Transport in nanotubes: Effect of remote impurity scattering

The theory of the remote Coulomb impurity scattering in single-wall carbon nanotubes is developed within a one-electron approximation. The Boltzmann equation is solved within the drift-diffusion model to obtain the tube conductivity. The conductivity depends on the type of the nanotube band structure (metal or semiconductor) and on the electron Fermi energy. We found that the exponential dependence of the conductivity on the Fermi energy is due to the Coulomb scattering rate having a strong dependence on the momentum transfer. We calculate intrasubband and intersubband scattering rates and present general expressions for the conductivity. Numerical results, as well as obtained analytical expressions, show that the degenerately doped semiconductor tubes may have very high mobility unless the doping level becomes too high and the intersubband transitions impede the electron transport.

Figure 1

(Color online) Electron energy dispersion for armchair [10,10] and zigzag [17,0] SWNT’s. Inset: Zoom out of the lowest subbands and the electrochemical potential (green dashed line).

Figure 2

(Color online) Conductivity of a zigzag [17,0] SWNT vs the electrochemical potential (the doping level).

Figure 3

(Color online) Bandstructures for zigzag SWNT’s of two types. Left: $[3q+1,0]$ SWNT; Right: $[3q-1,0]$ SWNT. Doping level is shown as horizontal lines: pink/green (lower/upper) line is for low/high doping level. Insets show the scattering rates for different scattering mechanisms as a function of energy as in left and right diagrams, respectively.

Figure 4

(Color online) Temperature dependence of the conductivity of a zigzag [17,0] SWNT vs the electrochemical potential in a vicinity of the second subband edge.