Ballistic conduction

Ballistic conduction is the characteristic of a material, known as a "ballistic conductor", which has crystalline properties that allow electrons to flow through the material without collisions. The material must be free of impurities that electrons could collide with. In ordinary conductors, flowing electrons continually collide with the atoms making up the material, slowing down the electrons and causing the material to heat, effectively creating resistance. Ballistic conduction differs from superconductivity due to the absence of the Meissner effect in the material.

Ballistic conduction occurs in some carbon nanotubes.

Ballistic conduction on micro-scale

Probably any conduction process over a short enough distance (~several nanometers) could be considered as ballistic conduction,because the probability of scattering on an impurity or phonon is very low at such a short distance.

Most common studies of ballistic conductivity has been conducted at this micro- or nano-scale, often at low temperature.For example nanowires and STM contacted molecules, metal particles or nano-scale semiconductor structures are often very good approximations of ballistic conductors.

"Ballisticity" of conduction is probabilistic. There are no totally ballistic conductors or totally non-ballistic conductors. Ballisticity is expressed as a probability that an electron will travel without scattering.

In so-called ballistic conductors (graphene, nanotubes, and some types of quantum well systems), the probability of scattering is low enough to consider conduction as ballistic on an almost macroscopic scale.

Importance of ballistic conductivity

Despite ballistic conductivity being connected with very low resistance of particular materials, the major importance is not energy efficient transport of power over long distance, but rather nanoscience and information processing electronics applications.

Ballistic conduction enables use of quantum mechanical properties of electron wave functions. Ballistic transport is coherent in wave mechanics terms. Phenomena like double-split interference, spacial resonance (and other optical or microwave-like effects) could be exploited in electronic systems at nanoscale.

Optical analogies of ballistic conduction

A comparison with light provides an analogy between ballistic and non-ballistic conduction.Ballistic electrons behave like light in a waveguide or a high-quality optical assembly. Non-ballistic electrons behave like light diffused in milk or reflected off a white wall or a piece of paper.

Electrons can be scattered several ways in a conductor. Electrons have several properties: wavelength (~energy), direction, phase, and spin orientation. Different materials have different scattering probabilities which cause different incoherence rates (stochasticity). Some kinds of scattering can only cause a change in electron direction, others can cause energy loss.

Consider a coherent source of electrons (like a laser) connected to a conductor. Over a limited distance, the electron wave function will remain coherent. You still can deterministically predict its behavior (and use it for computation theoretically). After some greater distance, scattering causes each electron to have a slightly different [phase] and/or direction. But there is still almost no energy loss. Like monochromatic light passing through milk, electrons undergo elastic interactions. Information about the state of the electrons at the input is then lost. Transport becomes statistical and stochastic. 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. Electrons which undergo inelastic interaction are then similar to non-monochromatic light.

For correct usage of this analogy consideration of several facts is needed:
*Photons are bosons and electrons are fermions.
*There is coulombic repulsion between electrons.Thus this analogy is good only for single-electron conduction because electron processes are strongly and nonlinear dependent on other electrons.
*It is more likely that an electron would lose energy than a photon would, because of the electron's non-zero rest mass.
*Electron interactions with the environment, each other, and other particles are generally stronger than interactions with and between photons.

References

Electronic Transport in Mesoscopic Systems, Supriyo Datta, Contributor: Haroon Ahmad,Alec Broers, Michael Pepper, Published 1997 by Cambridge University Press, ISBN 0521599431