mechanical exfoliation is the first approach to successfully fabricate monolayer graphene by A. K. Geim and K. S. Novoselov form The University of Manchester in 2004. Scotch tapes are used to peel off thin flake of graphite from HOPG. The thin flake is repeatedly peeled off further layers until there is only a few layer left. At last the thin layer of graphite is transferred to SiO2/Si substrate. The thickness can be determined using reflection and contrast spectroscopy as shown in Fig.

1-4 [5]. The graphene fabricated by mechanical exfoliation has high quality but with

poor film completeness and difficulties of precise control over the exact layer number.

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Fig. 1-3. The band structure of graphene shows six Dirac cones. (Fig. taken from J.

Hass [3])

Fig. 1-4. The optical microscope image of different layers of graphene on SiO2 (300nm).

(Fig. taken from Z. H. Ni [5])

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Mechanical exfoliation method is also disadvantageous for mass production. Therefore, the practical application of this approach is quite limited.

Graphene multi-layers can also be grown by epitaxial growth method on single crystal silicon carbide (SiC) by W. A. de Heer from Georgia Institute of Technology in 2007 [6]. The carbon-silicon covalent bond is broken by the energy provided when the substrate is heated up to 1600^oC under ultra-high vacuum environment. Then, the dangling carbon atoms on the surface constitute carbon-carbon covalent bond and form graphene thin film, as shown in Fig. 1-5. The epitaxially grown graphene is of high quality and larger area compared with the mechanical exfoliation method. However, the uniformity and layer numbers are again difficult to control. The other issue is that SiC substrates are very expensive, which makes this method a rare chosen approach for graphene growth nowadays.

Reduction form graphene oxide is another way to fabricate graphene. Concentrated sulfuric acid is used as an oxidizing agent to oxidize HOPG bulk, forming abundant functional groups: phenyl, epoxy, carbonyl, etc. The HOPG bulk can be broken into graphene oxide flakes because the van der Waals force between layer and layer is reduced. Then strong reductant such as hydrazine and NaBH4 is used to remove functional groups and restore the structure or high temperature annealing is applied to obtain monolayer of multilayer graphene, as shown is Fig. 1-6 [7]. The graphene

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Fig. 1-5. The STM image of graphene grown by epitaxial growth method. (Fig. taken from W. A. de Heer [6])

Fig. 1-6. (a) Graphene fabricated by oxidizing bulk HOPG (b) Graphene fabricated by reduction using high temperature annealing. (Fig. taken from X. Li [7])

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fabricated by the reduction of graphene oxide has relatively lower quality because the lattice is damaged during oxidization and the incompleteness of reduction. Although this method is more suitable for mass production, the graphene film quality is not good enough for electronic and optoelectronic applications.

The last method to fabricate graphene is chemical vapor deposition (CVD). CVD is a common technique to fabricate high-purity and high-quality solid thin films. Injected gas undergoes chemical reaction or decomposition and then deposit on substrate.

Because of the low pressure environment, unnecessary reaction can be eliminated. Thus the film uniformity and quality can be greatly enhanced. The film can be grown in single crystalline, polycrystalline or amorphous form by the control of growth parameters. Graphene grown using CVD mainly uses carbon source (methane (CH4), acetylene (C2H2), etc.) and the source undergoes decomposition under high temperature with the help of metal catalyst. Eventually, the graphene can be deposited onto various substrates. Graphene can be grown on several different metals with high quality with precise thickness control. For example, Platinum (Pt) [8], Iridium (Ir) [9], Cobalt (Co) [10], Gallium (Ga) [11], Nickel (Ni) [12], and Copper (Cu) [13], [14]. Metalloid can be used to grow graphene, such as Germanium [15], [16]. Using metalloid as the substrate can avoid the transfer process needed when growing on metal substrate. Furthermore, the growth of graphene can be integrated into commercial semiconductor process.

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Nonmetal substrates can also be used to grow graphene. Our group has successfully fabricated graphene grown directly on sapphire substrate, as shown in Fig. 1-7 [17].

Also, our group can further grow other two-dimensional materials such as molybdenum disulfide (MoS2) on graphene/sapphire substrate, as shown in Fig. 1-8 [18].