Carbon Nanotubes (CNTs)

Figure 2.2 shows typical electron microscopy images of carbon nanotubes. Since the first observation of multi-wall carbon nanotubes (MWNTs) by Iijima,^[16] much attraction has been drawn because of their excellent physical properties and potential applications in various fields. For example, carbon nanotube is probably the best conductor of electricity that can ever be possible.^[17-19] Carbon nanotube has comparable thermal conductivity with diamond along the tube axis^[20]. With the total area per nanotube bundle for normalizing the applied stress, the calculated Young’s modulous for an individual (10,10) nanotube is ~0.64 TPa.^[21]

Strong van der Waals attraction leads to spontaneous roping of many nanotubes which is important in certain applications.

The structural and electrical properties of CNTs could be found in articles^[22-25] and book.^[26-28] A CNT consists of either one cylindrical graphene sheet (Single-walled carbon nanotube, SWCNT) or several nested cylinders with an inter-layer spacing of 0.34 - 0.36 nm (Multi-walled carbon nanotube, MWCNT). Figure 2.3 shows the cutting graphite sheet along the dotted lines which connects two crystalline graphite equivalent sites on a 2-D.^[29] The circumference of CNTs can be expressed in term of the chiral vector, Ch, and chiral angle, θ. The chiral vector is given by Eq. (1):

Ch=na1+ma2≣(n,m) (n, m are integers, 0≦ |m| ≦ n ) (1) where a₁ and a ₂ are the primitive vectors length of which are both equal to 3 lC-C, with lC-C is the length of C-C bond. The chiral angel determines the amount of twist in the tube.

The chiral angles exist two limiting cases that are at 0^° and 30^°. The chiral angle is defined in Eq. (2) as

The zig-zag CNT corresponds to the case of m = 0, and the armchair CNT corresponds to

the case of n = m. The chiral CNT corresponds to the other (n, m) chiral vectors. The zig-zag CNT (n, 0) is generated from hexagon with θ= 0°, and armchair CNT (n, n) is formed from hexagon with θ= 30°. The chiral CNT is formed from hexagon with 0°＜θ＜30°. The inter-atomic spacing of carbon atom is known so that the rolled up vector of CNT can define the CNT diameter. The properties of carbon CNTs depend on the atomic arrangement, diameter, length, and the morphology.^[30]

There are many possibilities to form a cylinder with a graphene sheet^[33] and a few configurations are shown in Fig. 2.4. Figure 2.4(a)-(c) are SWCNTs of (a) zig-zag, (b) armchair and (c) chiral type. Figure 2.4(d) represents a MWCNT formed by four tubes of increasing diameter with a layer spacing of 0.34 nm. One can roll up the sheet along one of the symmetry axis: this gives either a zig-zag tube, or an armchair tube. It is also possible to roll up the sheet in a direction that differs from a symmetry axis: one obtains a chiral CNT.

Besides the chiral angle, the circumference of the cylinder can also be varied.

This diversity of possible configurations is indeed found in practice, and no particular type is preferentially formed. In most cases, the layers of MWCNTs are chiral^[31,16] and of different helicities.^[32] The lengths of SWCNTs and MWCNTs are usually well over 1 µm and diameters range from ~1 nm (for SWCNTs) to ~50 nm (for MWCNTs). Pristine SWCNTs are usually closed at both ends by fullerene-like halfspheres that contain both pentagons and hexagons.^[33]

The electronic properties of SWCNTs have been studied in a large number of theoretical works.[33,34,35-37] These models show that the electronic properties vary in a calculable way from metallic to semiconducting, depending on the tube chirality (n, m) given by^[26]

Metallic properties: n-m = 0 or (n-m)/3 = integer Semiconducting properties: (n-m)/3 ≠ integer

The study shows that about 1/3 of SWCNTs are metallic, while the other 2/3 of SWCNT are semiconducting with a band gap inversely proportional to the tube diameter. This is due to

the very unusual band structure of graphene and is absent in systems that can be described with usual free electron theory. Graphene is a zero-gap semiconductor with the energy bands of the p-electrons crossing the Fermi level at the edges of the Brillouin zone, leading to a Fermi surface made of six points.^[38] Graphene should show a metallic behavior at room temperature since electrons can easily cross from the valence to the conduction band.

However, it behaves as a semi-metal because the electronic density at the Fermi level is quite low. Rolling up the graphene sheet into a cylinder imposes periodic boundary conditions along the circumference and only a limited number of wave vectors are allowed in the direction perpendicular to the tube axis. When such wave vectors cross the edge of the Brillouin zone, and thus the Fermi surface, the CNT is metallic. This is the case for all armchair tubes and for one out of three zigzag and chiral tubes. Otherwise, the band structure of the CNT shows a gap leading to semiconducting behavior, with a band gap that scales approximately with the inverse of the tube radius. Band gaps of 0.4-1eV can be expected for SWCNTs (corresponding to diameters of 1.6-0.6nm). This simple model does not take into account the curvature of the tube which induces hybridization effects for very small tubes and generates a small band gap for most metallic tubes. The exceptions are armchair tubes that remain metallic due to their high symmetry.

These theoretical predictions made in 1992 were confirmed in 1998 by scanning tunneling spectroscopy.^[39,40] The scanning tunneling microscope has since then been used to image the atomic structure of SWCNTs,^[41,42] the electron wave function^[43] and to characterize the band structure.^[44] Numerous conductivity experiments on SWCNTs and MWCNTs yielded additional information.^[45-56] At low temperatures, SWCNTs behave as coherent quantum wires where the conduction occurs through discrete electron states over large distances. Transport measurements revealed that metallic SWCNTs show extremely long coherence lengths.^[56,57] MWCNTs show also these effects despite their larger diameter and multiple shells.^[58,59]

Fig. 2.3 Schematic diagram showing how a hexagonal sheet of graphite is rolled to form a CNT^[29].

Fig. 2.4 Models of different CNT structures^[60].

(b) (a)

Fig. 2.5 Structure of carbon nanofibers and nanotubes. (a) stacked cone sherringboned nanofiber and (b) nanotube^[68].

(a) (b)

Fig. 2.6 (a) SEM image of carbon nanofiber and (b) TEM image of an individual carbon nanofiber^[66].

2.1.2 Carbon Nanofibers^[61]

It has been known for over a century that filamentous carbon can be formed by the catalytic decomposition of carbon-containing gas on a hot metal surface. In a U.S. Patent published in 1889,^[62] it is reported that carbon filaments are grown from carbon-containing gases using an iron crucible. In the current literature, the term “nanofiber” is preferentially used, featuring distinction in size scale, while in the past simply “filamentous carbon,”

“carbon filaments,” and “carbon whiskers” were applied.^[63] In 1985 a form of carbon, buckminsterfullerene C60, was observed by a team headed by Kroto et al.,^[64] which led to the Nobel Prize in chemistry in 1997. This discovery was followed by Iijima’s^[16] demonstration in 1991 that carbon nanotubes are formed during arc-discharge synthesis of C60 and other fullerenes, triggering a deluge of interest in carbon nanofibers and nanotubes. In the 1990s the introduction of catalytic plasma-enhanced chemical vapor deposition (C-PECVD) provided additional control mechanisms over the growth of carbon nanostructures. In 1997 Chen et al.

used PECVD for nanofiber synthesis.^[65] Their work was followed by the better known work of Ren et al.^[66]

Carbon nanofibers (CNFs) are cylindrical or conical structures that have diameters varying from a few to hundreds of nanometers and lengths ranging from less than a micron to millimeters. The internal structure of carbon nanofibers varies and is comprised of different arrangements of modified graphene sheets. A graphene layer can be defined as a hexagonal network of covalently bonded carbon atoms or a single two-dimensional (2D) layer of a three dimensional (3D) graphite. In general, a nanofiber consists of stacked curved graphite layers that form cones [Fig. 2.5(b)] or “cups.”^[67,68] The stacked cone structure is often referred to as herringbones or fishboned as their cross-sectional transmission electron micrographs resemble a fish skeleton, while the stacked cups structure is most often referred to as a bamboo type, resembling the compartmentalized structure of a bamboo stem. Currently there is no strict

classification of nanofiber structures. The main distinguishing characteristic of nanofibers from nanotubes is the stacking of graphene sheets of varying shapes.

In comparison to carbon nanotubes, carbon nanofibers appear as rod-like in structure, as shown in Fig. 2.6.^[69,70] Several methods are used for synthesizing carbon nanofibers, such as microwave plasma chemical vapor deposition, hot filament chemical vapor deposition, plasma enhanced chemical vapor deposition, etc. Catalyst is usually the essential element for the growth of carbon nanofibers. Gated field emission devices using single carbon nanofiber cathodes has also been reported.^[71]

2.1.3 Carbon Nanotips

A carbon nanotip has a solid carbon structure which may be ether amorphous or graphite.

Compare to its root part, the diameter of its head is much smaller and normally less than 10nm. Both amorphous carbon and graphite are considered conducting metallically;^[72]

therefore, combine with its small radii, it is suitable for applications as field emitters.^[73] Other applications such as scanning probe microscope tips and nano indenters^[74] are also proposed mainly due to the chemical inertness of the carbon surface, and much higher bending stiffness compared to carbon nanotubes.

Different growth methods for fabricating carbon nanotips may include electron–beam -induced deposition (EBID),^[75-77] chemical vapor deposition (CVD),^[78–80] and plasma-enhanced chemical deposition (PECVD).^[81] In our previous work, well aligned carbon nanotips are grown on both bare silicon and platinum film by microwave plasma chemical vapor deposition.^[82-83] Generally, the growth of carbon nanotips needs no catalyst, so the top of the tip is only amorphous carbon or graphite. Fig. 2.7 (a) shows SEM plane view image of carbon nanotips, the tip angle is 29°. Fig. 2.7(b) shows TEM image of a single carbon nanotip, the image shows a sharp tip of graphite structure. Fig. 2.7(c) shows the field emission behavior that turns on at low electric field.

(a) (c)

(b)

Fig. 2.7 (a) top-view of SEM image of carbon nanotips, (b) a single carbon nanotip TEM image and (c) field emission property of carbon nanotips^[83].

2.2 Methods for Synthesizing Carbon Materials Arc Discharge

Arc discharge is the first and the effective way to produce single-wall carbon nanotubes (SWNTs) and multi-wall carbon nanotubes (MWNTs).^[84-86] The arc discharge equipment contains a stainless steal vacuum chamber with about 500 torr pressure filled with Helium.

Two separated graphite electrode are biased with high current density (50~150A) to about 25~40V. Arc is then induced, and the graphite target is vaporized. Products are deposited on cathode or chamber which includes fullerence, tubes, nano particles and amorphous carbon, etc. Impurities are one of its disadvantages, which need further purifications. Figure 2.8 shows schematic diagram of typical arc discharge equipment.^[87]

Laser Ablation

Smalley et al.^[88,89] discovered that single-wall carbon nanotubes can be produced by laser ablation with good quality and efficiency, which draws a lot of attention. A carbon target is evaporated by high power continuous CO2 laser or pulse Nd:YAG laser source. The evaporated species are carried out by Argon or Helium to the water-cooled copper finger or copper wire; single-wall nanotubes are then formed. One specialty is that no amorphous carbon is formed on nanotubes. It has to be noted that, fullerence and multi-wall nanotubes can also be obtained by this method. Fig. 2.9^[90] shows schematic diagram of laser ablation equipment.

Fig. 2.8 Schematic diagram of arc discharge equipment (Krätschmer-Huffmann).

Fig. 2.9 Oven laser-vaporization apparatus^[90].

Chemical Vapor Deposition (CVD)

Chemical vapor deposition includes thermal CVD, Hot filament CVD, microwave plasma CVD, etc. Catalysts are normally used for the growth of carbon related material.

Typically chemical vapor deposition are used for the production of carbon fibers.^[91,92] It is not until 1993 that Yacaman et. al.^[93] successfully use chemical vapor deposition to deposit carbon nanotubes. And till 1997 microwave plasma enhanced chemical vapor deposition is used to deposit carbon nanofibers and carbon nanotubes.^[94,95] Hydrocarbon gases are usually mixed with hydrogen (or ammonia) to be the reaction gas.^[96] Products may be carbon nanotubes, amorphous carbon, carbon fiber, or even carbon nano tips, which are correlated to growth temperature, flow rate, reaction gas, growth time, bias, and catalyst. Compare with the methods above, CVD has the advantage of low process temperature, relative good uniformity, convenience, large area growth, and easy for in-situ doping.^[97]

Bias Assisted Microwave Plasma Chemical Vapor Deposition (MPCVD)

Microwave plasma chemical vapor deposition is one of the important facilities for thin film deposition, micro manufacturing, and surface treatment.^[98] By the advantage of high ion density, high degree of dissociation, high reactivity, and low process temperature, a lot of kinds of substrates are capable of fabrication under low temperature with deposition and etching, which is meaningful for LSI process, microelectronic device, optoelectronic device, polymer, and thin film sensor.

By applying electric field, the reaction gas breakdown to induce electrons and ions. With electromagnetic field obtained by microwave or RF power, more electrons and ions are generated by colliding with the un-dissociated gas. Stable plasma is reached when the generation rate and consumption rate are equal for all species. Unlike traditional thermal plasma, temperature of electrons, ions, and neutral particles in low temperature plasma induced by discharge are not identical. The temperature of electron is about 1000^oK, while the

ions and neutral ones are below 500^oK. Therefore, low temperature plasma is a non-equilibrium plasma with not only few ions, electrons, but also excite state, transient state, and free radicals. By manipulating these high energy species, reaction which is hard for steady state species are attainable.

Take diatomic plasma for example, the procedure may appear as followed:

(Ⅰ)Ionization

A

+ e

→ A

+ 2 e

(Ⅱ)Dissociative ionization

A

+ e

→ A

+ A + 2 e

(Ⅲ)Attachment

A

+ e

→ A

(Ⅳ)Detachment

A

+ e

→ A

+ 2 e

(Ⅴ)Recombination

A

+ e

→ A

(Ⅵ)Atom recombination

2 A

→ A

*any polyatomic molecule is substituent for mentioned above.

(^•) stands for free radical.

Basically, microwave plasma chemical vapor deposition does not need any electrode or even heater. But in this thesis, bias plays an important role in the growth of nanomaterials, and also an essential term.

When a DC bias is added on to the substrate, before the ions pass through the plasma sheath area, the movement of the ions do not effect by the collision between the ions, comparatively and statistically. Also means the ions can strike the substrate directly and vertically by the applied field.^[99]

2.3 Growth Mechanism for Nanomaterials

Due to huge amount compound and various atomic bonding of carbon, plenty of kinds of methods are used for the growth of carbon related nanomaterials. Each method has its advantages, disadvantages, distinguishing feature, and a range for suitable use. Most of them have been successfully synthesize carbon nanotubes.

The model used for describing the growth of nanomaterials still is an issue because of the difficulty for observation under such extremely small scale. Even though, several mechanisms are brought up to characterize the behavior for the growth. Here we discuss some growth models which are considered to be the major mechanism for nanosize material.

Growth mechanism of various kind of bottom-up nanosize materials are generally considered to be three models: Vapor-Solid (VS) model, Vapor-Liquid-Solid (VLS) model, and recently, Solution-Liquid-Solid (SLS) model. Some modifications^[100] have also been published which will not be discussed here.

Vapor-Solid (VS) Model

Figure 2.10 shows an approximately growth model of vapor-solid growth mechanism.

The diagram takes the growth of GaN for example. Epitaxial growth can be achieved without catalyst or liquid phase. The sum of thermodynamic surface energy and heat of fusion become the driving force for VS growth. The growth rate of VS is dominated by the rate of atoms or molecules diffusion and rearrangement. Compare with the growth mechanism with catalyst, the VS mechanism has a lower growth rate.

Vapor-Liquid-Solid (VLS) Model

The mechanism^[101] was first introduced in the 1960s to explain the growth of silicon whiskers or tubular structures^[102]. In this model, growth occurs by precipitation from a

supersaturated liquid-metal-alloy droplet located at the top of whisker, into which silicon atoms are preferentially absorbed from the vapor phase. The similarity between the growth of carbon nanotubes and the VLS model has also been pointed out by Saito et al^[103-104] on the basis of their experimental findings for multi-walled nanotube growth in a purely carbon environment (Fig. 2.11). Solid carbon sublimates before it melts at ambient pressure, and therefore these investigators suggested that some other disordered carbon form with high fluidity, possibly induced by ion irradiation, should replace the liquid droplet.

Solid-Liquid-Solid (SLS) Model

Figure 2.12^[105] shows diagram of solution-liquid-solid growth mechanism which takes

Ⅲ-Ⅴ materials for example. No catalyst is used for solution-phase synthesis. The materials are produced as polycrystalline fibers or near-single-crystal whiskers having width of 10 to 150 nanometers and length of up to several micrometers^[106]. This mechanism shows that process analogous to vapor-liquid-solid growth operated at low temperatures, while requirement of a catalyst that melts below the solvent boiling point to be its potential limitation.

Fig. 2.10 Schematic diagram of vapor-solid (VS) growth model.

Fig. 2.11 Schematic diagram of VLS growth mechanism for nanotubes.^[103]

Fig. 2.12 Schematic depiction of SLS growth mechanism.^[105]

2.4 Introduction to Field Emission Theory

The science of field emission began in 1928,^[109] when Fowler and Nordheim presented the first quantum mechanical model for describing field induced electron emission from a metallic surface; a model still in use today. In deriving their model, Fowler and Nordheim first assumed that the conduction electrons in the emitting metal are describable as a free-flowing ’electron cloud’ - following Fermi-Dirac statistics -and are bound to the metal by an energy barrier at the surface. Under the influence of a field, these conduction electrons can be induced to tunnel through the barrier into vacuum, producing a field-induced electron emission from the metal surface. The presence of the electric field makes the width of the potential barrier finite and therefore permeable to the electrons. This can be seen in Fig. 2.13 which presents a diagram of the electron potential energy at the surface of a metal. Fowler and Nordheim further assumed that the surface barrier can be approximated with a one dimensional energy function without losing significant accuracy.

Field Emission from Metals

The dashed line in Figure 2.13 shows the shape of the barrier in the absence of an external electric field. The height of the barrier is equal to the work function of the metal, φ, which is defined as the energy required removing an electron from the Fermi level EF of the metal to a rest position just outside the material (the vacuum level). The solid line in Figure 2.13 corresponds to the shape of the barrier in the presence of the external electric field. As can be seen, in addition to the barrier becoming triangular in shape, the height of the barrier in the presence of the electric field E is smaller, with the lowering given by^[107]

2

where e is the elementary charge and ε0 is the permittivity of vacuum.

Fig. 2.13 Diagram of potential energy of electrons at the surface of a metal^[108].

Fig. 2.14 Diagram of the potential energy of electrons at the surface of an n-type semiconductor with field penetrates into the semiconductor interior.^[108]

Knowing the shape of the energy barrier, one can calculate the probability of an electron with a given energy tunneling through the barrier. Integrating the probability function multiplied by an electron supply function in the available range of electron energies leads to an expression for the tunneling current density J as a function of the external electric field E.

The tunneling current density can be expressed by Eq. (4) which is often referred to as the Fowler-Nordheim equation^[109]

where y=∆φ/φ with ∆φ given by Eq. (3), h is the Planck's constant, m is the electron mass,

where y=∆φ/φ with ∆φ given by Eq. (3), h is the Planck's constant, m is the electron mass,