**2. Electrical properties of carbon nanotubes**

One promising direction for the VLSI Design is the use of carbon nanotubes as the active part of the device, circuit or sensor. Carbon nanotubes (CNTs) are macromolecular onedimensional systems with unique physical and chemical properties (Zhou et al., 2007). Such properties are derived of that all chemical bonds are satisfied and they are very strong, which also leads to total mechanical, thermal and chemical stability (Baughman et al., 2002). The electronic structure and electrical properties of CNTs are derived from those of a layer of graphite (graphene sheet). The specific electrical properties of the carbon nanotubes are obtained as result of their particular band structure and the hexagonal shape of its first Brillouin zone. CNTs can carry out high electrical current densities at low electron energies. When high electron energies are used, this quantity of energy destroys the CNT structure, which is not desirable from any point of view (Mamalis et al., 2004; Terrones, 2003, 2004).

This section analyzes the electrical characteristics of carbon nanotubes and graphene nanoribbons through their physical structure with the aim of presenting the attractive interest for using them in VLSI Design. The advantages and drawbacks of the use of CNTs and graphene nanoribbons as active part of an electrical device are studied.

Among physical variables of the carbon nanotube related with the electrical performance are diameter, chirality, length, position, and orientation. Each graphene sheet is wrapped in accordance with a pair of indices (*n*, *m*), which represents the number of unit vectors along two directions in the honeycomb crystal lattice of graphene. If *m* = 0, the nanotubes are called zigzag nanotubes, if *n* = *m*, the nanotubes are called armchair nanotubes and otherwise, they are called chiral nanotubes (see Figure 2) (Hayden & Nielsch, 2011; Hetch et al., 2007; Marulanda, 2010).

Two physical properties of the graphene modify its electrical properties: symmetry and electronic structure. There are three types of electrical behavior as shown in Figure 3: 1) if *n* = *m*, the nanotube is metallic; 2) if *n*-*m* is equal to 3*j,* where *j* is a positive integer ("3*j*" rule), then the nanotube is semiconducting with a very small band gap, and 3) otherwise, the nanotube is a moderate semiconducting. The 3*j* rule has exceptions due to the curvature

electronics are biochemical sensors, data storage, RF applications, logic circuits and/or semiconductor materials (Xu et al., 2008). Nowadays, graphene nanoribbons (GNRs) or carbon nanotubes unrolled are presented as attractive candidate for next-generation of integrated circuit applications derived of the anomalous quantum Hall effects and massless

The main objective of this review related with carbon nanotubes and graphene nanoribbons is assessing the current status in VLSI design and provides a vision of the future requirements for electrical subsystems based on carbon nanotubes: technology, products and applications. This chapter presents a comprehensive study of the applicability of carbon nanotubes and graphene nanoribbons as base materials, with special emphasis into the advantages and limitations, in the design of elements for VLSI design such as interconnects, electronic devices such field-effect transistors, diodes and supercapacitors; optoelectronic devices such as solar cells and organic light-emitting diodes; electronic circuits such as logic gates, and digital modulators; and bio/chemical sensors such as biosensors and gas sensors.

One promising direction for the VLSI Design is the use of carbon nanotubes as the active part of the device, circuit or sensor. Carbon nanotubes (CNTs) are macromolecular onedimensional systems with unique physical and chemical properties (Zhou et al., 2007). Such properties are derived of that all chemical bonds are satisfied and they are very strong, which also leads to total mechanical, thermal and chemical stability (Baughman et al., 2002). The electronic structure and electrical properties of CNTs are derived from those of a layer of graphite (graphene sheet). The specific electrical properties of the carbon nanotubes are obtained as result of their particular band structure and the hexagonal shape of its first Brillouin zone. CNTs can carry out high electrical current densities at low electron energies. When high electron energies are used, this quantity of energy destroys the CNT structure, which is not desirable from any point of view (Mamalis et al., 2004; Terrones, 2003, 2004).

This section analyzes the electrical characteristics of carbon nanotubes and graphene nanoribbons through their physical structure with the aim of presenting the attractive interest for using them in VLSI Design. The advantages and drawbacks of the use of CNTs

Among physical variables of the carbon nanotube related with the electrical performance are diameter, chirality, length, position, and orientation. Each graphene sheet is wrapped in accordance with a pair of indices (*n*, *m*), which represents the number of unit vectors along two directions in the honeycomb crystal lattice of graphene. If *m* = 0, the nanotubes are called zigzag nanotubes, if *n* = *m*, the nanotubes are called armchair nanotubes and otherwise, they are called chiral nanotubes (see Figure 2) (Hayden & Nielsch, 2011; Hetch et

Two physical properties of the graphene modify its electrical properties: symmetry and electronic structure. There are three types of electrical behavior as shown in Figure 3: 1) if *n* = *m*, the nanotube is metallic; 2) if *n*-*m* is equal to 3*j,* where *j* is a positive integer ("3*j*" rule), then the nanotube is semiconducting with a very small band gap, and 3) otherwise, the nanotube is a moderate semiconducting. The 3*j* rule has exceptions due to the curvature

and graphene nanoribbons as active part of an electrical device are studied.

Dirac electronic behavior (Lu & Lieber, 2007).

**2. Electrical properties of carbon nanotubes** 

al., 2007; Marulanda, 2010).

effects in carbon nanotubes with small diameter, which can influence in the electrical properties. A metallic carbon nanotube can present semiconducting behavior and vice versa (Avouris, 2002).

Fig. 2. Classification of carbon nanotubes by chiral indices: zig-zag, chiral, and armchair.

Fig. 3. Classification of carbon nanotubes by electrical properties: (a) metallic nanotube, (b) semiconducting nanotube, and (c) moderate semiconducting nanotube.

The interaction among electrons in an one-dimensional conductor such as a carbon nanotube can be modeled as a Tomonaga-Luttinger liquid, since electronic properties are derived of the collective excitations of charge and spin waves with a bosonic nature, that is, mass-less current flow (Danilchenko et al., 2010). Carbon nanotubes show two different electrical behaviors depending of the range of temperature: ballistic current transport at room temperature and Coulomb blockade phenomena at low temperatures. Ballistic transport is presented when the effective distance between contacts, where voltage is applied, is shorter than the mean free path. Coulomb blockade occurs when electrons hop on to and off from a single atom between two contacts due to a high contact electrical resistance (Hierold, 2008; Léonard, 2009).

Carbon Nanotube- and Graphene Based Devices, Circuits and Sensors for VLSI Design 45

bundle is modified by the direction and magnitude of the applied electrical field and the electrostatic screening produced by the carbon nanotubes surrounding to a specific carbon nanotube, as shown in Figure 5. Such electrostatic screening leads to a tunable switching behavior which is induced by electric field perpendicular or transverse to the bundle axis. In the case of semiconducting nanotubes, the applied electrical field produces band gap closure; while for metallic nanotubes, it produces a band gap opening. In this way, only for metallic nanotubes it is possible to modulate the conductivity of the bundle through of the applied field and splitting of the valance and conduction bands thanks to the symmetry breaking of the electrostatic screening between adjacent nanotubes due to a weak electrical interaction presented in the intertube region between them. It is necessary to remember that the level of electrostatic screening inversely determines the electrostatic field and Coulomb potential of the ions in the nanotubes. For semiconducting nanotubes, the band gap is reduced thanks to the increase of size of valence and conduction bands generated by the Stark effect derived of the applied electrical field to the nanotubes (Haruehanroengra &

Fig. 5. Electrical field applied in a bundle of carbon nanotubes. Red arrow indicates the

Arrays of carbon nanotubes have electrical properties which can be controlled by means of its length, diameter, and chirality (Jain et al., 2011). A uniformity of the properties can be achieved when performance characteristics such as high yield, reproducibility, sensitivity, and specificity are guaranteed. This is obtained through synthesis procedures, dispersion procedures, and deposition processes whose quality allows us the integration of the carbon nanotubes with the same physical properties before and after of the dispersion of bundles

Due to the presence of bundles of nanotubes, it is necessary the development of methods which allow us to separate nanotubes for extending their use in electronic applications. Several methods to separate bundles based on monovalent side wall functionalization have been developed even with the aim of improving solubility, purification and exfoliation. Unfortunately, these methods can lead to disrupts *π* transitions, generate changes in electrical resistance, and can even produce the tube fragmentation due to the formation of impurity states near the Fermi level. New strategies based on the use of mixtures of metallic and semiconducting nanotubes are producing high mobility semiconducting combinations without laborious separation requirements to use all carbon nanotubes obtained during the

Wang, 2007).

direction of the field.

(Hong et al., 2010).

In particular, metallic carbon nanotubes allow that very large electrical currents can be used to design high speed nanoscale electronic devices due to its wide band gap. Metallic multiwall CNT can carry a current density on the order of 108 A/cm2 and have the capacity of dissipated power of 1.82 mW (Shacham-Diamand et al., 2009). Individual carbon nanotubes can be considered as quasi-one-dimensional (1D) conductors. Multi-walled nanotubes (MWNTs) are considered two-dimensional (2D) conductors due to their coaxial distribution of SWNTs with intertube spacing of ~ 3.4 Å. Metallic carbon nanotubes present high dielectric constant, while semiconducting carbon nanotubes have low dielectric constant (Joachim et al., 2000; Kang et al., 2007; Krompiewski, 2005).

One of the most promising applications of the electrical properties of carbon nanotubes is the use of them in the fabrication of electronic devices. Special interest is given to the use of soft and ductile matrices to portable, light, and flexible electronics. In the design of electronic devices, the precise and tunable control of the electronic properties is essential to the high performance VLSI circuits. During the synthesis of carbon nanotubes, both metallic and semiconducting carbon nanotubes are obtained (Kanungo et al., 2010), forming sets of carbon nanotubes called bundles. A bundle containing tens to hundreds of tubes is denominated a rope; in this structure, the carbon nanotubes are separated ~ 3.2 Å forming a close-packed triangular lattice where the diameters are almost identical (see Figure 4) (Hou et al., 2008).

Fig. 4. An ideal bundle of carbon nanotubes.

A bundle of carbon nanotubes is formed by van der Waals interactions among neighboring nanotubes. It is waited that cooperative effects among nanotubes be originated in a bundle (Kim et al., 2010). The presence of multiple carbon nanotubes can substantially reduce the electrical resistance to the electrical current carried out by them, if this is compared with the electrical resistance of an individual nanotube. It is true, only when the bundles have direct physical contact, non electrical, with any material in the device with the aim of reducing the temperature generated by the current carried out. The electrical transport in a bundle has interesting electrical properties such as single electron transport (Coulomb blockade allow us control the number of electrons in the electrical conduction one by one) and metallic resistivity (increased with the temperature). Additionally, the electronic transport in a

In particular, metallic carbon nanotubes allow that very large electrical currents can be used to design high speed nanoscale electronic devices due to its wide band gap. Metallic multiwall CNT can carry a current density on the order of 108 A/cm2 and have the capacity of dissipated power of 1.82 mW (Shacham-Diamand et al., 2009). Individual carbon nanotubes can be considered as quasi-one-dimensional (1D) conductors. Multi-walled nanotubes (MWNTs) are considered two-dimensional (2D) conductors due to their coaxial distribution of SWNTs with intertube spacing of ~ 3.4 Å. Metallic carbon nanotubes present high dielectric constant, while semiconducting carbon nanotubes have low dielectric

One of the most promising applications of the electrical properties of carbon nanotubes is the use of them in the fabrication of electronic devices. Special interest is given to the use of soft and ductile matrices to portable, light, and flexible electronics. In the design of electronic devices, the precise and tunable control of the electronic properties is essential to the high performance VLSI circuits. During the synthesis of carbon nanotubes, both metallic and semiconducting carbon nanotubes are obtained (Kanungo et al., 2010), forming sets of carbon nanotubes called bundles. A bundle containing tens to hundreds of tubes is denominated a rope; in this structure, the carbon nanotubes are separated ~ 3.2 Å forming a close-packed triangular lattice where the diameters are almost identical (see Figure 4) (Hou

A bundle of carbon nanotubes is formed by van der Waals interactions among neighboring nanotubes. It is waited that cooperative effects among nanotubes be originated in a bundle (Kim et al., 2010). The presence of multiple carbon nanotubes can substantially reduce the electrical resistance to the electrical current carried out by them, if this is compared with the electrical resistance of an individual nanotube. It is true, only when the bundles have direct physical contact, non electrical, with any material in the device with the aim of reducing the temperature generated by the current carried out. The electrical transport in a bundle has interesting electrical properties such as single electron transport (Coulomb blockade allow us control the number of electrons in the electrical conduction one by one) and metallic resistivity (increased with the temperature). Additionally, the electronic transport in a

constant (Joachim et al., 2000; Kang et al., 2007; Krompiewski, 2005).

et al., 2008).

Fig. 4. An ideal bundle of carbon nanotubes.

bundle is modified by the direction and magnitude of the applied electrical field and the electrostatic screening produced by the carbon nanotubes surrounding to a specific carbon nanotube, as shown in Figure 5. Such electrostatic screening leads to a tunable switching behavior which is induced by electric field perpendicular or transverse to the bundle axis. In the case of semiconducting nanotubes, the applied electrical field produces band gap closure; while for metallic nanotubes, it produces a band gap opening. In this way, only for metallic nanotubes it is possible to modulate the conductivity of the bundle through of the applied field and splitting of the valance and conduction bands thanks to the symmetry breaking of the electrostatic screening between adjacent nanotubes due to a weak electrical interaction presented in the intertube region between them. It is necessary to remember that the level of electrostatic screening inversely determines the electrostatic field and Coulomb potential of the ions in the nanotubes. For semiconducting nanotubes, the band gap is reduced thanks to the increase of size of valence and conduction bands generated by the Stark effect derived of the applied electrical field to the nanotubes (Haruehanroengra & Wang, 2007).

Fig. 5. Electrical field applied in a bundle of carbon nanotubes. Red arrow indicates the direction of the field.

Arrays of carbon nanotubes have electrical properties which can be controlled by means of its length, diameter, and chirality (Jain et al., 2011). A uniformity of the properties can be achieved when performance characteristics such as high yield, reproducibility, sensitivity, and specificity are guaranteed. This is obtained through synthesis procedures, dispersion procedures, and deposition processes whose quality allows us the integration of the carbon nanotubes with the same physical properties before and after of the dispersion of bundles (Hong et al., 2010).

Due to the presence of bundles of nanotubes, it is necessary the development of methods which allow us to separate nanotubes for extending their use in electronic applications. Several methods to separate bundles based on monovalent side wall functionalization have been developed even with the aim of improving solubility, purification and exfoliation. Unfortunately, these methods can lead to disrupts *π* transitions, generate changes in electrical resistance, and can even produce the tube fragmentation due to the formation of impurity states near the Fermi level. New strategies based on the use of mixtures of metallic and semiconducting nanotubes are producing high mobility semiconducting combinations without laborious separation requirements to use all carbon nanotubes obtained during the

Carbon Nanotube- and Graphene Based Devices, Circuits and Sensors for VLSI Design 47

Graphene has interesting electrical properties such as electron-hole symmetric band structure, high carrier mobilities, ballistic transport, and absence of band gap (Reddy et al., 2011). But also, some disadvantages associated with its use in field-effect transistors such as lack of gate control, high off-state leakage current and saturation not controlled by drain voltage. Different methodologies are being developed to overcome, adapt to, and even use these electrical characteristics for its application in electronic devices. The use of graphene as electronic material resides in the reduction of energy consumption, linear energy dispersion, carriers with zero mass, linear current-voltage characteristic, high Fermi velocities, very low channel electrical resistance, mobilities and saturation velocities for a high current-carrying capability (6 orders higher than copper), low density of states, and the increase of frequency operation of the devices based on these qualities (Geim & Novoselov, 2007). Depending of the bias voltage, the sheet of graphene can present electrical resistance in the range of Kiloohms to ohms for low voltages and high voltages, respectively. OFF-state leakage currents in field-effect transistors based on graphene are detrimental for digital circuits, but these are very useful to analog circuits where ON-state modulating small voltages and current signals are a common case. For applications as high performance RF circuits, the graphene offers an alternative material given that its cut-off frequency is very high, and it has high compatibility with VLSI systems based on silicon. Due to its nature structurally malleable, the electrical properties of the graphene can be favorably modified by mechanical strain and

stress (Geim, 2009). Graphene can also be used in interconnects and optoelectronics.

The interconnects distribute a large quantity of signals used for the diverse elements of a VLSI design such as clock signals, power, or ground in an integrated circuit (IC), and also to various circuits on a chip. Local, intermediate and global interconnects are the levels of operation of such interconnections. The use of Cu as material for interconnects represents a current paradigm for high-performance integrated circuits due to that line dimensions, and grain size become comparable to the bulk mean free path (MFP) of electrons ( 40 nm). In addition, higher RC delays reduce the operation speed of ICs. When a new proposal in VLSI design is done, the main characteristic must be the compatibility with current IC manufacturing. The two most promising potential candidates that can be used as material for interconnects are optical and carbon-nanotube (CNT) based interconnects (Cho et al.,

This section provides a summary of the novel challenges that are being realized in nanometer-scale on-chip interconnects. Special topics associated with the operational effects such as performance and reliability are analyzed, with the aim of identifying the electrical characteristics that can be obtained in resistivity, interconnect delay, and current-carrying capability. Finally, the prospective applications of GNRs for interconnects are discussed.

Carbon nanotubes can be integrated into multilevel interconnects to meet emerging needs: delay, lifetime, parasitic resistance, inductive effects, bandwidth density, electromigration (Hosseini & Shabro, 2010), energy efficiency, power dissipation, and lowering temperature of the interconnection. Additionally, the use of carbon nanotubes makes possible the development of three-dimensional hyper-integration architectures with a high performance: versatility, scalability, adaptability, high-density interconnects, and a reduced number of

**3. Carbon nanotube interconnects** 

2008; Koo et al., 2007; Kreupl et al., 2002).

synthesis. The use of divalent functionalizations which produce impurity states far away from the Fermi level, can even lead to generate high performance semiconducting inks of low cost which can be applied in printable VLSI electronics. In addition, divalent functionalization offers a different strategy to control the electrical properties slightly taking into account tube type, size, and chirality. Adequate addends used in the functionalization allow us to transform metallic nanotubes into semiconducting nanotubes (Javey, 2008).

In 2004, graphene arose as a product of exfoliation of graphite, with the form of a twodimensional sheet of sp2-hybridized carbon (Novoselov et al., 2004). In the same manner that carbon nanotubes, it has unique electrical, mechanical and thermal properties. Such properties have been exploited in the development of energy-storage materials, transparent conducting electrodes (Alkire et al., 2009; Hu et al., 2007), field-effect transistors, digital and analog integrated circuits, integrated circuit interconnects, solar cells, ultracapacitors, and electrochemical sensors such as single molecule gas detectors and biosensors. High electron mobility at room temperature, low electrical resistivity, and symmetry of carrier mobilities between electrons and holes, are the electrical properties attractive to apply graphene in the design of electronic devices of high-performance. A similar classification to the carbon nanotubes with respect to the electrical behavior of the graphene is illustrated in Figure 6.

Fig. 6. Classification of graphene by electrical properties: (a) metallic graphene, (b) semiconducting graphene, and (c) moderate semiconducting graphene.

Graphene nanoribbons (GNRs) can be defined as rectangles made from graphene sheets with widths going from a few nanometers to tens of nanometers and lengths from nanometers to micrometers. They are considered as quasi-1D nanomaterials and can have metallic (zigzag) or semiconducting (armchair (AGNR) or zigzag (ZGNR)) behavior depending of its chirality and orientation. Both types are denoted in accordance with the number of chains either, armchair or zigzag, found in its width. High electrical and thermal conductivity, low noise and bidimensional structure are properties which can be useful to produce integrated circuit interconnects with GNRs. The size of GNRs allows us to control the band gap of the material to be electrically manipulated in an electronic device generating a wide versatility of design (Ferry et al., 2009; Guildi & Martín, 2010).

GNRs possess a richer energy band structure than the graphene, since an external electric field can be used to tune a specific bandgap (Chen, X. et al., 2011). Semiconducting AGNRs have electrical behavior as semiconductor material of indistinct manner with respect to the carbon chain position, and metallic AGNRs present both metallic as semiconducting behavior which is related with the change of chain associated with the "3*j* rule" in carbon chain position (Law et al., 2004; Philip-Wong, 2011).

Graphene has interesting electrical properties such as electron-hole symmetric band structure, high carrier mobilities, ballistic transport, and absence of band gap (Reddy et al., 2011). But also, some disadvantages associated with its use in field-effect transistors such as lack of gate control, high off-state leakage current and saturation not controlled by drain voltage. Different methodologies are being developed to overcome, adapt to, and even use these electrical characteristics for its application in electronic devices. The use of graphene as electronic material resides in the reduction of energy consumption, linear energy dispersion, carriers with zero mass, linear current-voltage characteristic, high Fermi velocities, very low channel electrical resistance, mobilities and saturation velocities for a high current-carrying capability (6 orders higher than copper), low density of states, and the increase of frequency operation of the devices based on these qualities (Geim & Novoselov, 2007). Depending of the bias voltage, the sheet of graphene can present electrical resistance in the range of Kiloohms to ohms for low voltages and high voltages, respectively. OFF-state leakage currents in field-effect transistors based on graphene are detrimental for digital circuits, but these are very useful to analog circuits where ON-state modulating small voltages and current signals are a common case. For applications as high performance RF circuits, the graphene offers an alternative material given that its cut-off frequency is very high, and it has high compatibility with VLSI systems based on silicon. Due to its nature structurally malleable, the electrical properties of the graphene can be favorably modified by mechanical strain and stress (Geim, 2009). Graphene can also be used in interconnects and optoelectronics.
