1. Introduction

Nanoelectronics research is upgrading due to the increases of consumer demand of electronics device in small scale. Nanotechnology research area encourages the researchers to work on nanomaterials as an immerging technology for future. Carbon nanotube (CNT) is a potential material in the field on nanotechnology that has the ability to overcome almost all the limitations of other nanomaterials for its excellent electrical and mechanical properties. Therefore, one of the potential uses of CNT is to place as gate channel of a FET is called carbon nanotube field effect transistor (CNTFET). Silicon-based circuit is moving towards its physical limitation point according to the proven experiment [1]. Due to similar ballistic transport and high career portability of silicon material, CNTFET can be a good replacement of silicon [2] while CNT can

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

be acted as a semiconducting material [3, 4]. Nanotube is able to show its excellent electrical properties in designing digital devices [5, 6] in small scales. Another special characteristic also to be highlighted for nanotube is I-V features which enable to use the CNT in MOS transistors [7– 10]. According to device physics, the performance of the chip can be improved by reducing the size but there is a limitation about the reduction of silicon device size. Nano-hardware, which was created from the 1990s, has turned out to be a standout amongst the most dynamic research subjects in this day and age. The nanoelectronics innovation, which can fundamentally diminish the transistor measure, is particularly alluring to individuals. Single-walled carbon nanotube is mostly used in transistor [11]. Ballistic transport properties of MOS transistor are unchanged while the gate channel Si is substituted by nanotube [12]. In perspective of the outstanding sizelessening issues of traditional Si-based hardware, there have as of late been serious examinations on new advances in light of nano-organized materials which are shaped by sorted-out development and self get-together strategies. CVD process was used in the laboratory to grow nanotube from dielectrophoresis in early ages of its generation [13]. The first CNTFET was fabricated for prototype testing [14] which allows the researchers to work on this promising field of nanotechnology. CNTFET shows good performance in designing logic gates for integrated circuit modeling [15, 16]. Therefore, CNTFET can be a promising research in the near future.

## 2. Carbon nanotubes properties

#### 2.1. Geometry of carbon nanotubes

A carbon nanotube can be characterized by chiral vector and its length and a vector called the chiral vector. Chiral vector is the sum of the multipliers of the two base vectors, like Eq. (1) [17–20]

$$\mathbf{C}\_{\mathbf{h}} = m\mathbf{a}\_1 + n\mathbf{a}\_2 \tag{1}$$

To all the more decisively acquire the moment vector T, we can get it from the m, n segments of the Ch vector. On the off-chance that we demonstrate the parts of T with t1 and t2, as T is opposite to the Ch, the inward result of these vectors is equivalent to zero and we can conclude

The briefest vector t1 and t2 that are legitimate as per Eq. (3) can be isolated t1 and t2 by their most prominent normal devisor or in short shape most noteworthy basic divisor (gcd), to acquire the briefest nuclear site vector towards the path, opposite to the Ch vector. dR as in

> <sup>t</sup><sup>1</sup> <sup>¼</sup> <sup>2</sup><sup>m</sup> <sup>þ</sup> <sup>n</sup> dR

> <sup>t</sup><sup>2</sup> <sup>¼</sup> <sup>2</sup><sup>n</sup> <sup>þ</sup> <sup>m</sup> dR

The angle between the chiral vector and the a<sup>1</sup> base vector is called the chiral angle, the twist

angle or the helix angle and is denoted by θ<sup>c</sup> and can be obtained in Eq. (7)

Eq. (4), t1, t2 can be accomplished in Eqs. (5) and (6)

t1∗a1 þ t2∗a2 ¼ 0 (3)

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dR ¼ gcd ð Þ m þ n; 2n þ m (4)

(5)

(6)

Eq. (3)

Figure 1. The nanotube unit cell.

The coordinates of the graphene sheet (m,n) allows finding the chiral vector (Ch) of the nanotube.

The two-dimensional graphene lattice in real space can be created by translating one unit cell by the vectors T ¼ na<sup>1</sup> þ ma<sup>2</sup> with integer combinations (n, m), where a<sup>1</sup> and a<sup>2</sup> are basis vectors and is shown in Figure 1,

$$\begin{aligned} \overline{a}\_1 &= a\_0 \left( \frac{\sqrt{3}}{2} \widehat{\mathbf{x}} + \frac{1}{2} \widehat{\mathbf{y}} \right) \\ \overline{a}\_2 &= a\_0 \left( \frac{\sqrt{3}}{2} \widehat{\mathbf{x}} - \frac{1}{2} \widehat{\mathbf{y}} \right) \end{aligned} \tag{2}$$

a<sup>0</sup> ¼ 3acc is the length of the basis vector, and acc ≈ 1:42 Å is the nearest neighbor C-C bonding distance.

Figure 1. The nanotube unit cell.

be acted as a semiconducting material [3, 4]. Nanotube is able to show its excellent electrical properties in designing digital devices [5, 6] in small scales. Another special characteristic also to be highlighted for nanotube is I-V features which enable to use the CNT in MOS transistors [7– 10]. According to device physics, the performance of the chip can be improved by reducing the size but there is a limitation about the reduction of silicon device size. Nano-hardware, which was created from the 1990s, has turned out to be a standout amongst the most dynamic research subjects in this day and age. The nanoelectronics innovation, which can fundamentally diminish the transistor measure, is particularly alluring to individuals. Single-walled carbon nanotube is mostly used in transistor [11]. Ballistic transport properties of MOS transistor are unchanged while the gate channel Si is substituted by nanotube [12]. In perspective of the outstanding sizelessening issues of traditional Si-based hardware, there have as of late been serious examinations on new advances in light of nano-organized materials which are shaped by sorted-out development and self get-together strategies. CVD process was used in the laboratory to grow nanotube from dielectrophoresis in early ages of its generation [13]. The first CNTFET was fabricated for prototype testing [14] which allows the researchers to work on this promising field of nanotechnology. CNTFET shows good performance in designing logic gates for integrated circuit model-

ing [15, 16]. Therefore, CNTFET can be a promising research in the near future.

A carbon nanotube can be characterized by chiral vector and its length and a vector called the chiral vector. Chiral vector is the sum of the multipliers of the two base vectors, like Eq. (1) [17–20]

The coordinates of the graphene sheet (m,n) allows finding the chiral vector (Ch) of the

The two-dimensional graphene lattice in real space can be created by translating one unit cell by the vectors T ¼ na<sup>1</sup> þ ma<sup>2</sup> with integer combinations (n, m), where a<sup>1</sup> and a<sup>2</sup> are basis

> ffiffiffi 3 p <sup>2</sup> <sup>b</sup><sup>x</sup> <sup>þ</sup> 1 2 by

> ffiffiffi 3 p <sup>2</sup> <sup>b</sup><sup>x</sup> � <sup>1</sup> 2 by

a<sup>0</sup> ¼ 3acc is the length of the basis vector, and acc ≈ 1:42 Å is the nearest neighbor C-C bonding

!

a<sup>1</sup> ¼ a<sup>0</sup>

a<sup>2</sup> ¼ a<sup>0</sup>

Ch ¼ ma1 þ na2 (1)

! (2)

2. Carbon nanotubes properties

4 Design, Simulation and Construction of Field Effect Transistors

2.1. Geometry of carbon nanotubes

vectors and is shown in Figure 1,

nanotube.

distance.

To all the more decisively acquire the moment vector T, we can get it from the m, n segments of the Ch vector. On the off-chance that we demonstrate the parts of T with t1 and t2, as T is opposite to the Ch, the inward result of these vectors is equivalent to zero and we can conclude Eq. (3)

$$t\_1 \ast \mathbf{a}\_1 + t\_2 \ast \mathbf{a}\_2 = 0 \tag{3}$$

The briefest vector t1 and t2 that are legitimate as per Eq. (3) can be isolated t1 and t2 by their most prominent normal devisor or in short shape most noteworthy basic divisor (gcd), to acquire the briefest nuclear site vector towards the path, opposite to the Ch vector. dR as in Eq. (4), t1, t2 can be accomplished in Eqs. (5) and (6)

$$d\_{\mathbb{R}} = \gcd\left(m+n, 2n+m\right) \tag{4}$$

$$t\_1 = \frac{2m + n}{d\_R} \tag{5}$$

$$t\_2 = \frac{2n + m}{d\_R} \tag{6}$$

The angle between the chiral vector and the a<sup>1</sup> base vector is called the chiral angle, the twist angle or the helix angle and is denoted by θ<sup>c</sup> and can be obtained in Eq. (7)

$$\Theta\_c = \operatorname{Arctg}\left(\frac{\sqrt{3}m}{2n+m}\right) \tag{7}$$

Here, we should take note of that to consider a one of a kind chiral plot for each nanotube; the point is expressed by an incentive in the locale (0, 30�). Utilizing these definitions, the breadth of the tube can be processed utilizing the balance of the length of the Ch and the nanotube's periphery; lastly, we can acquire the measurement characterized by

$$\mathbf{d}\_{\mathbf{t}} = \frac{\mathbf{L}}{\pi} = \frac{\mathbf{a}}{\pi} \sqrt{\mathbf{n}^2 + \mathbf{n}\mathbf{m} + \mathbf{m}^2} \tag{8}$$

The length of the chiral vector is the peripheral length of the nanotube:

$$L = |\mathbb{C}\_h| = a\sqrt{n^2 + nm + m^2} \tag{9}$$

The bandgap of a single wall nanotube (SWNT) is defined by

$$E\_{\rm g} = 2\gamma\_0 a\_{\rm cc} / d\_t \tag{10}$$

From Eq. (4), if (n-m) is divisible by 3, then nanotube is metallic, otherwise the nanotube is semiconducting.

Now, the number of atom of the nanotube is defined by

$$N\_{at} = 4\* \frac{n^2 + m^2 + nm}{d\_R} \tag{11}$$

2.4. Electrical properties

Carbon nanotubes (CNTs) have outstanding electrical properties based on the chirality. There are two types of carbon nanotube, such as single-walled carbon nanotube (SWCNT) and multiple-walled carbon nanotube (MWCNT) based on the requirements of the CNT in the integrated circuit (IC) design [21–23]. Figure 3 shows the different types of carbon nanotube. A single-walled carbon nanotube has only one shell with a small diameter usually less than 2 nm.

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Figure 2. Classifications of different CNTs: (a) armchair, (b) zigzag and (c) chiral (François, 2009).

Figure 3. Diagram of carbon nanotube: (a) single-walled and (b) multi-walled (François, 2009).

#### 2.2. Classification of carbon nanotubes

Carbon nanotube (CNT) is classified into three groups as shown in Figure 2: (1) armchair, (2) zigzag and (3) chiral, based on the geometrical arrangements of the graphene during the form tube formation.

If the Ch is defined as ð Þ n; 0 , it is given the name zigzag nanotube and if the Ch is defined as ð Þ n; n , then the tube is called armchair, and these refer to the form shaped on the circumference of the tube.

#### 2.3. Carbon nanotube formation

#### 2.3.1. Armchair tubes

If the chiral indices (m, n) of a nanotube in a zone-folding region can be divisible by 3, then it becomes metallic. These nanotubes are called 'zone folding metallic', or shortly, ZF-M tubes.

#### 2.3.2. Zigzag tubes (semiconducting tubes with bandgap)

The primary band gap of a nanotube is considered as semiconducting material if the Chirality (m, n) in the zone folding area is not divisible by 3. We should allude to these nanotubes as 'zone collapsing semiconducting', or in a matter of seconds, ZF-S tubes.

Figure 2. Classifications of different CNTs: (a) armchair, (b) zigzag and (c) chiral (François, 2009).

## 2.4. Electrical properties

θ<sup>c</sup> ¼ Arctg

periphery; lastly, we can acquire the measurement characterized by

6 Design, Simulation and Construction of Field Effect Transistors

dt <sup>¼</sup> <sup>L</sup> <sup>π</sup> <sup>¼</sup> <sup>a</sup> π

The length of the chiral vector is the peripheral length of the nanotube:

The bandgap of a single wall nanotube (SWNT) is defined by

Now, the number of atom of the nanotube is defined by

2.3.2. Zigzag tubes (semiconducting tubes with bandgap)

'zone collapsing semiconducting', or in a matter of seconds, ZF-S tubes.

2.2. Classification of carbon nanotubes

2.3. Carbon nanotube formation

semiconducting.

tube formation.

2.3.1. Armchair tubes

Here, we should take note of that to consider a one of a kind chiral plot for each nanotube; the point is expressed by an incentive in the locale (0, 30�). Utilizing these definitions, the breadth of the tube can be processed utilizing the balance of the length of the Ch and the nanotube's

<sup>L</sup> <sup>¼</sup> <sup>∣</sup>Ch<sup>∣</sup> <sup>¼</sup> <sup>a</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

From Eq. (4), if (n-m) is divisible by 3, then nanotube is metallic, otherwise the nanotube is

Nat <sup>¼</sup> <sup>4</sup><sup>∗</sup> <sup>n</sup><sup>2</sup> <sup>þ</sup> <sup>m</sup><sup>2</sup> <sup>þ</sup> nm

Carbon nanotube (CNT) is classified into three groups as shown in Figure 2: (1) armchair, (2) zigzag and (3) chiral, based on the geometrical arrangements of the graphene during the form

If the Ch is defined as ð Þ n; 0 , it is given the name zigzag nanotube and if the Ch is defined as ð Þ n; n , then the tube is called armchair, and these refer to the form shaped on the circumference of the tube.

If the chiral indices (m, n) of a nanotube in a zone-folding region can be divisible by 3, then it becomes metallic. These nanotubes are called 'zone folding metallic', or shortly, ZF-M tubes.

The primary band gap of a nanotube is considered as semiconducting material if the Chirality (m, n) in the zone folding area is not divisible by 3. We should allude to these nanotubes as

dR

ffiffiffi 3 <sup>p</sup> <sup>m</sup> 2n þ m !

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n2 þ nm þ m2

n<sup>2</sup> þ nm þ m<sup>2</sup>

<sup>p</sup> (8)

<sup>p</sup> (9)

E<sup>g</sup> ¼ 2γ0acc=dt (10)

(7)

(11)

Carbon nanotubes (CNTs) have outstanding electrical properties based on the chirality. There are two types of carbon nanotube, such as single-walled carbon nanotube (SWCNT) and multiple-walled carbon nanotube (MWCNT) based on the requirements of the CNT in the integrated circuit (IC) design [21–23]. Figure 3 shows the different types of carbon nanotube. A single-walled carbon nanotube has only one shell with a small diameter usually less than 2 nm.

Figure 3. Diagram of carbon nanotube: (a) single-walled and (b) multi-walled (François, 2009).

Figure 4. Bandgap versus radius for zigzag nanotube.

As well as multi-walled carbon nanotube consists of two or more concentric cylindrical shells with the diameter of 2–30 nm.

The electrical properties of a nanotube can be realized from its bandgap. Semiconducting nanotube is a novel choice for the transistor development. Thus, Figure 4 shows bandgap versus radius for semiconducting (zigzag) nanotubes. The bandgap decreases inversely with an increase in diameter. The points with a zero bandgap correspond to metallic nanotubes which satisfy n = 3i, where i is an integer.
