**5. Carbon nanotube based circuits**

Carbon nanotubes can be exploited as molecular device elements and molecular wires. Each device element is based on a suspended, crossed nanotube geometry that leads to bistable, electrostatically switchable ON/OFF states. Such device elements can be addressed by means of control elements to manipulate large arrays (1012 elements or more) using carbon nanotube interconnects (Ishikawa et al., 2009; Tulevski et al., 2007).

This section discusses circuits based on carbon nanotubes that have been proposed in the last decade for VLSI Design. The necessary steps to leading to the carbon nanotubes based circuits toward integrated circuits are analyzed in detail. Different realizations of analog and digital circuits are studied, which can be used for integrated circuits in VLSI Design. The advantages and limitations of the performance of such circuits in their analog and digital versions are summarized.

The electrical properties of carbon nanotubes are making possible the complete design of VLSI systems under a unique active material (Hosseini & Shabro, 2010). Semiconducting carbon nanotubes can be used to build transistors, devices and circuits, while metallic carbon nanotubes are used to build interconnects and vias. Circuits such as ring oscillators (Pesetski et al., 2008), inverter pair (Nouchi et al., 2008), NOR gate, nonvolatile random access memory, etc. can be designed with field-effect transistors based on carbon nanotubes. Nowadays, simulation software has shown that CNT transistor circuits can operate at upper GHz frequencies (Vasileska & Goodnick, 2010).

The integration of multiple field-effect transistors can be realized to build digital logic circuits. In circuits where back-gated transistors are used, the same gate voltage is applied to all transistors associated with the circuit. Therefore, to increase the potentially of such circuits different strategies are being developed with the aim of applying different voltages to the gates in each transistor associated with the circuit. In digital circuits, the transistors must have electrical characteristics that can favor high performance such as: high gain, high ON/OFF ratio, excellent capacitive coupling between the gate and nanotube, and roomtemperature operation (Cao et al, 2006; Jamaa, 2011). Until now, one-, two-, and threetransistor circuits have showed digital logic operations, giving place to logic inverters, NOR gates, static random-access memory cells, and AC ring oscillators (Wang, C., 2008).

Logic inverters are logical devices with one input and one output (see Figure 10 (a)). A logic inverter converts a logical "0" into a logical "1", and vice versa (Bachtold et al., 2001). Therefore, an inverter circuit operates as a basic logic gate to swap between two logical voltage levels "0" and "1". NOR gates are logical devices with two or more inputs and one output. A NOR gate of two inputs operates as follows: an output "1" is obtained when both inputs are "0", and an output "0" is achieved when one or both inputs are "1". A static random-access memory (SRAM) cell is built as a latch by feeding the output of two serial logical inverters together, that is, a bistable circuit generated to store each bit (Rueckes et al., 2000). Each cell has three different states: standby (the circuit is idle, both logic inverters are blocked to be used), reading (the data has been requested, first logic inverter is used) and

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

Carbon nanotubes can be exploited as molecular device elements and molecular wires. Each device element is based on a suspended, crossed nanotube geometry that leads to bistable, electrostatically switchable ON/OFF states. Such device elements can be addressed by means of control elements to manipulate large arrays (1012 elements or more) using carbon

This section discusses circuits based on carbon nanotubes that have been proposed in the last decade for VLSI Design. The necessary steps to leading to the carbon nanotubes based circuits toward integrated circuits are analyzed in detail. Different realizations of analog and digital circuits are studied, which can be used for integrated circuits in VLSI Design. The advantages and limitations of the performance of such circuits in their analog and digital

The electrical properties of carbon nanotubes are making possible the complete design of VLSI systems under a unique active material (Hosseini & Shabro, 2010). Semiconducting carbon nanotubes can be used to build transistors, devices and circuits, while metallic carbon nanotubes are used to build interconnects and vias. Circuits such as ring oscillators (Pesetski et al., 2008), inverter pair (Nouchi et al., 2008), NOR gate, nonvolatile random access memory, etc. can be designed with field-effect transistors based on carbon nanotubes. Nowadays, simulation software has shown that CNT transistor circuits can operate at upper

The integration of multiple field-effect transistors can be realized to build digital logic circuits. In circuits where back-gated transistors are used, the same gate voltage is applied to all transistors associated with the circuit. Therefore, to increase the potentially of such circuits different strategies are being developed with the aim of applying different voltages to the gates in each transistor associated with the circuit. In digital circuits, the transistors must have electrical characteristics that can favor high performance such as: high gain, high ON/OFF ratio, excellent capacitive coupling between the gate and nanotube, and roomtemperature operation (Cao et al, 2006; Jamaa, 2011). Until now, one-, two-, and threetransistor circuits have showed digital logic operations, giving place to logic inverters, NOR

gates, static random-access memory cells, and AC ring oscillators (Wang, C., 2008).

Logic inverters are logical devices with one input and one output (see Figure 10 (a)). A logic inverter converts a logical "0" into a logical "1", and vice versa (Bachtold et al., 2001). Therefore, an inverter circuit operates as a basic logic gate to swap between two logical voltage levels "0" and "1". NOR gates are logical devices with two or more inputs and one output. A NOR gate of two inputs operates as follows: an output "1" is obtained when both inputs are "0", and an output "0" is achieved when one or both inputs are "1". A static random-access memory (SRAM) cell is built as a latch by feeding the output of two serial logical inverters together, that is, a bistable circuit generated to store each bit (Rueckes et al., 2000). Each cell has three different states: standby (the circuit is idle, both logic inverters are blocked to be used), reading (the data has been requested, first logic inverter is used) and

nanotube interconnects (Ishikawa et al., 2009; Tulevski et al., 2007).

**5. Carbon nanotube based circuits** 

GHz frequencies (Vasileska & Goodnick, 2010).

versions are summarized.

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 inverter oscillates as a function of time.

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 configuration due to the different output logic voltage levels.

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

Carbon Nanotube- and Graphene Based Devices, Circuits and Sensors for VLSI Design 57

Carbon nanotubes are promising candidates for designing gas sensors due to their excellent chemical and superficial properties derived of their chemical composition and high-aspectratio between its length and diameter, respectively. Levels as low as ppt (parts per trillion) or ppb (parts per billion) can be detected in comparison with their predecessors based on microsystems (MEMS) which could detect only ppm (parts per million). The basic structures used to design gas sensors are based on chemoresistors and FETs with one-dimensional nanostructures. An excellent biosensor or gas sensor is obtained when an appropriate control of the chemical and physical variables associated with the detection is presented. Therefore, the use of one-dimensional nanostructures improves the sensitivity, selectivity,

stability, and response time (Balasubramanian & Burghard, 2006; Rivas et al., 2009).

and CNT-based field-effect transistors are highlighted.

subject (Dong et al., 2008; Jia et al., 2008).

This section analyses the different proposes of carbon nanotube based biosensors and carbon nanotube based gas sensors that were published in the last decade. This review discusses various design methodologies for CNT-based biosensors and CNT-based gas sensors as well as their application for the detection of specific biomolecules and gases. Recent developments associated with the topologies to design CNT-based chemiresistors

Carbon nanotubes and graphene are technologically attractive to develop sensors due to four great characteristics: 1) each atom in its structure is physically accessible under any environment condition; 2) any perturbation in atoms can be electrically measured; 3) structural stability; 4) superior sensing performance at room temperature; and 5) tunable electrical properties (Wong et al., 2010). These characteristics have allowed the development of chemical, molecular and biological sensors (Oliveira & Mascaro, 2011; Wang, 2009).

Traditionally, pristine high-quality nanotubes are functionalized with functional groups to produce chemical or biochemical coatings (Wang, J., 2005; Zourob, 2010) or sites where very high sensitivity and selectivity to specific gases or to biochemical species is presented. Such gases or biochemical species can be detected by means of a change in electrical resistivity or capacitance presented in individual carbon nanotubes or bundles of them with the presence of this species. The change presented can be an increase or a reduction with respect to the value of the electrical parameter without the chemical or biochemical specie before mentioned (Chen, P.-C. et al., 2010). The chemical and biochemical sensors based on carbon nanotubes have even achieved sensitivities in the order of parts per billion to parts per million for specific gases or biochemical species depending of the molecule size and physicochemical properties (Bradley et al., 2003). Therefore, in any occasions it is necessary to add catalysts to improve the chemical activity during the chemical or biochemical detection (Cao & Rogers, 2009). In particular, the functionalization required by the biosensors regularly needs to favor the biocompatibility with the biological environment and realize the monitoring of information related with biological events and processes (Gruner, 2006; Ishikawa et al., 2009, 2010). In this manner, the biological species must be not affected by the biochemical interaction between the biosensor and the associated biological

The basic construction blocks to design chemical or biochemical sensors based on carbon nanotubes can be divided into two different configurations: two-terminal CNT devices or three-terminal transistor-like structures. In the case of two-terminals devices, these can be modeled by an electrical resistor or an electrical capacitor (see Figure 11). In the case of

CNTs can be used to yield radio-frequency analog electronic devices such as narrow band amplifiers operating in the VHF frequency band with power gains as high as 14 dB. Examples of advanced analog circuits based on carbon nanotubes are resonant antennas, fixed RF amplifiers, RF mixers, and audio amplifiers. Hundred of devices, interconnected into desired planar layouts on commercial substrates are possible; thereby such systems can achieve complex functionality (Kocabas et al., 2008).

In RF applications, GFETs achieve high carrier mobility and saturation velocity (Lin et al., 2011). Mixers are RF circuits that are used to create new frequencies from two electrical signals applied to it. These signals have different frequency and when they are applied to the mixer, then are obtained two new signals corresponding to the sum and difference of the original frequencies. They are used to shift signals from one frequency range to another, for its transmission in RF systems such as radio transmitters. The radio frequency mixer based on graphene can produce frequencies up to 10 GHz, therefore, secure applications such as cell phones and military communications are feasible (Lin et al., 2011). Any limitations can be found for the use to full scale of graphene in VLSI circuits: different ohmic contact between materials, poor adhesion between metals and oxides, and high vulnerability to damage in the integration processes.

Among the main characteristics that graphene offers for VLSI Design are flexible, transparent material, and it operates to room temperature. Thanks to their electrical properties, the graphene is an ideal material to build more energy-efficient computers and other nanoelectronic devices. Nowadays, it is necessary to develop methods that allow us to separate graphene nanoribbons by a thin nonconductive material. Among the proposals that have been made are the use of one-atom-thick sheets of alloys of boron and nitrogen whose electrical behavior is nonconductive, and whose physical appearance is similar to graphene. The contents of such alloy must be controlled due to the geometrical arrangements that can be obtained.

Due to the ambipolarity (conduction of holes and electrons with equal efficiency), it is possible to design electronic devices (Vaillancourt et al., 2008; Xu et al., 2008). In Figure 10 (b), a digital modulator for communications circuits based on graphene is illustrated. This circuit is based on a graphene transistor including two gates: gate 1 controls the magnitude of current flowing through the transistor, and gate 2 controls the polarity of this current. The electrical operation of this circuit is similar to an electronic inverter, where gate 1 delivers a digital data stream as input, and it modulates such signal with the carrier wave applied to the drain to mix both signals, given place to a modulated signal.

### **6. Carbon nanotube based biosensors and gas sensors**

Chemical sensors include a class of devices capable of detecting gas molecules or chemical signals in biological cells. Significant progress has been achieved in the detection of explosives, nerve agents, toxic gases and nontoxic gases due to the threat of terrorism and the need for homeland security. The biosensors and gas sensors based on one-dimensional nanostructures are very attractive, because they present high sensitivity and fastest response to the surrounding environment, thanks to their reduced dimensions and large surface-tovolume ratio (Sinha et al., 2006; Star et al., 2004; Wong et al., 2010).

CNTs can be used to yield radio-frequency analog electronic devices such as narrow band amplifiers operating in the VHF frequency band with power gains as high as 14 dB. Examples of advanced analog circuits based on carbon nanotubes are resonant antennas, fixed RF amplifiers, RF mixers, and audio amplifiers. Hundred of devices, interconnected into desired planar layouts on commercial substrates are possible; thereby such systems can

In RF applications, GFETs achieve high carrier mobility and saturation velocity (Lin et al., 2011). Mixers are RF circuits that are used to create new frequencies from two electrical signals applied to it. These signals have different frequency and when they are applied to the mixer, then are obtained two new signals corresponding to the sum and difference of the original frequencies. They are used to shift signals from one frequency range to another, for its transmission in RF systems such as radio transmitters. The radio frequency mixer based on graphene can produce frequencies up to 10 GHz, therefore, secure applications such as cell phones and military communications are feasible (Lin et al., 2011). Any limitations can be found for the use to full scale of graphene in VLSI circuits: different ohmic contact between materials, poor adhesion between metals and oxides, and high vulnerability to

Among the main characteristics that graphene offers for VLSI Design are flexible, transparent material, and it operates to room temperature. Thanks to their electrical properties, the graphene is an ideal material to build more energy-efficient computers and other nanoelectronic devices. Nowadays, it is necessary to develop methods that allow us to separate graphene nanoribbons by a thin nonconductive material. Among the proposals that have been made are the use of one-atom-thick sheets of alloys of boron and nitrogen whose electrical behavior is nonconductive, and whose physical appearance is similar to graphene. The contents of such alloy must be controlled due to the geometrical arrangements that can

Due to the ambipolarity (conduction of holes and electrons with equal efficiency), it is possible to design electronic devices (Vaillancourt et al., 2008; Xu et al., 2008). In Figure 10 (b), a digital modulator for communications circuits based on graphene is illustrated. This circuit is based on a graphene transistor including two gates: gate 1 controls the magnitude of current flowing through the transistor, and gate 2 controls the polarity of this current. The electrical operation of this circuit is similar to an electronic inverter, where gate 1 delivers a digital data stream as input, and it modulates such signal with the carrier wave applied to

Chemical sensors include a class of devices capable of detecting gas molecules or chemical signals in biological cells. Significant progress has been achieved in the detection of explosives, nerve agents, toxic gases and nontoxic gases due to the threat of terrorism and the need for homeland security. The biosensors and gas sensors based on one-dimensional nanostructures are very attractive, because they present high sensitivity and fastest response to the surrounding environment, thanks to their reduced dimensions and large surface-to-

the drain to mix both signals, given place to a modulated signal.

**6. Carbon nanotube based biosensors and gas sensors** 

volume ratio (Sinha et al., 2006; Star et al., 2004; Wong et al., 2010).

achieve complex functionality (Kocabas et al., 2008).

damage in the integration processes.

be obtained.

Carbon nanotubes are promising candidates for designing gas sensors due to their excellent chemical and superficial properties derived of their chemical composition and high-aspectratio between its length and diameter, respectively. Levels as low as ppt (parts per trillion) or ppb (parts per billion) can be detected in comparison with their predecessors based on microsystems (MEMS) which could detect only ppm (parts per million). The basic structures used to design gas sensors are based on chemoresistors and FETs with one-dimensional nanostructures. An excellent biosensor or gas sensor is obtained when an appropriate control of the chemical and physical variables associated with the detection is presented. Therefore, the use of one-dimensional nanostructures improves the sensitivity, selectivity, stability, and response time (Balasubramanian & Burghard, 2006; Rivas et al., 2009).

This section analyses the different proposes of carbon nanotube based biosensors and carbon nanotube based gas sensors that were published in the last decade. This review discusses various design methodologies for CNT-based biosensors and CNT-based gas sensors as well as their application for the detection of specific biomolecules and gases. Recent developments associated with the topologies to design CNT-based chemiresistors and CNT-based field-effect transistors are highlighted.

Carbon nanotubes and graphene are technologically attractive to develop sensors due to four great characteristics: 1) each atom in its structure is physically accessible under any environment condition; 2) any perturbation in atoms can be electrically measured; 3) structural stability; 4) superior sensing performance at room temperature; and 5) tunable electrical properties (Wong et al., 2010). These characteristics have allowed the development of chemical, molecular and biological sensors (Oliveira & Mascaro, 2011; Wang, 2009).

Traditionally, pristine high-quality nanotubes are functionalized with functional groups to produce chemical or biochemical coatings (Wang, J., 2005; Zourob, 2010) or sites where very high sensitivity and selectivity to specific gases or to biochemical species is presented. Such gases or biochemical species can be detected by means of a change in electrical resistivity or capacitance presented in individual carbon nanotubes or bundles of them with the presence of this species. The change presented can be an increase or a reduction with respect to the value of the electrical parameter without the chemical or biochemical specie before mentioned (Chen, P.-C. et al., 2010). The chemical and biochemical sensors based on carbon nanotubes have even achieved sensitivities in the order of parts per billion to parts per million for specific gases or biochemical species depending of the molecule size and physicochemical properties (Bradley et al., 2003). Therefore, in any occasions it is necessary to add catalysts to improve the chemical activity during the chemical or biochemical detection (Cao & Rogers, 2009). In particular, the functionalization required by the biosensors regularly needs to favor the biocompatibility with the biological environment and realize the monitoring of information related with biological events and processes (Gruner, 2006; Ishikawa et al., 2009, 2010). In this manner, the biological species must be not affected by the biochemical interaction between the biosensor and the associated biological subject (Dong et al., 2008; Jia et al., 2008).

The basic construction blocks to design chemical or biochemical sensors based on carbon nanotubes can be divided into two different configurations: two-terminal CNT devices or three-terminal transistor-like structures. In the case of two-terminals devices, these can be modeled by an electrical resistor or an electrical capacitor (see Figure 11). In the case of

Carbon Nanotube- and Graphene Based Devices, Circuits and Sensors for VLSI Design 59

This work was supported by ITESI, CONACYT under thematic network RedNyN agreement I0110/229/09, and PROMEP agreement 92434. The first author thank to his wife

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**8. Acknowledgement** 

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**9. References** 

and son for their time and patience to realize this study.

3-527-31420-1, Federal Republic of Germany.

three-terminals, they are modeled by a bipolar junction transistor (BJT) or a metal-oxidesemiconductor field effect transistor (MOSFET), the latter being the most common for VLSI systems (Zhao et al., 2008).

Fig. 11. Cross section of resistive gas sensors and biosensors: (a) sensors based on carbon nanotubes, and (b) sensors based on graphene.

The use of complex morphologies and structures based on composites containing carbon nanotubes and polymers in the design of gas sensors, has allowed the detection of polar and nonpolar gases making use of the change of dielectric constant to enhance sensitivity to minute quantities of gas molecules (Jesse et al., 2006; Mahar et al., 2007).

Graphene is exploited due to its inexhaustible structural defects and functional groups. These are advantageous in electroanalysis and electrocatalysis for electrochemical applications such as gas sensors and biosensors. Physisorbed ambient impurities by graphene such as water and oxygen can produce an effect similar to hole-doping and therefore a behavior similar to a *p*-type material (Traversi et al., 2009). Then, the graphene can be exploited as a sensing material for the design of chemical and/or biochemical sensors. When graphene is doped, well-identified localized states are added and band gap is introduced to the electrical properties generating an interesting alternative to design sensors (Barrios-Vargas et al., 2011).

The main changes to be realized in the optimization of performance of gas sensors are the search of methods which allow us to synthesize identical and reproducible CNTs will give place to gas sensors with high quality and high performance, independently of the type of chemical functionalization required for the detection.
