Ballistic conduction

In mesoscopic physics, ballistic conduction (ballistic transport) is the transport of charge carriers (usually electrons) in a medium, having negligible electrical resistivity caused by scattering. Without scattering, electrons simply obey Newton's second law of motion at non-relativistic speeds. In mesoscopic physics, ballistic conduction (ballistic transport) is the transport of charge carriers (usually electrons) in a medium, having negligible electrical resistivity caused by scattering. Without scattering, electrons simply obey Newton's second law of motion at non-relativistic speeds. 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. For a given particle, a mean free path can be described as being the average length that the electron can travel freely, i.e., before a collision, which could change its momentum. The mean free path can be increased by reducing the number of impurities in a crystal or by lowering its temperature. Ballistic transport is observed when the mean free path of the electron is (much) longer than the dimension of the medium through which the electron travels. The electron alters its motion only upon collision with the walls. In the case of a wire suspended in air/vacuum the surface of the wire plays the role of the box reflecting the electrons and preventing them from exiting toward the empty space/open air. This is because there is an energy to be paid to extract the electron from the medium (work function). For example, ballistic transport can be observed in a metal nanowire: this is simply because the wire is of the size of a nanometer (10−9 meters) and the mean free path can be longer than that in a metal. Ballistic conduction is the unimpeded flow of charge, or energy-carrying particles, over relatively long distances in a material. Normally, transport of electrons (or holes) is dominated by scattering events, which relax the carrier momentum in an effort to bring the conducting material to equilibrium. Thus, ballistic transport in a material is determined by how ballistically conductive that material is. Ballistic conduction differs from superconductivity due to the absence of the Meissner effect in the material. A ballistic conductor would stop conducting if the driving force is turned off, whereas in a superconductor current would continue to flow after the driving supply is disconnected. 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. Ballistic conduction is not limited to electrons (or holes) but can also apply to phonons. It is theoretically possible for ballistic conduction to be extended to other quasi-particles, but this has not been experimentally verified. In general, carriers will exhibit ballistic conduction when L ≤ λ M F P {displaystyle Lleq lambda _{MFP}} where L {displaystyle L} is the length of the active part of the device (i.e., a channel in a MOSFET). λ M F P {displaystyle lambda _{MFP}} is the mean free path for the carrier which can be given by Matthiessen's Rule, written here for electrons: