**4. Carbon nanotube based devices**

As active part of electronic devices, the CNTs have been used to control their electrical properties. In this manner, carbon nanotubes can implement electronic devices such as diodes, transistors, Schottky rectifiers (Behman et al., 2008), supercapacitors (Chen, P.-C. et al, 2009), solar cells (Jia et al., 2011; Nogueira et al., 2007), and organic light-emitting diodes, by combining semiconductor and metallic behaviors (Terrones, 2003, 2004; Tseng et al., 2004). Different strategies and topologies have been proposed with the aim of improving their performance. Transistors and Schottky rectifiers can be obtained by means of metallicsemiconducting junctions (Hur et al., 2004).

This section analyses the performance characteristics, topologies, and applications of the electronic devices fabricated by means of carbon nanotubes with emphasis to VLSI Design. It is explained as the choice of material is critical for a successful application with high performance in electronic devices such as field-effect transistors, *p*-*n* diodes, supercapacitors, solar cells, and organic-light-emitting diodes.

The development of the carbon nanotube field-effect transistors (CNFETs) was due to the historical motivation of reducing or make insignificant short-channel effects, and to improve performance of transistors in these length scales (Burke, 2004). The use of semiconducting carbon nanotubes is strategic given that metallic nanotubes cannot be fully switched off. The main advantages of this type of transistors are: ballistic electron transport over its lengths (Hasan et al., 2006), higher current density, lower power consumption with respect to silicon versions, and faster operation speed (Burghard et al., 2009). There are four main topologies to design CNT field-effect transistors: 1) back-gated CNTFETs, 2) top-gated CNTFETs, 3) wrap-around gate CNTFETs, and 4) suspended CNTFETs, as shown in Figure 8.

Fig. 8. Cross sections of different geometries of carbon nanotube field-effect transistors: (a) back-gated CNTFETs, (b) top-gated CNTFETs, (c) wrap-around gate CNTFETs, and (d) suspended CNTFETs.

As active part of electronic devices, the CNTs have been used to control their electrical properties. In this manner, carbon nanotubes can implement electronic devices such as diodes, transistors, Schottky rectifiers (Behman et al., 2008), supercapacitors (Chen, P.-C. et al, 2009), solar cells (Jia et al., 2011; Nogueira et al., 2007), and organic light-emitting diodes, by combining semiconductor and metallic behaviors (Terrones, 2003, 2004; Tseng et al., 2004). Different strategies and topologies have been proposed with the aim of improving their performance. Transistors and Schottky rectifiers can be obtained by means of metallic-

This section analyses the performance characteristics, topologies, and applications of the electronic devices fabricated by means of carbon nanotubes with emphasis to VLSI Design. It is explained as the choice of material is critical for a successful application with high performance in electronic devices such as field-effect transistors, *p*-*n* diodes,

The development of the carbon nanotube field-effect transistors (CNFETs) was due to the historical motivation of reducing or make insignificant short-channel effects, and to improve performance of transistors in these length scales (Burke, 2004). The use of semiconducting carbon nanotubes is strategic given that metallic nanotubes cannot be fully switched off. The main advantages of this type of transistors are: ballistic electron transport over its lengths (Hasan et al., 2006), higher current density, lower power consumption with respect to silicon versions, and faster operation speed (Burghard et al., 2009). There are four main topologies to design CNT field-effect transistors: 1) back-gated CNTFETs, 2) top-gated CNTFETs, 3)

wrap-around gate CNTFETs, and 4) suspended CNTFETs, as shown in Figure 8.

Fig. 8. Cross sections of different geometries of carbon nanotube field-effect transistors: (a) back-gated CNTFETs, (b) top-gated CNTFETs, (c) wrap-around gate CNTFETs, and (d)

**4. Carbon nanotube based devices** 

semiconducting junctions (Hur et al., 2004).

suspended CNTFETs.

supercapacitors, solar cells, and organic-light-emitting diodes.

In the case of back-gated CNTFETs, the main disadvantages found for its use are a poor contact between the gate dielectric and CNT, difficult switching between ON and OFF states when low-voltages are applied, and a Schottky barrier between CNTs and drain and source regions. In the case of top-gated CNTFETs, these offer several advantages over back-gated CNTFETs, but it fabrication process is more complicated (Singh et al., 2004). In wrap-around gate CNTFETs, the entire circumference of the nanotube is gated and therefore, electrical performance is enormously improved, reducing leakage current and increases the device ON/OFF ratio. Finally, in the case of suspended CNTFETs is searched the reduction of the contact between the substrate and gate oxide, and therefore, it decreases scattering at the CNT-substrate interface with the drawback of limiting its use in applications where high ON/OFF ratio are required (Kocabas et al., 2005, 2006).

The CNTFETs can be classified in two types: 1) *n*-type CNTFETs, when electrons are majority carriers for positive gate voltages, and 2) *p*-type CNTFETs, when holes are majority carriers for negative gate voltages. An ohmic contact is found when a current-voltage relationship is linear and symmetric (electrons and holes are transported in the same time), while a Schottky-barrier is presented when current-voltage relationship is non-linear and asymmetric (a unique type of electrical carrier is transported) (Lin, A. et al., 2009).

Four electrical transport regimes can be found in transistors based on carbon nanotubes, which are distinguished in accordance with the length of the nanotube compared with their mean free path, and by the type of contact between the nanotubes and the source/drain metals: 1) *ohmic-contact ballistic,* when charge injection is realized by the source and drain contacts into the carbon nanotubes and vice versa, producing a high current flow; 2) *ohmiccontact diffusive,* when bidirectional charge transport suffers scattering between source and drain contacts and carbon nanotubes with a limited current flow; 3) *Schottky-barrier ballistic*, when the gate voltage controls the thickness of the barrier and drain voltage can lower the barrier producing bidirectional high current flow: in ON-state, electrons tunneling from the source, and in OFF-state, holes tunneling form the drain; and 4) *Schottky-barrier diffusive*, when the combination of gate and drain voltages reduces the Schottky barrier and the charge transport suffers scattering producing a reduced current flow (Appenzeller et al., 2005; Cao et al., 2007).

With the introduction of graphene as active material for electronic devices, new field-effect transistors were introduced, namely these are called GFETs. A GFET uses as active material, graphene, for ballistic transport of carriers. As it was illustrated for carbon nanotube, also can be built four types of GFETs: 1) back-gated GFETs, 2) top-gated GFETs, 3) wrap-around gate GFETs, and 4) suspended GFETs. Last two topologies are not available now, but these will be fabricated in a pair of years. Back-gated GFETs present large parasitic capacitances and poor gate control. However, when smooth edges of the graphene nanoribbons are achieved, ON/OFF ratios as high as 106 are obtained, which is attractive for digital applications. Top-gated GFETs are the preferred option for analogical practical applications. In wrap-around gate GFETs, the entire rectangle of the graphene nanoribbon will be gated (see Figure 9).

Nowadays, carbon nanotube-based field-effect transistors (FETs) have operating characteristics that are comparable with those devices based on silicon. The active part in field-effect transistors is the electrical channel established by means of the carbon nanotube

Carbon Nanotube- and Graphene Based Devices, Circuits and Sensors for VLSI Design 53

Carbon nanotubes together with ceramic materials can be used to design supercapacitors by means of heterogeneous films. The use of ceramic materials allows increasing their electrical energy accumulated as voltage, while carbon nanotubes offer the properties of flexibility and transparence. Among the optimized properties are specific capacitance, power density, energy density, and long operation cycles. Supercapacitors require electrodes with large surface area, which can be obtained by means of sets of carbon nanotubes operating as electrical conductive networks (Lekakou et al., 2011). These electrodes must be capable of supporting high power and energy density, with reduced internal electrical resistance and

Flexible electronics is now a reality thanks to the successful development of the organic electronics working to low-temperature (Lin, C.-T. et al., 2011). Devices such as organic thin film transistors (OTFTs), large-area displays (Wang, C., 2009), solar cells (Rowell et al., 2006), organic light-emitting diodes (OLEDs), and sensors can be implemented based on carbon nanotubes. The electrical properties improved with the use of carbon nanotubes are transistor on-off ratio, threshold voltage, and transistor transconductance. Additionally to the electrical properties, this type of devices can be fabricated to low-cost. Carbon nanotubes can be used to fabricate transparent conductive thin films (Facchetti & Marks, 2010; Ginley, 2010) which are exploited as hole-injection electrodes for organic light-emitting diodes (OLEDs) either for rigid glass or flexible substrates (Wang, 2010; Wiederrecht, 2010; Zhang et al., 2006). The incorporation of CNTs in polymer matrices used to design OLEDs allow changing electrical characteristics of the polymer due to that the CNTs operate as doping materials. Carbon nanotubes introduce additional energy levels or forming carrier traps in the host polymers, therefore, the CNTs facilitate and block the transport of charge carrier and improving the performance at specific dopant concentrations. Such concentrations must be controlled by percolation and functionalization of the carbon nanotubes with the

The integration of hybrid materials forming heterojunctions has allowed improving the efficiency of solar cells by means of the reduction of internal resistance, which is directly associated with the fill factor, transport and separation of charges that are useful for an optimal performance. Additionally, the use of carbon nanotubes provides the possibility of tailoring the electrical and structural properties to increase the optical efficiency of the light applied to the solar cell. Two great operative advantages of carbon nanotubes are being exploited in organic photovoltaics: higher electrical charge transport properties and elevated number of exciton dissociation centers (Nismy et al., 2010). Such dissociation makes that holes are transported by a hopping mechanism and the electrons are transferred through the nanotube. The ballistic transport of the electrons in carbon nanotubes produces very high carrier mobility in the active layer. Through a well-distributed percolation and careful functionalization of carbon nanotubes it is possible increase the charge transported thanks to the multiple transfer pathways among nanotubes. If carbon nanotubes are used as transparent electrodes in solar cells, then they collect electrical charge carriers (Hatakeyama

The main strategy to come is the use of multiple nanotubes operating in parallel either individually or forming well-defined bundles with the aim of controlling the on-current in a wide range of electrical current going from micro-amperes to mili-amperes. In this manner,

produced with lower cost.

polymer.

et al., 2010, Liu, X et al., 2005).

in the substrate connecting source and drain terminals. SWNTs have been the ideal candidates as semiconducting materials due to that them can be doped to address the type of conductivity either *n*-type or *p*-type and, in this way, to manipulate the level of electrical conduction. The carbon nanotube based FETs can achieve high gain (> 10), a large on-off ratio (>105), and room-temperature operation (Lefenfeld, et al., 2003).

Carbon nanotubes and graphene nanoribbons are very sensitive to their environments including charges, vacuum levels, and environment chemical components, due to their ultrasmall diameters and large surface-to-volume ratios. Carrier mobility in carbon nanotubes is very susceptible to charge fluctuations derived of the defects located at the ambient surrounding the CNTs and graphene nanoribbons. The mobility fluctuation is the dominant 1/*f* noise mechanism for the narrow channel carbon nanotubes operating in strong inversion region with a small source-drain bias.

Fig. 9. Cross sections of different geometries of graphene field-effect transistors: (a) backgated GFETs, (b) top-gated GFETs, (c) wrap-around gate GFETs, and (d) suspended GFETs.

At ambient temperature, semiconducting SWNTs generally show unipolar *p*-type behavior. By doping with potassium, the unipolar *p*-type behavior can be switched to unipolar *n*-type behavior. *p*-*n* Diodes can be designed by covering one-half of the gate of a single channel field-effect transistor with polymers such as polyethylenimine (PEI) and poly(methyl methacrylate) (PMMA) (Mallick et al., 2010; Zhou, Y. et al., 2004).

Those field-effect transistors that have been fabricated with functionalized nanotubes exhibit high electron mobilities, high on-current, and very high on/off ratios which are necessary in high-speed transistors, single- and few-electron memories, and chemical/biochemical sensors. Studies on scaling resistivity are being realized with the aim of identifying the influence of device parameters in the on/off ratio (Sangwan et al., 2010).

A supercapacitor is an electrochemical capacitor with relatively high energy density of small size and lightweight (hundreds of times greater than those of electrolytic capacitors).

in the substrate connecting source and drain terminals. SWNTs have been the ideal candidates as semiconducting materials due to that them can be doped to address the type of conductivity either *n*-type or *p*-type and, in this way, to manipulate the level of electrical conduction. The carbon nanotube based FETs can achieve high gain (> 10), a large on-off

Carbon nanotubes and graphene nanoribbons are very sensitive to their environments including charges, vacuum levels, and environment chemical components, due to their ultrasmall diameters and large surface-to-volume ratios. Carrier mobility in carbon nanotubes is very susceptible to charge fluctuations derived of the defects located at the ambient surrounding the CNTs and graphene nanoribbons. The mobility fluctuation is the dominant 1/*f* noise mechanism for the narrow channel carbon nanotubes operating in

Fig. 9. Cross sections of different geometries of graphene field-effect transistors: (a) backgated GFETs, (b) top-gated GFETs, (c) wrap-around gate GFETs, and (d) suspended GFETs.

methacrylate) (PMMA) (Mallick et al., 2010; Zhou, Y. et al., 2004).

influence of device parameters in the on/off ratio (Sangwan et al., 2010).

At ambient temperature, semiconducting SWNTs generally show unipolar *p*-type behavior. By doping with potassium, the unipolar *p*-type behavior can be switched to unipolar *n*-type behavior. *p*-*n* Diodes can be designed by covering one-half of the gate of a single channel field-effect transistor with polymers such as polyethylenimine (PEI) and poly(methyl

Those field-effect transistors that have been fabricated with functionalized nanotubes exhibit high electron mobilities, high on-current, and very high on/off ratios which are necessary in high-speed transistors, single- and few-electron memories, and chemical/biochemical sensors. Studies on scaling resistivity are being realized with the aim of identifying the

A supercapacitor is an electrochemical capacitor with relatively high energy density of small size and lightweight (hundreds of times greater than those of electrolytic capacitors).

ratio (>105), and room-temperature operation (Lefenfeld, et al., 2003).

strong inversion region with a small source-drain bias.

Carbon nanotubes together with ceramic materials can be used to design supercapacitors by means of heterogeneous films. The use of ceramic materials allows increasing their electrical energy accumulated as voltage, while carbon nanotubes offer the properties of flexibility and transparence. Among the optimized properties are specific capacitance, power density, energy density, and long operation cycles. Supercapacitors require electrodes with large surface area, which can be obtained by means of sets of carbon nanotubes operating as electrical conductive networks (Lekakou et al., 2011). These electrodes must be capable of supporting high power and energy density, with reduced internal electrical resistance and produced with lower cost.

Flexible electronics is now a reality thanks to the successful development of the organic electronics working to low-temperature (Lin, C.-T. et al., 2011). Devices such as organic thin film transistors (OTFTs), large-area displays (Wang, C., 2009), solar cells (Rowell et al., 2006), organic light-emitting diodes (OLEDs), and sensors can be implemented based on carbon nanotubes. The electrical properties improved with the use of carbon nanotubes are transistor on-off ratio, threshold voltage, and transistor transconductance. Additionally to the electrical properties, this type of devices can be fabricated to low-cost. Carbon nanotubes can be used to fabricate transparent conductive thin films (Facchetti & Marks, 2010; Ginley, 2010) which are exploited as hole-injection electrodes for organic light-emitting diodes (OLEDs) either for rigid glass or flexible substrates (Wang, 2010; Wiederrecht, 2010; Zhang et al., 2006). The incorporation of CNTs in polymer matrices used to design OLEDs allow changing electrical characteristics of the polymer due to that the CNTs operate as doping materials. Carbon nanotubes introduce additional energy levels or forming carrier traps in the host polymers, therefore, the CNTs facilitate and block the transport of charge carrier and improving the performance at specific dopant concentrations. Such concentrations must be controlled by percolation and functionalization of the carbon nanotubes with the polymer.

The integration of hybrid materials forming heterojunctions has allowed improving the efficiency of solar cells by means of the reduction of internal resistance, which is directly associated with the fill factor, transport and separation of charges that are useful for an optimal performance. Additionally, the use of carbon nanotubes provides the possibility of tailoring the electrical and structural properties to increase the optical efficiency of the light applied to the solar cell. Two great operative advantages of carbon nanotubes are being exploited in organic photovoltaics: higher electrical charge transport properties and elevated number of exciton dissociation centers (Nismy et al., 2010). Such dissociation makes that holes are transported by a hopping mechanism and the electrons are transferred through the nanotube. The ballistic transport of the electrons in carbon nanotubes produces very high carrier mobility in the active layer. Through a well-distributed percolation and careful functionalization of carbon nanotubes it is possible increase the charge transported thanks to the multiple transfer pathways among nanotubes. If carbon nanotubes are used as transparent electrodes in solar cells, then they collect electrical charge carriers (Hatakeyama et al., 2010, Liu, X et al., 2005).

The main strategy to come is the use of multiple nanotubes operating in parallel either individually or forming well-defined bundles with the aim of controlling the on-current in a wide range of electrical current going from micro-amperes to mili-amperes. In this manner,

Carbon Nanotube- and Graphene Based Devices, Circuits and Sensors for VLSI Design 55

writing (updating the contents, second logic inverter is used). An AC ring oscillator produces an oscillating AC voltage signal by means of the connection of three logical inverters in a ring, that is, the output of the last inverter is fed to the input of the first inverter. Such circuit has not statically stable solution, since the output voltage of each

Digital circuits based on carbon nanotubes depends of the diameter of them, because it is directly proportional to the Schottky barrier height formed by the carbon nanotube and metal contacts of the source and drain terminals (Andriotis et al., 2006, 2007, 2008; Javey & Kong, 2009). In addition, larger diameters reduce the ION/IOFF ratio and voltage swing, which is the key to achieve very high speed operation and high definition of the output signal, respectively. In the same way, diameters in the range of 1 to 1.5 nm have the highest performance in current drive, which allow us to reduce the delay and increase the short circuit power that are used during switching (Cao & Rogers, 2008). Given the demand of driving large capacitive loads, the carbon nanotube based transistors must be designed with complex architectures to support high current densities. This last implies the use of efficient methodologies for controlled dispersion of carbon nanotubes or the design of bundles with high-uniformity in diameter, chirality, and orientation. The first logic inverter based on graphene (Traversi et al., 2009) was operated to low power consumption and presents inability to the direct connection in cascade

Fig. 10. VLSI circuits: (a) Carbon nanotube-based logic inverter, and (b) graphene-based

inverter oscillates as a function of time.

digital modulator.

configuration due to the different output logic voltage levels.

it is very useful to develop methodologies to produce arrays of nanotubes with wellcharacterized characteristics with the aim of obtaining high-performance applications.
