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# Ballistic transport

In solid state physics, the term ballistic transport refers to the transport of electrons in a medium where the electrical resistivity due to the scattering, by the atoms, molecules or impurities in the medium itself, is negligible or absent. Without scattering, the electron will simply obey Newton's second law of motion for relatively slow speed (i.e. much below the speed of light). Under a constant electric field at a fixed direction, the electron will move in a straight line and will continue to accelerate.

In general the resistivity exists because an electron, while moving inside a medium, is scattered by impurities, defects, or by the atoms/molecules composing the medium that simply oscillate around their equilibrium position (in a solid), or generically by any freely moving atom/molecule composing the medium, in a gas or liquid.

For a given medium one can associate to a moving electron a mean free path as the average length that the electron can travel freely, i.e. before hitting against something and deviating from its original path, possibly losing some kinetic energy. The mean free path can be increased by reducing the number of impurities in a crystal or by lowering its temperature (except for some material like semi-conductors).

Ballistic transport is observed when the mean free path of the electron is (much) bigger than the size of the box that contains/delimits the medium through which the electron travels, such that the electron alters its motion only by hitting against the walls. In the case of a wire supended 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).

E.g. 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 bigger than that in a metal [1]

Quasi-ballistic transport can be observed in a semiconductor, for example, in modern MOS transistors. Professor Mark Lundstrom of Purdue University has published a lot on quasi-ballistic transport theory in modern MOS transistors. Lundstrom's theory explains why the low-field mobility is important even at high electric field [1]-[2]. This is contradictory to the conventional theory that at high electric field the saturation velocity is important while the low field mobility is not important. This concept is important for strain engineering because strain engineering can be used to increase low-field mobility, which can make carrier transport faster even at high electric field according to Lundstrom's theory.

[1] M.S. Lundstrom, “Elementary Scattering Theory of the Si MOSFET”, IEEE Electron Dev. Lett., vol 18, pp. 361-363 (1997).

[2] M.S. Lundstrom, “On the Mobility Versus Drain Current Relation for a Nanoscale MOSFET”, IEEE Electron Dev. Lett., vol. 22, pp. 293-295 (2001).