Ballistic transport in nanowires and carbon nanotubes

The charge carriers in nanowires (NWs), carbon nanotubes (CNTs), and those confined to a very high magnetic field have one-dimensional (1D) character as quasi-free propagation of electron waves with analog energy spectrum exists only in one direction. The energy spectrum is quantum (or digital) in other two cartesian directions where electron waves are standing waves. In the quantum limit, an electron (hole) occupies the lowest (highest) digitized/quantized state giving it a distinct 1D character. The energy E = v
_F
| k | in carbon-based devices is linearly dependent on the wave vector k, where v
_F
≈ 10
⁶
m/s. This is in direct contrast to parabolic character E = ħ
²
k
²
/2m* in solids with effective mass m*, for example in silicon NWs. The probability of changing wavevector from +ve to -ve direction through scattering or vice versa is greatly reduced and hence high mobility is expected, especially at low temperatures. The crucial outcome of this paper is the answer to the question: Does a higher mobility leads to a higher ultimate saturation velocity? The distribution function in a high electric field ε is then naturally asymmetrical affected by the energy ±qεℓ absorbed or emitted by a carrier of charge q during its ballistic flight in a mean free path ℓ. The ultimate drift in response to a high electric field results in unidirectional streaming of the otherwise randomly-oriented velocity vectors in equilibrium. The high-field drift limited by the intrinsic velocity is ballistic, unaffected by scattering-limited processes. The ultimate velocity is further limited to an emission of a quantum either in the form of an optical phonon or a photon by an electron excited to a higher state by the applied electric field. The velocity does not depend on scattering parameters. Ballistic processes as a result of reduction in length of a CNT or NW below the scattering-limited mean free path ℓ in the quasi-free direction are also discussed.