Ballistic conduction
In general, the resistivity of a material exists because an electron, while moving inside a medium, is scattered by impurities, defects, thermal fluctuations of ions in a crystalline solid, or, generally, by any freely-moving atom/molecule composing a gas or liquid.
Without scattering, electrons simply obey Newton's second law of motion at non-relativistic speeds.
The mean free path can be increased by reducing the number of impurities in a crystal or by lowering its temperature.
Ballistic conduction is typically observed in quasi-1D structures, such as carbon nanotubes or silicon nanowires, because of extreme size quantization effects in these materials.
[1] Ballistic conduction differs from superconductivity due to 1) a finite, non-zero resistance and 2) the absence of the Meissner effect in the material.
The presence of resistance implies that the heat is dissipated in the leads outside of the "ballistic" conductor, where inelastic scattering effects can take place.
is the mean free path for the carrier which can be given by Matthiessen's rule, written here for electrons: where In terms of scattering mechanisms, optical phonon emission normally dominates, depending on the material and transport conditions.
To get these characteristic scattering rates, one would need to derive a Hamiltonian and solve Fermi's golden rule for the system in question.
For the 1D graphene nanoribbon field effect transistor (GNR-FET) on the right (where the channel is assumed to be ballistic), the current from A to B, given by the Boltzmann transport equation, is where gs = 2, due to spin degeneracy, e is the electron charge, h is the Planck constant,
are the Fermi levels of A and B, M(E) is the number of propagating modes in the channel, f′(E) is the deviation from the equilibrium electron distribution (perturbation), and T(E) is the transmission probability (T = 1 for ballistic).
[citation needed] Based on the definition of conductance and the voltage separation between the Fermi levels is approximately
Conversely, the quantum confinement in the 1D GNR channel constricts the number of modes to carrier degeneracy and restrictions from the energy dispersion relationship and the Brillouin zone.
[3][4] Ballistic conduction enables use of quantum mechanical properties of electron wave functions.
In such cases, when the radius of the contact spot is smaller than the mean free path of electrons
Non-ballistic electrons behave like light diffused in milk or reflected off a white wall or a piece of paper.
From the resistance point of view, stochastic (not oriented) movement of electrons is useless even if they carry the same energy – they move thermally.
If the electrons undergo inelastic interactions too, they lose energy and the result is a second mechanism of resistance.
[6] The dominant scattering mechanism at room temperature is that of electrons emitting optical phonons.
So a nanotube or graphene nanoribbon could be a good ballistic conductor if the electrons in transit don't scatter with too many phonons and if the device is about 100 nm long.
Such a transport regime has been found to depend on the nanoribbon edge structure and the electron energy.
