Work function in the context of "Field emission"

Thermionic emission is the liberation of charged particles from a hot electrode whose thermal energy gives some particles enough kinetic energy to escape the material's surface. The particles, sometimes called thermions in early literature, are now known to be ions or electrons. Thermal electron emission specifically refers to emission of electrons and occurs when thermal energy overcomes the material's work function.

After emission, an opposite charge of equal magnitude to the emitted charge is initially left behind in the emitting region. But if the emitter is connected to a battery, that remaining charge is neutralized by charge supplied by the battery as particles are emitted, so the emitter will have the same charge it had before emission. This facilitates additional emission to sustain an electric current. Thomas Edison in 1880 while inventing his light bulb noticed this current, so subsequent scientists referred to the current as the Edison effect, though it wasn't until after the 1897 discovery of the electron that scientists understood that electrons were emitted and why.

In mesoscopic physics, ballistic conduction (ballistic transport) is the unimpeded flow (or transport) of charge carriers (usually electrons), or energy-carrying particles, over relatively long distances in a material. 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. Without scattering, electrons simply obey Newton's second law of motion at non-relativistic speeds.

The mean free path of a particle can be described as the average length that the particle 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 particle is (much) longer than the dimension of the medium through which the particle travels. The particle 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).