12 Carbon Nanotubes: Properties and Applications
Dr. Anchal Srivastava
Contents of this Unit
1. Introduction
2. Properties of CNTs
2.1.Electronic Band Structure of Carbon Nanotubes (CNTs)
2.2.Band Structure of CNTs from Graphene
2.3.Metallic and Semiconducting Properties of Zigzag CNTs
2.4.Electronic Properties of CNTs
2.5.Mechanical Properties of CNTs
2.6.Magnetic Properties of CNTs
2.7.Thermal Properties of CNTs
3. Application of CNTs
3.1.CNTs: A Futuristic Hydrogen Storage material
3.2.Uses of CNTs as a Field Emitter
4. Summary
Learning Outcomes
- After studying this module, you shall be able to
- Learn the electronic band structure of carbon nanotubes and how it derived from graphene. Understand various kinds of properties of carbon nanotubes depending on its structure.
- Know the different applications of carbon nanotubes such as structural, electromagnetic, electroacoustic, chemical, mechanical, optical etc.
1. Introduction
A carbon atom can form various types of allotropes. In 3D structures, diamond and graphite are the allotropes of carbon. Carbon also forms low-dimensional (2D, 1D or 0D) allotropes collectively known as carbon nanomaterials. Examples of such nanomaterials are 1D carbon nanotubes (CNTs) and 0D fullerenes. In the list of carbon nanomaterials, graphene is known as 2D single layer of graphite. The sp2 bonds in graphene are stronger than sp3 bonds in diamond that makes graphene the strongest material (Sarkar et al. 2011). The lattice structure of graphene in real space consists of hexagonal arrangement of carbon atoms as shown in Fig. 1(a). An isolated carbon atom has four valence electrons in its 2s, and 2p atomic orbitals. While forming into graphene, three atomic orbitals of the carbon atom, 2s, 2px, and 2py, are hybridized into three sp2 orbitals. These sp2 orbitals are in the same plane while the remaining 2pz is perpendicular to other orbitals as shown in Fig. 1(b) (Sarkar et al. 2011). The σ bonds between the adjacent carbon atoms are formed by the sp2 hybridized orbitals, whereas the 2pz orbitals form the π bonds that are out of the plane of graphene (Javey and Kong, 2009).
Fig.1 Basic (a) hexagonal and (b) orbital structure of graphene (Reproduced with permission from Sarkar et al. 2011)
This module presents the unique atomic structure and properties of carbon nanotube (CNT). The electronic band structure of carbon nanotube along with their small size and low dimension are responsible for their unique electrical, mechanical, and thermal properties. This module summarizes the electronic band structure of one-dimensional CNTs, various transport properties, and their real-world applications.
2. Properties of CNTs
The atomic arrangements of carbon atoms are responsible for the unique electrical, thermal, and mechanical properties of CNTs. These properties are discussed below:
2.1 Electronic Band Structure of Carbon Nanotubes (CNTs)
In order to explain the band structure of CNTs, it is essential to understand the band structure of graphene. Generally, electrical transport properties in graphene are determined by electrons and holes near the Fermi level. This is because electrons near the Fermi level have easy access to the conduction band, leaving behind the holes in the valence band. In graphene, the π orbitals are responsible for the electronic transport properties as they lie near the Fermi level. The band structure of graphene can be obtained by “tight binding approximations” method (Wallace 1947; Minto 2004; Satio et al. 1992). In Fig. 2(a), a unit cell of graphene is shown with two non-equivalent carbon atoms A and B. With suitable combination of two unit vectors a1 and a2, all other atoms can be translated back to either A or B. The reciprocal lattice of graphene with unit vectors, b1 and b2 is shown in Fig. 2(b). To obtain the band structure of graphene in π orbitals, the solutions of Schrödinger equation is required which states that
Where H is the Hamiltonian, Ψ is the total wave function, and E is the energy of electrons in the π orbitals of graphene. Due to the periodic structure of graphene, the total wave function can be constructed from a linear combination of Bloch functions ui that has a periodicity of the lattice. In the tight binding approximation, an atomic wave function is used to represent the Bloch function ui. The ui for each atom can be constructed from 2pz orbitals of atoms A and B as (Javey and Kong 2009).
where X(r) represents the 2pz orbital wave function for an isolated carbon atom. Thus, Ψ in (1) can be expressed as (Javey and Kong 2009)
Substituting Eqs. (3) into (1), the Schrödinger equation can be solved in a matrix form that can be expressed as (Javey and Kong 2009)
It is easier to neglect the overlap between 2pz wave functions of different atoms, i.e., SAB = SBA = 0. For normalized case, the values can be assumed as SAA = SBB = 1; then, Eq. (4) is simplified to (Javey and Kong 2009)
Further, by symmetry of the graphene lattice (atoms A and B are not distinguishable), it is observed that HAA = HBB and HAB = HBA*. Therefore, Eq. (7) leads to the solution
HAA (=HBB) can be obtained by inserting Eqs. (2) into (5) as (Javey and Kong 2009)
where ρi is a vector connecting atom A to its three nearest neighbor B atoms (as in Fig. 2a). By referring to the coordinate system of the graphene in Fig. 2(a), the following expression can be obtained (Javey and Kong 2009)
γ0 represents the strength of exchange interaction between nearest neighbor atoms that is known as the tight-binding integral or transfer integral. Therefore, from Eqs. (10) and (12), the energy dispersion in Eq. (8) can be obtained as (Javey and Kong 2009)
In Eq. (13), negative sign represents the valence band of graphene produced by bonding π orbitals, while positive sign denotes conduction band formed by antibonding π* orbitals. The dispersion relation in Eq. (13) is plotted in Fig. 3 along high-symmetry points in the reciprocal space with E0 = 0. Figure 4 a, b represents the surface and contour plots of the energy dispersion, respectively. The six K points at the corners of the Brillouin zone are the main feature of the energy dispersion of graphene. At these points, the conduction and valence bands meet resulting in zero band gap in graphene. It can also be noted that the two K points (K1 and K2) are non-equivalent due to symmetry. The circular contour around each K point in Fig. 4 b indicates the conic shape of dispersion near each K point.
2.2 Band Structure of CNTs from Graphene
CNTs can be uniquely defined by chiral vector, C = n1a1 + n2a2, where n1 and n2 are integers and a1 and a2 are unit vectors of the graphene lattice as shown in Fig. 5.
Fig. 3 Energy dispersion of graphene along high-symmetry points as indicated in Fig. 2(b)
Fig. 4 (a) Surface plot and (b) contour plot of the energy dispersion in graphene as given by Eq. (13). Note that there are six K points where the bandgap becomes zero. Among the six K points, only two are non-equivalent, denoted by K1 and K2 (Reproduced with permission from Javey and Kong 2009)
A graphene sheet is rolled up to form CNT in such a way that two carbon atoms coincide. With wrapping indices n1 and n2, CNTs can be uniquely defined and described.
Since CNT is a rolled-up sheet of graphene, an appropriate boundary condition is required to explore the band structure. If CNT can be considered as an infinitely long cylinder, there are two wave vectors associated with it: (1) the wave vector parallel to CNT axis k|| that is continuous in nature due to the infinitely long length of CNTs and (2) the perpendicular wave vector k⊥ that is along the circumference of CNT. These two wave vectors must satisfy a periodic boundary condition (i.e., the wave function repeats itself as it rotates 2π around a CNT) (Javey and Kong 2009)
where D represents the diameter of CNT and m is an integer. The quantized values of allowed k⊥ for CNTs are obtained from the boundary condition.
Fig. 6 (a) A first Brillouin zone of graphene with conic energy dispersions at six K points. The allowed k⊥ states in CNT are presented by dashed lines. The band structure of CNT is obtained by cross sections as indicated. Zoom-ups of the energy dispersion near one of the K points are schematically shown along with the cross sections by allowed k⊥ states and resulting 1D energy dispersions (b) a metallic CNT and (c) a semiconducting CNT (Reproduced with permission from Javey and Kong 2009)
The cross-sectional cutting of the energy dispersion with the allowed k⊥ states results in 1D band structure of graphene as shown in Fig. 6a. This is called zone folding scheme of obtaining the band structure of CNTs. Each cross-sectional cutting gives rise to 1D sub-band. The spacing between allowed k⊥ states and their angles with respect to the surface Brillouin zone determine the 1D band structures of CNTs. The band structure near the Fermi level is given by allowed k⊥ states that are closest to the K points. When the allowed k⊥ states pass directly through the K points as shown in Fig. 6b, the energy dispersion has two linear bands crossing at the Fermi level without a bandgap. However, if the allowed k⊥ states miss the K points as shown in Fig. 6c, there are two parabolic 1D bands with an energy bandgap. Therefore, two different kinds of CNTs can be expected depending on the wrapping indices, firstly, the metallic CNTs without bandgap as in Fig. 6b, and secondly, the semiconducting CNTs with bandgap as in Fig. 6c.
2.3 Metallicity and Semiconducting Properties of Zigzag CNTs
Using the approach of 1D sub-band discussed in previous subsection, the 1D sub-band closest to the K points for zigzag CNTs is investigated here. The zigzag CNTs can be either metallic or semiconducting depending on their chiral indices. Since the circumference is n.a (C = na1), the boundary condition in Eq. (14) becomes (Javey and Kong 2009)
There is an allowed kx that coincides with K point at (0, 4π/3a). This condition arises when n has a value in multiple of 3 (n = 3q, where q is an integer). Therefore, by substitution in Eq. (15) (Javey and Kong 2009)
There is always an integer m (=2q) that makes kx pass through K points so that these kinds of CNTs (with n = 3q) are always metallic without bandgap as shown in Fig. 6b. There are two cases when n is not a multiple of 3. If n = 3q + 1, the kx is closest to the K point at m = 2q + 1 (as in Fig. 6c).
Similarly, for n = 3q − 1, the allowed kx closest to K is when m = 2q − 1; hence (Javey and Kong 2009)
In these two cases, allowed kx misses the K point by (Javey and Kong 2009)
From Eq. (19), it is inferred that the smallest misalignment between an allowed kx and a K point is inversely proportional to the diameter. Thus, from the slope of a cone near K points (Eq. 14), the bandgap Eg can be expressed as
(b) p = 1, 2; semiconducting with a bandgap, Eg ∼ 0.7 eV/D (nm).
Similar treatment can also be applied for armchair CNTs (n, n), arriving at the conclusion that they are always metallic.
2.4 Electronic Properties of CNTs
Solid-state devices in which electrons are confined to two-dimensional planes have provided some of the most exciting scientific and technological breakthrough of the 50 years. From metal-oxide-silicon field effect transistors to gallium-arsenide hetrostructures, these devices have played a key role in microelectronics revolution and re critical components in a wide array of products from computer to compact-disc players. From a more parochial perspective, the study of electrons in two-dimensional system has also been responsible for two Nobel prizes in physics- to Klaus von Klitzing in 1985 and to Robert Laughlin, Horst Stormer and Daniel Tsui in 1998. This is testimony to the basic as well as applied interest of such devices.
Experiments on these devices (1-D systems) have shown, for example, that the conductance of “ballistic” 1-D systems-in which electrons travel the length of channel without being scattered- -is quantized in units of 2/ℎ , where ‘e’ is the charge on the electron and h is the Planck constant. Single –wall carbon nanotubes fit his bill remarkably well.
2.5 Mechanical Properties of CNTs
σ bonding is the strongest in nature, and thus a nanotube that is structured with all σ bonding is regarded as the ultimate fiber with the strength in its tube axis. Both experimental measurements and theoretical calculations agree that a nanotube is as stiff as or stiffer than diamond with the highest Young’s modulus and tensile strength. Most theoretical calculations are carried out for perfect structures and give very consistent results. Table 1 summarizes calculated Young’s modulus (tube axis elastic constant) and tensile strength for (10,
10) SWNT and bundle and MWNT with comparison with other materials. The calculation is in agreement with experiments on average. Experimental results show broad discrepancy, especially for MWNTs, because MWNTs contain different amount of defects from different growth approaches.
In general, various types of defect-free nanotubes are stronger than graphite. This is mainly because the axial component of σ bonding is greatly increased when a graphite sheet is rolled over to form a seamless cylindrical structure or a SWNT. Young’s modulus is independent of tube chirality, but dependent on tube diameter. The highest value is from tube diameter between 1 and 2 nm, about 1 TPa. Large tube is approaching graphite and smaller one is less mechanically stable. When different diameters of SWNTs consist in a coaxial MWNT, the Young’s modulus will take the highest value of a SWNT plus contributions from coaxial inter-tube coupling or Van der Waals force. Thus, the Young’s modulus for MWNT is higher than a SWNT, typically 1.1 to 1.3 TPa, as determined both experimentally and theoretically. On the other hand, when many SWNTs are held together in a bundle or a rope, the weak Van der Waal force induces a strong shearing among the packed SWNTs. This does not increase but decreases the Young’s modulus. It is shown experimentally that the Young’s modulus decreases from 1 TPa to 100 GPa when the diameter of a SWNT bundle increases from 3 nm (about 7 (10,10) SWNTs) to 20 nm.
Fig.7 Band gap change of SWNTs under uniaxial strain (>0 for tension and <0 for compression) and torsional strain (>0) for net bond stretching and <0 for net bond compression).
TABLE 1 Mechanical Property of Nanotubes
| Young’s modulus | Tensile Strength | Density | |
| (GPa) | (GPa) | (g/cm3) | |
| MWNT | 1200 | ~150 | 2.6 |
| SWNT | 1054 | 75 | 1.3 |
| SWNT bundle | 563 | ~150 | 1.3 |
| Graphite (in-plane) | 350 | 2.5 | 2.6 |
| Steel | 208 | 0.4 | 7.8 |
Source: J. Lu and J. Han, Int. J. High Speed Electron. Sys. 9, 101 (1998).
The elastic response of a nanotube to deformation is also very remarkable. Most hard materials fail with a strain of 1% or less due to propagation of dislocations and defects. Both theory and experiment show that CNTs can sustain up to 15% tensile strain before fracture. Thus the tensile strength of individual nanotube can be as high as 150 GPa, assuming 1 TPa for Young’s modulus. Such a high strain is attributed to an elastic buckling through which high stress is released. Elastic buckling also exists in twisting and bending deformation of nanotubes. All elastic deformation including tensile (stretching and compression), twisting, and bending in a nanotube is nonlinear, featured by elastic buckling up to ~15% or even higher strain. This is another unique property of nanotubes, and such a high elastic strain for several deformation modes is originated from sp2 rehybridization in nanotubes through which the high strain gets released.
However, sp2 rehybridization will lead to change in electronic properties of a nanotube. A position vector in a deformed nanotube or graphite sheet can be written as r = ro + r where r can be deformed lattice vector a or chiral vector C described in previection. Using a similar approach to deriving electronic properties of a nanotube from graphite, the following relations are obtained:
In this relation, Ego is zero strain band gap, θ is nanotube chiral angle, εl and εr are tensile and torsion strain, respectively; and ν is Poisson’s ratio. Parameter p is defined by (n – m) = 3q + p such that p = 0 for metallic tube; p = 1 for type I semiconductor tube, for example, (10, 0); and p = –1 for type II semiconductor tube, for example, (8, 0). Thus, function sgn(2p +1) = 1, 1 and –1, respectively, for these three types of tubes. Equation (21) predicts that all chiral or asymmetric tubes (0 < θ <30°) will experience change in electronic properties for either tensile or torsional strain whereas symmetric armchair or zigzag tubes may or may not change their electronic properties. In asymmetric tubes, either strain will cause asymmetric σ – π rehybridization and therefore change in electronic properties. However, effect of strain on a symmetric tube is not so straightforward. A detailed explanation is given in the original publications together with analysis of DOS. Figure 7 shows band gap change for different nanotubes.
The most interesting is the predicted metal-insulator transition. The armchair tube is intrinsically metallic but will open a band gap under torsional strain. The zigzag (3q, 0) metallic tube, instead, will open a band gap under tensile strain, not torsional strain. The chiral metallic tube, for example, (9, 3), will open band gap in either case. The above theory can also be extended to tube bending. For pure bending where bond stretching and compression cancel each other along tube circumference without torsion deformation, the band gap should not change from that predicted from Equation (21). However, there are exceptions. For example, when a SWNT with two ends fixed by two electrode leads is subject to a bending deformation applied by an AFM tip, the deformation also generates a net tensile stretching strain. Metal-insulator (semiconductor) transition and a decrease in conductance with strain are indeed observed experimentally in this case. Experiments have confirmed the predicted remarkable electromechanical properties of nanotubes or electronic response to mechanical deformation. Equation (21) does not include sp2 hybridization effect. Again, the effect is found very small, similar to that for the tube under no deformation, shows striking features of electromechanical properties of a nanotube such as splitting and merging of VHS peaks including band gap opening and closing under mechanical deformation.
There has not been much effort studying the electromechanical properties of SWNT bundles and MWNTs. Inter-tube coupling may play a larger role in electromechanical properties as it does for Young’s modulus and tensile strength.
Fig. 8 DOS with (dash line) and without (solid line) consideration of s-p rehybridization for three typical SWNTS. Values on the right side are stains. A small band gap of 0.02 eV at zero strain, caused by tube curvature or rehybridization, is seen for tube (18, 0). Striking features of electromechanical properties include splitting and merging of VHS peaks including band gap opening and closing.
2.6 Magnetic Properties of CNTs
Similar to mechanical and electromechanical properties, magnetic and electromagnetic properties of CNTs are also of great interest. The magnetic properties are studied with electron spin resonance (ESR), which is very important in understanding electronic properties, for example, for graphite and conjugated materials. Once again, there is a large discrepancy from different experimental measurements, especially in transport properties, because of sample quality and alignment whereas qualitatively they agree with theoretical calculations. Magnetic properties such as anisotropic g-factor and susceptibility of nanotubes are expected to be similar to those for graphite while some unusual properties may exist for nanotubes. Indeed, it is found from ESR that the average observed g-value of 2.012 and spin susceptibility of 7 10-9 emu/g in MWNTs are only slightly lower than 2.018 and 2 10-8 emu/g in graphite. Some interesting properties are also found from ESR studies of Pauli behavior. For example, aligned MWNTs are metallic or semi metallic. The measured susceptibility gives the density of state at the Fermi level of 1.5 10–3 states/eV/atom, also comparable with that for in-plane graphite. The carrier concentration is about 1019cm–3, as compared with an upper limit of 1019 cm–3 from Hall measurement. However, similar observations have not been made for SWNTs and bundles. The possible reason is sample alignment difficulties and strong electron correlation, which may block non-conduction ESR signal.
2.7 Thermal Properties of CNTs
CNTs can exhibit superconductivity below 20 K (approximately −253 ºC) due to the strong in-plane C– C bonds of graphene. The strong C-C bond provides the exceptional strength and stiffness against axial strains. Moreover, the larger inter-plane and zero in-plane thermal expansion of SWNTs results in high flexibility against non-axial strains.
Due to their high thermal conductivity and large in-plane expansion, CNTs exhibit exciting prospects in nanoscale molecular electronics, sensing and actuating devices, reinforcing additive fibers in functional composite materials, etc. Recent experimental measurements suggest that the CNT embedded matrices are stronger in comparison to bare polymer matrices (Wei et al. 2002). Therefore, it is expected that the nanotube may also significantly improve the thermo-mechanical and the thermal properties of the composite materials.
3. Application of CNTs
CNTs have not only unique atomic arrangements but also have unique properties (Li et al. 2009a) that include large current carrying capability (Wei et al. 2001), long ballistic transport length (Javey and Kong 2009), high thermal conductivity (Collins et al. 2001a), and mechanical strength (Berber et al. 2000). These extraordinary properties of CNTs qualifies them exciting prospects and variety of applications in the area of microelectronics/nanoelectronics (Avorious et al. 2007), spintronics (Tsukagoshi et al. 1999), optics (Misewich et al. 2003), material science (Wang et al. 2000), mechanical (Yu et al. 2000), and biological fields (Yu et al. 2000; Lu et al. 2009). Particularly, in the area of nanoelectronics, CNTs and graphene nanoribbons (GNRs) demonstrates wide range of applications such as energy storage [supercapacitor (Du et al. 2005)] devices; energy conversion devices that includes thermoelectric (Wei et al. 2009) and photovoltaic (Ago et al. 1999) devices; field emission displays and radiation sources (Choi et al. 1999); nanometer semiconductor transistors (Collins et al. 2001a), nanoelectromechanical systems (NEMS) (Dadgour et al. 2008), electrostatic discharge (ESD) protection (Hyperion Catalysis), interconnects (Kreupl et al. 2002; Li et al. 2009a), and passives (Li and Banerjee 2008a). The applications of CNTs in different fields are listed below.
3.1 CNTs: A Futuristic Hydrogen Storage Material
In addition to being able to store electrical energy, there has been some research in using carbon nanotubes to store hydrogen to be used as a fuel source. By taking advantage of the capillary effects of the small carbon nanotubes, it is possible to condense gases in high density inside single-walled nanotubes. This allows for gases, most notably hydrogen (H2), to be stored at high densities without being condensed into a liquid. Potentially, this storage method could be used on vehicles in place of gas fuel tanks for a hydrogen-powered car. A current issue regarding hydrogen-powered vehicles is the on-board storage of the fuel. Current storage methods involve cooling and condensing the H2 gas to a liquid state for storage which causes a loss of potential energy (25–45%) when compared to the energy associated with the gaseous state. Storage using SWNTs would allow one to keep the H2 in its gaseous state, thereby increasing the storage efficiency. This method allows for a volume to energy ratio slightly smaller to that of current gas powered vehicles, allowing for a slightly lower but comparable range. An area of controversy and frequent experimentation regarding the storage of hydrogen by adsorption in carbon nanotubes is the efficiency by which this process occurs. The effectiveness of hydrogen storage is integral to its use as a primary fuel source since hydrogen only contains about one fourth the energy per unit volume as gasoline. Studies however show that what is the most important is the surface area of the materials used. Hence activated carbon with surface area of 2600 m2/g can store up to 5, 8% w/w. In all these carbonaceous materials, hydrogen is stored by physisorption at 70-90K.
3.2 Uses of CNTs as a Field Emitter
Modern technology makes a wide use of controlled propagation of electrons in vacuum. There are several examples, for instance, in CRT displays, vacuum electronics, microwave amplification, electron microscopy, x-ray generation, plasma processing, gas ionization, ion-beam neutralization, electron-beam evaporation, and electron-beam lithography. This broad range of applications finds its origins in the properties of free-flowing electrons: their energy (momentum) can be modified with ease using electric fields to accelerate or decelerate them, their trajectory can be controlled with electric or magnetic fields, and their generation and detection can be directly controlled with conventional electronics. No other type of particle radiation offers such latitude of control. At the basis of each system utilizing electrons in vacuum is an electron source. Several techniques are known to extract electrons from matter, but by far the most common one to date is thermionic emission. With thermionic emission, the source is heated at high temperature (~1000°C) to give its free electrons the thermal energy required to overcome the surface potential barrier. Practically speaking, a thermionic source is usually a tungsten filament (Figure 9) or a porous tungsten matrix impregnated with a material allowing reduction of the work function (dispenser cathodes). During operation, the cathode temperature is raised by resistive or other means of heating, and emitted electrons are collected with an electric field. Although thermionic emission is a simple and well-proven technique, it does not provide good power efficiency because the high operating temperature necessarily comes with energy loss by radiation. Other disadvantages include the inertia of the emitter, the dimensional changes from thermal expansion, the out gassing of species that contribute to vacuum degradation and a limited lifetime from the thermal cycling.
Fig. 9 Principle of thermionic emitter: a metal is heated high enough to give the free electrons enough energy to overcome the surface potential barrier.
Fig. 10 Schematic diagram of a field emitter; the electric field around the sharp tip is enhanced to the point electrons can tunnel through the surface potential barrier.
Among alternative means of electron generation, field emission is regarded as one of the best choices in many applications. Field emission involves extraction of electrons from a conducting solid by an electric field. Unlike thermionic emission, no heat is required for obtaining field emission. Field emission can provide extremely high current densities (up to 107 A·cm-2 at the emitting site) and produces a low energy spread of the emitted electrons. Extremely high electric fields (several kV/μm) are required for the electrons to tunnel through the surface potential barrier. Such high fields can practically be obtained using only the phenomenon of local field enhancement. A conducting solid shaped as sharp tips shows a geometrical enhancement of the electric field around the tip, the electric field lines being concentrated around the regions of small radius of curvature (Figure 10). When sharp cathodes are used for field emission, the macroscopic electric field required to induce a current is reduced to the point where macroscopic fields of a few V/μm can be sufficient. Field emission is typically analyzed with the Fowler-Nordheim (FN) model, which describes the tunneling of electrons through a metal-vacuum potential barrier. Figure 11 shows the expression of the FN model of a tip-shaped emitter. This model shows that maximizing the current output for a given applied voltage requires a material with a low work function that is shaped as sharp as possible to offer the highest field enhancement factor. The FN model is not rigorous in the description of field emission from CNT because it describes the emission from a flat metallic at 0 K. Although it is not strictly satisfactory in describing the physics of the emission from CNT, it is practical for analyzing field emission measurements. Consequently, field emission data are often presented in an FN representation (FN plots) for which an FN regime is carried by a straight line with a negative slope. More-rigorous models describing the emission from CNT are being developed.
Fig. 11 FN model of field emission from a metallic tip; typical FN plot in which field emission appears as a straight line with a negative slope. I, emitted current; V, applied voltage; φ, workfunction of the material; β, field enhancement factor.
Fig.12 Schematic structure of a micro-machined array of gated tips.
Very sharp field emitting microstructures were proposed and developed by Spindt in the form of micromachined miniature tips. The structure of such a micro-machined field emitter array (Spindt cathode) is presented in Figure 12. The emission relies on having very small radii of curvature of the tips. Consequently it is crucial to the preservation of the performance of the cathode that the tip sharpness remains unaltered. It has been observed that these tips are very sensitive, and sputtering of cation tends to dull the tip. Much effort was dedicated to the application of these Spindt cathodes, but this technology was proved to be expensive to scale and shows limited reliability in technical vacuum conditions. A variety of field emitting thin films has been proposed as an alternative to the micro-machined tip arrays for reduced fabrication cost and improved robustness. The potential of CNTs for field emission was first discussed in 1995. Increasing attention has ever since been devoted by the scientific and industrial communities to this possible application of nanotubes. At the time of writing, this technology is still under development, but some commercial applications are already being reported.
4. Summary
- In this module you have understand the followings
- The electronic band structure of CNTs derived from graphene and the metallicity/semiconducting properties of zigzag CNTs.
- CNTs exhibit superconductivity below 20 K (approximately -253 °C).
- Young’s modulus of SWNTs varies in the range of 1.22 TPa–1.26 TPa depending on the size and chirality.
- The measured resistivity of the SWNT ropes is in the order of 10−4 Ω cm at 27 ºC.
- The different applications of carbon nanotubes such as structural, electromagnetic, electroacoustic, chemical, mechanical, optical etc.
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