Ballistic conduction

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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 the electrons will be capable of colliding 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 in the material. Ballistic conduction differs from superconductivity due to the absence of the Meissner effect in the material.

Ballistic conduction occurs in some carbon nanotubes.

Contents 1 Ballistic conduction on micro-scale 2 Importance of ballistic conductivity 3 Optical analogies of ballistic conduction 4 References

[edit] Ballistic conduction on micro-scale

Probably any conduction process on enough short distance (~several nanometers) could be considered as ballistic conduction, because probability of scattering on impurity or phonon (most obvious) is very low on this short distance.

Most common studies of ballistic conductivity has been conducted on this micro- and nano-scale level, 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.

It is necessary to realize that "ballisticity" of conduction is a probabilistic quality. There are no totally ballistic conductors or totally non-ballistic conductors. The degree of balisticity of any conduction is given as a probability that the electron will fly through a particular system without scattering.

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

[edit] Importance of ballistic conductivity

Despite ballistic conductivity is really connected with very low resistance of particular material, the major importance isn't energy efficient transport of power on the long distance but nanoscience and information processing electronics applications.

Ballistic conduction enables utilization of quantum mechanical properties of electron wave function. The ballistic transport is coherent in the terms of wave mechanics, so such phenomenons like double-split interference, spacial resonance (and other optical or microwave-like principles) could be exploited in electronic systems on nanoscale.

[edit] Optical analogies of ballistic conduction

A comparison with light provides a helpful analogy between ballistic and non-ballistic conduction. Ballistically conducted electrons behave like light in a waveguide or a quality optical assembly. On the other hand, non-ballistically conducted electrons behave like light diffused in milk or reflected off of a white wall or a piece of paper.

As in optics, there are several different ways an electron can be scattered in a conductor. Electrons have several properties: wavelength (~energy), direction, phase, spin orientation… In materials there are different probabilities of scattering processes which cause different rates of incoherence (stochasticity) in these properties. Some kinds of scattering can only cause a change in the direction of an electron, other can cause energy loss.

You can imagine coherent source of electrons (like laser in optics) connected to the conductor. In particular distance there will be the electron wave function still coherent (like a laser beam) and you still can deterministically predict its behavior (and use it for computation theoretically), in some distance the scattering cause that each electron we measure at the output of system will have slightly different [phase] and/or direction but still almost none energy loss (like monochromatic light which goes through milk) - this electron undergoes elastic interactions. In these case we loss many information about the state of the electrons in the input and the transport become statistical and stochastic. From the resistance point of view is the stochastic (not oriented) movement of electrons useless even if they carry the same energy - they move thermally. If the electrons undergoes inelastic interactions too, they loss energy and the result is second mechanism of resistance. Electrons which undergoes inelastic interaction are then similar to non-monochromatic rather white light.

For correct usage of this analogy consideration of several facts is needed:

• Photons are bosons and electrons fermions
• There is coulombic repulsion between electrons

Thus this analogy is good only for single-electron conduction because electron process are is strongly dependent of other electrons and nonlinear.

• Electron could lose part of its energy (~slow down) more likely than photon because of its non-zero rest mass.
• Electron interaction with the environment, with each other and with other particles are generally stronger than interactions of photons.

[edit] References

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