**2.1 Properties and applications of carbon nanotubes**

Graphene is a two-dimensional analogue of carbon-based graphite material that has exceptional electrical characteristics, e.g., mobilities up to 15,000– 200,000 cm2 /Vs, derived from the bonding characteristics of the carbon sheets [5].

There are multiple pathways for creating graphene sheets, which include: exfoliation, unzipping through etching, growth from sublimation, and epitaxial growth from a catalyst layer [11]. The absence of a band gap in graphene limits voltage and power gains that may be achieved through operation of a device in the saturation regime. To overcome this, several doping strategies as shown in **Figure 2** have been proposed and tested, including: electrostatic doping, chemical doping, and stress or geometry restricted doping by breaking the graphene periodicity [5, 11]. Since it can be doped electrostatically, graphene provides a useful solution for certain electronic applications such the channels in field effect transistors (FETs) [12].

Carbon nanotubes (CNTs), which like graphene are allotropes of carbon, may be considered formed of hexagonal sheets of graphene rolled into cylinders (**Figure 3**). CNTs exhibit bandgaps in the range of zero to ~2 eV, and demonstrate metallic or semiconducting behavior depending mainly on their diameter and orientation of the hexagonal graphene structure along the axis of the tube (armchair, zigzag, or

**Figure 2.**

*Diagram showing multiple mechanisms for inducing a band gap in graphene [5, 11].*

#### **Figure 3.**

*Structural models of carbon nanotubes categorized based on the number of walls. (a) SWCNTs structures based on their chirality (zigzag, armchair, and chiral). (b) Structure of MWCNTs made up of two concentric shells. (c) MWCNTs composed of many overlapping shells [13].*

chiral) as illustrated in **Figure 3(a)** [13]. CNTs can exhibit exceptional conductivity, and as a result have found application in nanoscale FETs that have enabled novel devices including intermolecular logic gates [5].

CNTs fall under two main categories: single-walled carbon nanotubes (SWCNTs), like those shown in **Figure 3(a)**, and multiwalled carbon nanotubes (MWCNTs), depicted in **Figure 3(b)** and **(c)** [14]. As their names suggest, SWCNTs comprise single sheets of graphene for the outer walls, while MWCNTs are composed of multiple overlapping sheets of graphene rolled up in cylindrical forms. The lengths of SWCNTs are usually in the 50–300 nm range (though up to centimeter lengths are possible) with typical diameters of 1–2 nm, while diameters of MWCNTs can exceed 100 nm [13].

#### **2.2 Designing optimal microbolometer elements with CNTs**

The novel application we are considering involves using CNT materials in the design of bolometer elements for MWIR and LWIR band detection and imaging.

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*Nanostructure Technology for EO/IR Detector Applications*

These pixel elements are fabricated above the CMOS readout circuit unit cells. The focus will be on the development of relatively small (5–10 μm) bolometer unit cells with enhanced temperature coefficients of resistance (TCRs) and frequency response in the 1–10 kHz range. The feasibility of such arrays makes possible a significant number of defense and commercial applications involving uncooled IR

Detectors of IR radiation can be generally separated into two distinct categories: photon-based and thermal-based detectors [15, 16]. Photon-based detectors involve the absorption of incident photons as governed by the bandgap of the detector material, where the absorbed photons create electron-hole pairs that produce a photocurrent. Photon detectors may be further classified as p-n junction detectors, avalanche photodiodes, photoconductors, and Schottky diodes. Photon-based IR absorbers have a fast absorption response, but typically require cooling due to

Thermal-based IR detectors, though normally characterized by a much slower absorption response, commonly operate at room temperature and typically have higher responsivities at longer (e.g., IR band) wavelengths [15]. In such devices, the absorption of incident IR radiation raises the temperature of the material. In pyrometers, this is achieved through changes in electrical polarization, while in bolometers by changes in the resistance of the absorbing material. Through incorporating CNT absorbing material into bolometer pixel elements these temperaturebased resistance changes may be further enhanced, thereby enabling improved

The temperature that a bolometer pixel reaches after exposure to IR radiation can be determined by measuring its electrical resistance. This in turn may be achieved by comparing this resistance to a lookup table, or by using knowledge of the temperature coefficient of resistance (TCR). A large TCR, which corresponds to a higher thermal resistance that results in a larger rise in temperature, is desirable

The TCR of a material is defined as the change in electrical resistance per degree Kelvin divided by the absolute electrical resistance measured at the

> *Re* \_\_\_ *dRe*

The electrical resistance of a pixel after it reaches a temperature ∆*T* above its

*Re*(*T*) = *Re*(*T*0)(1 + *TCR*) (2)

Microbolometers are specific types of bolometers used as detectors in thermal cameras that have traditionally been based on vanadium oxide (VOx) or amorphous

From this relationship, the pixel temperature may be calculated.

*dT* (1)

*DOI: http://dx.doi.org/10.5772/intechopen.85741*

*2.2.1 Photon- vs. thermal-based detectors*

detection and imaging capabilities.

*2.2.2 Temperature coefficient of resistance*

for achieving greater temperature resolution.

*TCR* = \_\_1

detection and imaging.

thermal effects.

quiescent point:

ambient becomes:

*2.2.3 CNTs as bolometric elements*

These pixel elements are fabricated above the CMOS readout circuit unit cells. The focus will be on the development of relatively small (5–10 μm) bolometer unit cells with enhanced temperature coefficients of resistance (TCRs) and frequency response in the 1–10 kHz range. The feasibility of such arrays makes possible a significant number of defense and commercial applications involving uncooled IR detection and imaging.

#### *2.2.1 Photon- vs. thermal-based detectors*

*Nanorods and Nanocomposites*

**72**

**Figure 3.**

chiral) as illustrated in **Figure 3(a)** [13]. CNTs can exhibit exceptional conductivity, and as a result have found application in nanoscale FETs that have enabled novel

*Structural models of carbon nanotubes categorized based on the number of walls. (a) SWCNTs structures based on their chirality (zigzag, armchair, and chiral). (b) Structure of MWCNTs made up of two concentric* 

The novel application we are considering involves using CNT materials in the design of bolometer elements for MWIR and LWIR band detection and imaging.

CNTs fall under two main categories: single-walled carbon nanotubes (SWCNTs), like those shown in **Figure 3(a)**, and multiwalled carbon nanotubes (MWCNTs), depicted in **Figure 3(b)** and **(c)** [14]. As their names suggest, SWCNTs comprise single sheets of graphene for the outer walls, while MWCNTs are composed of multiple overlapping sheets of graphene rolled up in cylindrical forms. The lengths of SWCNTs are usually in the 50–300 nm range (though up to centimeter lengths are possible) with typical diameters of 1–2 nm, while diameters

**2.2 Designing optimal microbolometer elements with CNTs**

devices including intermolecular logic gates [5].

*shells. (c) MWCNTs composed of many overlapping shells [13].*

of MWCNTs can exceed 100 nm [13].

Detectors of IR radiation can be generally separated into two distinct categories: photon-based and thermal-based detectors [15, 16]. Photon-based detectors involve the absorption of incident photons as governed by the bandgap of the detector material, where the absorbed photons create electron-hole pairs that produce a photocurrent. Photon detectors may be further classified as p-n junction detectors, avalanche photodiodes, photoconductors, and Schottky diodes. Photon-based IR absorbers have a fast absorption response, but typically require cooling due to thermal effects.

Thermal-based IR detectors, though normally characterized by a much slower absorption response, commonly operate at room temperature and typically have higher responsivities at longer (e.g., IR band) wavelengths [15]. In such devices, the absorption of incident IR radiation raises the temperature of the material. In pyrometers, this is achieved through changes in electrical polarization, while in bolometers by changes in the resistance of the absorbing material. Through incorporating CNT absorbing material into bolometer pixel elements these temperaturebased resistance changes may be further enhanced, thereby enabling improved detection and imaging capabilities.

#### *2.2.2 Temperature coefficient of resistance*

The temperature that a bolometer pixel reaches after exposure to IR radiation can be determined by measuring its electrical resistance. This in turn may be achieved by comparing this resistance to a lookup table, or by using knowledge of the temperature coefficient of resistance (TCR). A large TCR, which corresponds to a higher thermal resistance that results in a larger rise in temperature, is desirable for achieving greater temperature resolution.

The TCR of a material is defined as the change in electrical resistance per degree Kelvin divided by the absolute electrical resistance measured at the quiescent point:

$$TCR = \frac{1}{R\_\epsilon} \frac{dR\_\epsilon}{dT} \tag{1}$$

The electrical resistance of a pixel after it reaches a temperature ∆*T* above its ambient becomes:

$$R\_\epsilon(T) = R\_\epsilon(T\_0) \left(\mathbf{1} + T\mathbf{CR}\right) \tag{2}$$

From this relationship, the pixel temperature may be calculated.

#### *2.2.3 CNTs as bolometric elements*

Microbolometers are specific types of bolometers used as detectors in thermal cameras that have traditionally been based on vanadium oxide (VOx) or amorphous

#### *Nanorods and Nanocomposites*

silicon material on silicon. Using carbon-based CNT detector elements in IR microbolometer pixels is attractive due to their high mobility, large thermal resistance, and intrinsically high TCR values [4]. The high thermal conductivity, high strength, and other optical and electrical properties of CNTs that can be varied over a wide spectral range likewise contribute towards their usefulness in this application.

The low electrical resistance and corresponding high conductivity of CNTs are mainly attributed to electrons tunneling between adjacent nanotubes and corresponding unimpeded flow of electrical current. The tunnel barrier height between the CNTs directly impacts the amount of heating that takes place for a given electric field. Assuming that electrons can transport across it, this barrier is governed by Fowler-Nordheim-type tunneling or thermionic emission. The expected associated TCR values can be calculated using the following expression:

$$I = q \int\_0^\infty T\_t(E) v(E) DOS(E) f(E, T) dE \tag{3}$$

where *Tt*, *v*, *DOS*, and *f* are the transmission coefficient, thermal velocity, density of states, and distribution function, respectively, for electrons in the CNT. We have performed this calculation of TCR and current as a function of barrier height and electric field, and these results are shown in **Figure 4** [16].

The theoretical TCR values for a CNT film are plotted in **Figure 4(a)** as a function of the electric field between the nanotubes and the barrier height. The calculations predict a comparatively very large TCR, which can be attributed to the relatively large barrier height between adjacent SWCNTs. If a relatively low barrier height on the order of 0.06 eV is assumed, then a TCR of approximately 2.5% is obtained. It is noted that a TCR of this magnitude is associated with very low output currents. **Figure 4(b)** shows the plotted bolometer current density as a function of barrier height and electric field.

Research on this CNT absorber material has provided proof-of-principle demonstrations of extraordinary TCRs in devices [7]. Within the temperature region where the composite material undergoes a volume phase transition, considerable changes in resistance are observed. Negative TCRs of magnitude larger than −10%/°C were determined, and other composite structures with thinner suspended

#### **Figure 4.**

*(a) Contour plot of TCR vs. electric field and barrier height between SWCNTs of the film (color bar scale in units of %TCR); (b) bolometer current as a function of electric field and barrier height (color bars scale in units of amperes) [16].*

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*Nanostructure Technology for EO/IR Detector Applications*

threefold enhancement in detector responsivity.

films achieved TCRs in excess of −50%/°C. Such high TCR values enable up to a

This section includes an assessment of the design of bolometer elements using carbon nanotubes as both the IR absorbing material and electrical response material [14]. The aim is to first determine the thermal response of the bolometer absorber, and then establish how the electrical characteristics of the CNT material are altered by changes in temperature following IR absorption. Here the focus is on an absorbing material composed of a CNT film comprising randomly situated CNTs each of

To determine the temperature of the material in the presence of IR radiation, we start with the heat flow equation. This partial differential equation relates the time rate of change in temperature to the position and the rate of net heat that is

<sup>∂</sup>*<sup>t</sup>* <sup>=</sup> κ∇<sup>2</sup>*<sup>T</sup>* <sup>+</sup> *Hnet* (4)

), *κ* is the thermal diffusion coef-

). To

absorbed by the material as a function of time and position:

where *Cv* is the thermal capacitance (J/K cm3

\_\_\_ ∂*T*

ficient (W/K cm), and *Hnet* is the net power absorbed by the material (W/cm3

solve this equation for the CNT bolometer, we must first determine *Cv* and *κ* for the

To determine the heat capacity of a carbon nanotube, we first determine the internal vibrational energy of the CNT, and then take the derivative with respect to temperature. The internal energy is found by calculating the energy of each vibrational mode, multiplying by the probability that the mode is populated using Bose-Einstein statistics, and then summing over all the allowed

Since the number of allowed modes is dependent on the diameter and wrapping angle of the CNTs, we must take a statistical sample. After multiplying the heat capacity of the individual CNTs by the number of CNTs in the film to provide a reasonable value for the heat capacity of the film, and inserting numerical values for physical constants, we arrive at the following average numerical value for the

*Cvt* ≈ 1.4 × 10−18*Ld* (5)

where *L* is the CNT length in microns and *d* is the CNT diameter in nanometers.

In addition to the thermal capacitance, we need to determine the thermal diffusion coefficient and then the thermal resistance of a single CNT. Experiments on isolated CNTs have involved fitting the coefficient of thermal diffusion to data,

*DOI: http://dx.doi.org/10.5772/intechopen.85741*

**2.3 Model for CNT-based IR bolometers**

2 nm thickness.

*2.3.1 Heat flow equation*

CNT and CNT film.

thermal capacity of a CNT:

*2.3.3 CNT thermal diffusion coefficient*

obtaining the following expression [16]:

modes.

*Cv*

*2.3.2 Thermal capacitance of CNT absorber*

films achieved TCRs in excess of −50%/°C. Such high TCR values enable up to a threefold enhancement in detector responsivity.
