ABSTRACT

In the present research, we have used Vppπ = 2.5 eV [17]. Kx and Ky are the wave vectors of carbon nanotubes [17,18], and they are given by 3 3 3h3h2 3 ( + ) + ( – )= 2x j a n m C a k n mK C and h2h2 ( – )+ 3 + ,2 (= )y j a n m akC n mK Cwhere, Ch is the chiral vector given by Ch = na1 + ma2 and a1 and a2are the unit vectors for the graphene hexagonal structure [2]. 2.1.2 Density of StatesNumerical techniques are needed to compute the density of states from Eq. (2.1) due to its complexity. However, an approximate density of states calculation has already been found for carbon nanotubes [14,22] and is described as follows:

4( ) = 2 , ED E dE dE 

where Ecmini is the minimum energy value for the given conduction band. Ecmini is found by determining the energy minimum value for the respective conduction band using Eq. (2.1). The first conduction band, Ecmin, can also be obtained from the following approximated equation [17]: g ppcmin ,= =2 3E aVE d π (2.3)where d is the diameter of the carbon nanotube and Eg is the energy bandgap. 2.2 Effective MassGiven the complete description of the energy dispersion for carbon nanotubes, Eq. (2.1) can also be used to calculate the electron effective mass for each band. We can use the effective mass relationship in a semiconductor [23] for calculating the effective electron mass in a CNT (n,m) as follows:

dk

     

(2.4) Table 2.1 summarizes the electron effective mass for various carbon nanotubes (n,m) calculated from Eqs. (2.4) and (2.1). Table 2.1 Effective mass of electrons in carbon nanotubes

(n,m) Effective mass of electrons (m*)(6,1) 0.255 m0(7,3) 0.116 m0(9,2) 0.099 m0(11,3) 0.108 m0†m0 is the mass of the electron (9.109 × 10-31 kg). 2.3 Carrier ConcentrationThe carrier concentration in a semiconductor is given by [23-25] ccnt = ( ) ( ) ,En D E f E dE

F c( – + )/2 –1/2 –1cnt c c0pp 8= ( + )( +2 ) (1+ )3 E E E kTn E E E E E e dEV a      π (2.7)

In deriving Eq. (2.7), the limits of integration in Eq. (2.6) have been changed by replacing the variable E with (Ec + E). Furthermore, the summation has also been dropped as the Fermi function becomes negligible for conduction energy band minimums beyond the first band.