Carbon Nanotubes in Passive RF Applications

Abstract

Carbon nanotubes are characterized by unique electrical properties which make them good candidates for different applications in electronics and electrical engineering. In this chapter we focus mainly on electrical properties of single wall conducting carbon nanotubes in high frequency, electromagnetic waves interaction with carbon nanotubes and the possible passive RF applications. The term “high frequency” here refers to the frequency band from gigahertz to terahertz. This chapter starts from microscopic view by discussing electrodynamics of carbon nanotubes to show the mechanism of time varying electromagnetic field interaction with carbon nanotubes (Slepyan et al., 1999; Slepyan et al., 2008; Mikki & Kishk 2008). Based on these electrodynamics properties, an equivalent dynamic surface conductivity is developed to represent a macroscopic view for the interaction of high frequency electromagnetic fields with carbon nanotubes (Hanson, 2005). This equivalent surface conductivity of carbon nanotube is characterized by complex value with negative imaginary part. This negative imaginary part represents an inductive effect in carbon nanotubes. This inductive effect is due to chiral property of the electric current flow along the carbon nanotube (Slepyan et al., 1998; Miyamoto et al. 1999). This inductivity has a significant effect on reducing the wave velocity of electromagnetic wave propagation along carbon nanotube. This wave velocity reduction corresponds to decreasing the wavelength. This property is quite important in passive RF applications like passive circuits and antennas, since the dimensions of these applications depend mainly on the wave length (Slepyan et al., 1999; Slepyan et al., 2008; Attiya, 2009). Based on the macroscopic surface conductivity of carbon nanotube, the problems of electromagnetic fields interaction with carbon nanotubes can be presented in similar ways to conventional problems related to cylindrical structures with finite surface conductivity. In this way the problem of carbon nanotube antennas can be presented as an electric field integral equation problem which can be treated numerically by method of moments (Hanson, 2005; Hao & Hnason, 2006). Similarly, the problem of surface wave propagation along carbon nanotubes can be presented as a boundary value problem where the difference between the tangential magnetic fields on the two sides of the wall of the carbon nanotube would equal the induced current on the wall of the carbon nanotube. This induced current depends on the tangential electric field along the carbon nanotube and the surface conductivity. This boundary value problem is solved to obtain the field distribution and the complex propagation constants of the surface wave modes propagating along carbon