Illustrated Physics
physics, drawn
Concept

Thermionic emission — where it appears

The escape of electrons from a hot metal surface, because the fast tail of their energies exceeds the work function. Richardson's law gives the current as the square of the temperature times an exponential, which makes it rise steeply as the metal heats.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

A barrier the metal was supposed to choose. The barrier height at a metal contact on n-type silicon against the metal's work function, from Bardeen's model with interface-state densities of none, 10¹² per cm² per eV, 10¹³ per cm² per eV, 10¹⁴ per cm² per eV, a 0.5 nm gap and a neutrality level a third of the gap above the valence band. With no interface states the barrier is Schottky and Mott's φₘ − χ, rising one for one with the work function: from aluminium to platinum, 0.23 to 1.60 eV. With 10¹² per cm² per eV the slope is 0.92 and the same metals give 0.27 to 1.53 eV; with 10¹³ per cm² per eV the slope is 0.53 and the same metals give 0.48 to 1.20 eV; with 10¹⁴ per cm² per eV the slope is 0.10 and the same metals give 0.71 to 0.84 eV. Dense enough interface states pin every barrier near 0.76 eV, and the metal hardly matters.

The barrier the metal cannot choose

Put a metal on a semiconductor and a barrier forms at the interface. The obvious theory says its height is the difference between the metal's work function and the semiconductor's electron affinity. Platinum and aluminium differ by nearly an electronvolt and a half in work function, so they should make wildly different contacts. On silicon and gallium arsenide they do not: nearly every metal gives nearly the same barrier. Bardeen explained why in 1947. A thin layer of electronic states at the interface screens the metal, and it takes only a few such states per hundred surface atoms to pin the barrier wherever they put it.

quantum · Bands The potential a stream of charge bends. The potential and electric field across a vacuum gap of width d with a voltage V across it, drawn in units of V and V/d. With no charge in the gap the potential is a straight line and the field uniform. With a stream of charge crossing, the charge's own field pushes the potential curve down, and the current can rise only until the field at the emitter falls to zero: past that the next particle would be pushed back. At that limit the potential goes as the four-thirds power of the distance and the field as the cube root, so the emitter sees no field at all and the far side sees four-thirds of what it saw before. Child and Langmuir found the same curve independently, in 1911 and 1913, and it fixes the current completely.

The current a vacuum will not carry

A vacuum has no resistance, and yet a gap of empty space will carry only so much current for a given voltage, however freely its cathode offers electrons. The charge already crossing cancels the field that would pull the next one off. Gauss's law gives the result in a few lines, and it says something odd about ion engines: their thrust per square metre does not depend on what the ion is, and it is exactly the electric stress on their grid.

electromagnetism · Gauss's law

Named alongside it

The objects these essays reach for when they reach for this one.

Band bendingChild langmuir lawDepletion regionFermi levelFermi level pinningGausss lawInterface statesIon thrusterMaxwell stressPerveanceSchottky barrierSpace charge

All concepts