CHAPTER 6 CARBON NANOTUBE AND ITS RF APPLICATION

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1 CHAPTER 6 CARBON NANOTUBE AND ITS RF APPLICATION 6.1 Introduction In this chapter we have made a theoretical study about carbon nanotubes electrical properties and their utility in antenna applications. Ever since the first invention of carbon nanotube (CNT) by Ijima in the year 1991, there has been a lot of research into their physical, mechanical, thermal, electrical, electronics and radio frequency (RF) properties. This led to the development of sensors, microelectronics, solar cells, electronic components, interconnects, coatings and films etc. The measurement of individual carbon nanotubes confirms that they are either a one-dimensional material with excellent conductor or semiconductor. Because of excellent conductivity properties researchers studied electromagnetic wave interaction of CNTs and ac conductivity in comparison with conventional conductors like silver and copper wires of same size. G.W. Hanson [104] presented a detailed conductivity difference between CNT and copper. He concluded that ac conductivity is characterized by an inductive effect. According to research paper [104], stored kinetic energy in the CNT causes inductive effect. Peter Burke [103] introduced CNT transmission line equivalent circuit model. To the normal inductance and capacitance, quantum capacitance and kinetic inductance effects are added that represents the conductivity of CNT transmission line section. These two additional lumped elements lead to two main effects on electromagnetic wave propagation in CNT: high characteristic impedance and slow wave propagation. These two properties lead to reduction in size of passive circuits and antenna. Burke et al. [108] have highlighted a detailed study on CNT dipole antenna. In next sections we study detailed CNT structure when it is either good conductor or semiconductor followed by radio frequency model for antenna applications. Further, we 175

2 study how CNT is modeled as dipole antenna and its radiation characteristics at THz frequency. Finally we discuss advantages and disadvantages of CNT antennas. 6.2 Carbon Nanotube Structure and as a Conductor. Carbon nanotubes are long cylindrical carbon molecules with a diameter in few nanometers and length up to few centimeters. CNT can be classified as single wall carbon tube (SWCNT) and multiwall carbon nanotube (MWCNT). A SWCNT can be regarded as rolled up sheet of graphene as shown in Fig. 6.1 [115], with a diameter close to 1 nm and length thousand times of diameter. MWCNTs are made by SWCNT inside one another. The SWCNT and MWCNT structure is illustrated in Fig. 6.2 [5]. Researchers have proven that CNTs can be semiconducting or metallic with higher conductivity depend upon chirality of the CNT. Based on nanotube axis the nanotube can be armchair or zigzag or chirality. Armchair and zigzag nanotubes are metallic. For RF property and CNT antenna studies we have selected armchair nanotubes as they are high metallic properties. The metallic and semiconducting nanotube geometric structure is illustrated in Fig. 6.3 [102]. As metal is an integral part of any antenna structure, it is necessary to understand metallic nanotube RF behavior and its effect on nano antenna radiation properties like bandwidth, radiation resistance, efficiency etc. Fig. 6.1: Graphene sheet with carbon atom [115] 176

(a) Metallic (b) Semiconducting [102] 6.

found that CNTs can be grown in length from nano meter to a few

For RF applications a SWCNT of diameter d referenced to a ground

3 (a) (b) Fig. 6.2: carbon nanotube (a) SWCNT, (b) MWCNT, [5] (a) (b) Fig. 6.3: Carbon nanotube (a) Metallic (b) Semiconducting [102] 6.3 Carbon Nanotube Radio Frequency (RF) Model From research it is found that CNTs can be grown in length from nano meter to a few centimeters, and few nano meters in diameter. For RF applications a SWCNT of diameter d referenced to a ground at a height h can be modeled as a transmission line with lumped impedances electrostatic capacitance and magnetic inductance. Fig. 6.4 shows CNT over 177

4 ground plane and basic transmission line model for bulk metal. C. P. Burke [103] has developed an corresponding RF circuit model for a SWCNT over a very conductive ground flat as illustrated in Fig. 6.4(c). In RF circuit model of SWCNT, in addition to electrostatic capacitance (C ES ) and magnetic inductance (L M ), there are other two lumped impedanceskinetic inductance (L K ) and quantum capacitance (C Q ) in transmission line. The kinetic inductance is result of excess kinetic energy given to electrons, typically very larger than the magnetic inductance. Because of this huge inductance, nanotubes act as a quantum transmission line for radio waves. (a) (b) (c) Fig. 6.4: Transmission line model (a) CNT over ground plane (b) Basic transmission line model (c) SWCNT transmission line model 178

5 In [4], the expressions and calculated values for kinetic inductance L K and quantum capacitance C Q are given by h LK = 2e 2 v F (6.1) 2e C Q = hv 2 F (6.2) Where h is planks constant, e is charge of electron and v F =8x10 5 m/s is Fermi velocity of carbon nanotube. From Equations (6.1) and (6.2), numerically L K =16 nh/µm and C Q =100 af/µm. The other important parameter is characteristic impedance of nanotube. The characteristic impedance of any transmission line is given by the square root of the ratio of inductance to capacitance per part length. The characteristic impedance Z c of nano transmission line is given by Z C LK h = 12.5kΩ 2 C 2e Q (6.3) Similarly, one more important parameter in CNT is wave velocity v F, is given by v F = 1 C L Q K (6.4) The wave velocity in CNT is normally about 100 times lesser than the velocity EM wave. This is because the kinetic inductance in eq. (6.4) in CNT is about 10,000 times higher than the magnetic inductance per unit length [108]. The importance of wave length in CNT is it miniaturizes the CNT antenna by 100 times for a given frequency. 6.4 Carbon Nanotube Antennas CNT has possible use as sensors, transistors, field emission devices and other electronic applications. In this section we discuss use of CNT as an antenna element. 179

6 Researchers have done work on suitability of CNT for antenna applications. Since CNT exhibit ballistic transport and have a relaxation time which is 50 times greater than in copper [110], they are being considered as a conducting metal. CNT antennas were studied using transmission line model [108]. While modeling CNT antenna, several effects were considered by researchers. The important effects are: slow wave propagation and high characteristic impedance. These effects offer CNTs applicability for receiving and transmitting electromagnetic signals. CNT antennas are analyzed in GHz and below THz frequency range [104] and [105] GHz Carbon Nanotune Antennas Using Hallen s type integral equation, G.W. Hansen investigated carbon nanotube dipole antenna which is based on quantum mechanical conductivity. Efficiency (e r ), Current profile and the input impedance (Z in ) are given and compared to copper antenna of same shape and size [104]. Initially he modeled solid copper dipole antennas of length (L) 0.47λ for micrometer and nanometer radius (a) at 120 GHz. The results obtained are listed in Table 6.1 for analysis. Table 6.1: Input impedance and efficiency of solid copper dipole antenna for micrometer and nanometer thickness radius [104]. Dipole antenna radius Input Impedance (ohm) Efficiency a = 3.75 µm a = 20 nm a = 2 nm Z pc in= j7.36 Z σ in= j5.76 Z pc in= j5.76 Z σ in= j5.76 Z pc in=62.08-j Z σ in=19788 j

7 Where Z pc in perfect copper input impedance and Z σ in is bulk copper input impedance. From Table 6.1 it will become clear that for very smaller radius values (in nm range) the bulk copper antenna input impedance become very large and efficiency drastically reduces. The reasons for this drastic change are due to grain and surface boundary scattering causes a considerable raise in surface resistance of copper. However, it must be noted that common perfect conductor estimation is not significant. Now the same antenna structure is built with CNT for L = 10 µm and a = nm experimented for various values of frequencies. Table 6.2 illustrates the results of experiment with CNT dipole antenna. Table 6.2: Input impedance and efficiency of CNT dipole antenna at various frequencies [104]. Frequency Input Impedance (ohm) Efficiency 10 GHz Z CNT in= j GHz Z CNT in= j GHz Z CNT in= j GHz Z CNT in= j Where Z CNT in, is input impedance of CNT dipole antenna. From Table 6.2, it is clear that at 160 GHz, CNT dipole antenna input impedance is drastically reduces to j0.014 and efficiency is in the order of 10-6, when compared to bulk copper dipole antenna of approximately same size. Finally we conclude that some properties of CNT antenna is quite different from copper antenna of same dimensions. Despite low values of efficiency, the radiation pattern of CNT dipole antenna is same as that of short dipole antenna. And, the directivity of CNT antenna is approximately equal to 1.5 although gain G will be small value of efficiency. The CNT antenna may be used to rectify the THz signal to power microscopic or nanoscopic circuits. Thus the research paper [104] presents fundamental radiation properties of CNT dipole antennas. 181

8 Similarly, CNT antennas are analyzed for infrared and optical range. In this case armchair CNT is used to construct dipole antenna. An armchair CNT antenna having radius a is leaning down z-axis is shown in Fig. 6.5 [106]. It is found that efficiency and gain for dissimilar CNT length are alike. For L = 50, 150, and 1000 nm dipoles in and optical range. This corresponds to 56 GHz for a = nm and 225 GHz for a = nm, the efficiency and gain are same. Hence, unlike standard macroscopic radius metal dipole antennas, the Fig. 6.5: Armchair nanotube antenna [106] efficiency and gain of CNT dipole antennas are very small and high input impedance due to their small radius. These properties may be useful for linking CNT antenna to nano electronic circuits. With the advances in synthesis techniques several groups extending nano fabrication expertise to produce straight, electrically unbroken individual SWCNTs with lengths from µm to 10 cm [107]. These lengths are in the order of mm wave and microwave wavelength. In 2004, Burke et al. [108] have grown 400 µm lengths SWNT. The experiment shows that the resistance per unit length is 1000 Ω per micron. At 1.5 nm diameter the conductivity is 10 9 S/m which is ten times higher than copper metal. With high surface resistance per unit length, CNT antenna may likely to function in the high loss area. The advantage of CNT as dipole antenna is that it can serve as an outstanding impedance matching circuit between high impedance devices and free space [109]. However the drawback is low efficiency. In [108] the efficiency achieved is -90 db. 182

9 The other research group investigated CNT as dipole antenna in 2008 [110], based on customized kernel function for the integral equation to model surface resistance. A computational result for the integral equation gives the current distribution over the carbon nanotube. The antenna efficiency and driving point impedance were calculated from current distribution. For 100 GHz operating frequency, efficiency and input impedance for ideal conductor, copper and dipole CNT antennas with length L=0.47 λ are verified. The result is listed in Table 6.3 and it is found that for smaller nm radius the input impedance and efficiency of copper and CNT dipole antenna are comparable. The efficiency of copper dipoles may be even lesser than CNT, since additional surface and grain scattering is not taken into account. However the CNTs conductivity will be not varied by gain or surface scattering because of their normal structure. Besides efficiency the reduction in CNT antenna is size is also investigated. Normally, the first resonance would be at 7.5 THz. However, the first resonance occurred at 160 GHz. As a result, the wave length on the dipole CNT antenna is decreased by a value 50 which is denoted as slow wave factor. The low efficiency of CNT antennas restricts their application only to on-chip communication systems or chip-to-chip. Table 6.3: Input impedance and efficiency of perfect conductor, copper and CNT dipole antenna radius (a) Input Impedance (ohm) Efficiency 3 µm 30 nm 3 nm Z pc = 67 j19 Z CNT = 140 j2575 Z cu = 75 j1727 Z pc = 63 j82 Z CNT = 950 j7934 Z cu = 666 j4733 Z pc = 62 j109 Z CNT = 1819 j10730 Z cu = 1978 j

10 Where Z pc, Z CNT and Z cu are input impedances of perfect conductor, CNT and copper respectively. In continuation of research work on CNT antennas, research group in [111] presented CNT antenna shown in Fig. 6.6(a). This new concept CNT antenna is close to physical realization of classical dipole antenna. In classical dipole antenna it was assumed that the radius of dipole was larger than skin depth and lower resistance losses in determining the current distribution on antenna. However the above assumptions are meaningless for CNT antenna as CNT diameter is lesser than several skin depths and having large resistance and inductance. Therefore the current distribution on CNT antenna is 1-dimensional where as it is 2-dimensional on classical antenna. Fig. 6.6(b) and (c) illustrates current distribution on CNT dipole antenna and classical wire dipole antenna. The main difference in current distribution is that the current distribution on CNT dipole is periodic with a wavelength about 100 times lesser than the wavelength of free space for a given frequency because of large resistance and inductance present in CNT. In CNT the wave velocity is about 100 times smaller than the (a) (b) (c) Fig. 6.6: Carbon nanotube antenna (a) Concept CNT (b) current distribution on CNT antenna (c) current distribution on classical wire antenna [111] 184

47 GHz (b) 7.3 GHz [112] 6.4.2 THz Carbon Nanotube Antennas Few researchers characterized electromagnetic properties of SWCNT antennas in THz frequency [112] [114].

11 speed of light. The kinetic inductance per unit length in CNT is about 1000 times higher than the magnetic inductance per unit length. Hence the wave velocity is 100 times lesser than the light speed [111]. Their calculation shows CNT antenna has -90dB efficiency. Fig. 6.7: Armchair/Zigzag SWCNT dipole antenna [112] (a) (b) Fig.6.8: Radiation pattern of armchair CNT antenna at (a) 2.47 GHz (b) 7.3 GHz [112] THz Carbon Nanotube Antennas Few researchers characterized electromagnetic properties of SWCNT antennas in THz frequency [112] [114]. Their result shows a significant portion of THz wave was contributed from CNT antenna. The construction of armchair (always metallic) CNT antenna is illustrated in Fig.6.7 for L = 0.5λ at r = (5, 0, 0) and r = (10, 0, 0) µm. The result shows that antenna resonates at 2.47 THz and 7.38 THz. The VSWR is less than 1.5 corresponding to S11 less than -10dB with a bandwidth of 8.9% and 3.1%. The radiation patterns are illustrated in Fig However, CNT antenna shows low emission power and low efficiency compared to photo detector antenna. In order to improve the above two parameters, 185

(d) 10: Radiation pattern of (a) single CNT (b) 10

12 Fig. 6.9: Carbon nanotube antenna array [114] (a) (b) (c) (d) Fig. 6.10: Radiation pattern of (a) single CNT (b) 10 elements array CNT antenna (c) 50 element array CNT antenna (d) 100 element array antenna [114] 186

13 researchers made use of CNT array as dipole antenna. Fig. 6.9 shows CNT array antenna where as Fig shows radiation pattern. The same research group characterized zig-zag CNT array antenna for input impedance, emission power and efficiency at f c = 2.4 THz for a CNT radius R = nm. The CNT array elements are 10, 50 and 100. It is found that with CNT array elements dipole antenna gain increases and input impedance decreases. It is also noted that directivity increases with increase in CNT array elements. 6.5 CNT Advantages and Disadvantages Advantages: 1. Metallic CNTs have conduction and current densities that meet or exceed the best metals, thus suitable for nano interconnects and antennas [102]. 2. Semiconducting CNT s have mobilities and transconductances that meet or exceed the known best semiconductors, thus suitable for sensors, FETs etc.[102]. 3. It is found that radius values for CNT on the scale of nanometers, CNT s can exhibit significantly less loss than cylindrical copper antennas having same size. Thus CNT s may be an appropriate choice as an antenna or interconnect [105]. 4. In the metallic conductive mode CNT s have very high electrical conductivity and are believed to conduct through a mechanism of ballistic transport. The advantage of ballistic transport is that the surface resistance of the nanotube is free of its length. Because of their non-ohmic property and large thermal stability, CNT s have an expected current carrying capacity of 1 billion A/square cm about 1000 times than the copper metal [112]. 5. CNT can be a greater impedance matching network to get from free space to high impedance devices. 6. CNT s are free from corrosion and having lesser density in comparison with copper. 187

14 Disadvantages: 1. Challenging is the concern of device fabrication using CNT s. One may not get pure metal or semiconducting CNT s. CNT;s are a mixture of semiconductors and metal. Efforts are under way to address these concerns [102]. 2. To date, there is no consistent, rapid, and reproducible approaches are available to create the same type of CNT s. Efforts are under way to address these issues. 3. CNT antennas are found to exhibit longitudinal current resonance frequencies have very high input impedances. Due to extremely small radius, CNT antenna exhibit very low efficiency (reported: -90 db) [106]. 4. Because of CNT s basic structure as a rod, CNT s are suitable for dipole antenna. Till date only dipole antennas are modeled, analyzed and experimented. At the moment, arbitrary antenna geometries are little known. 5. The low efficiency of CNT antenna restricts the signal transmission to very short distances at present in e.g. on-chip communication system or chip-to-chip [110]. 6. Nano antennas of CNT exhibit inherently a very high resistance per unit length. A low resistance may be achievable if the CNT is doped or CNT arrays are created [110]. 7. The experimental measured results in RF field are few and far between, because of the difficulties in manufacturing and measurement [111]. 8. At present CNT s are very costly. In next chapter we highlight the conclusion and remarks drawn from the research study. The chapter also includes the futuristic scope for further study and investigation. 188

Carbon Nanotubes Composite Materials for Dipole Antennas at Terahertz Range

Progress In Electromagnetics Research M, Vol. 66, 11 18, 2018 Carbon Nanotubes Composite Materials for Dipole Antennas at Terahertz Range Yaseen N. Jurn 1, 2, *, Mohamedfareq Abdulmalek 3, and Hasliza