Ballistic transport
Encyclopedia
Ballistic transport is the transport
of electrons in a medium with negligible
electrical resistivity due to scattering
. Without scattering, electrons simply obey Newton's second law of motion at non-relativistic speeds
.
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 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
).
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
meters) and the mean free path can be bigger than that in a metal
Transport Phenomena
Transport Phenomena is the first textbook that is about transport phenomena. It is specifically designed for chemical engineering students...
of electrons in a medium with negligible
Negligible
Negligible refers to the quantities so small that they can be ignored when studying the larger effect. Although related to the more mathematical concepts of infinitesimal, the idea of negligibility is particularly useful in practical disciplines like physics, chemistry, mechanical and electronic...
electrical resistivity due to scattering
Scattering
Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of...
. Without scattering, electrons simply obey Newton's second law of motion at non-relativistic speeds
Relativistic particle
A relativistic particle is a particle which moves with a relativistic speed; that is, a speed comparable to the speed of light. This is achieved by photons to the extent that effects described by special relativity are able to describe those of such particles themselves...
.
In general, the resistivity
Resistivity
Electrical resistivity is a measure of how strongly a material opposes the flow of electric current. A low resistivity indicates a material that readily allows the movement of electric charge. The SI unit of electrical resistivity is the ohm metre...
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
Mean free path
In physics, the mean free path is the average distance covered by a moving particle between successive impacts which modify its direction or energy or other particle properties.-Derivation:...
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
Kinetic energy
The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...
. 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 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
Work function
In solid-state physics, the work function is the minimum energy needed to remove an electron from a solid to a point immediately outside the solid surface...
).
E.g. ballistic transport can be observed in a metal nanowire
Nanowire
A nanowire is a nanostructure, with the diameter of the order of a nanometer . Alternatively, nanowires can be defined as structures that have a thickness or diameter constrained to tens of nanometers or less and an unconstrained length. At these scales, quantum mechanical effects are important —...
: this is simply because the wire is of the size of a nanometer (10
meters) and the mean free path can be bigger than that in a metal