Fowler Nordheim
This is the Fowler-Nordheim equation for field emission — electrons tunnelling through a potential barrier under a strong applied electric field, rather than being thermally excited over it (as in Richardson-Dushman).
- is the emission current density.
- is the applied electric field at the surface.
- is the work function of the emitter.
- and are Fowler-Nordheim constants that collect together fundamental constants (, , ). Typically A·eV·V and eV·V·m
The prefactor relates to the supply of electrons at the Fermi level and the transmission probability at low barrier. The exponential term is the dominant factor — it captures the WKB tunnelling probability through the triangular barrier formed when the strong field bends the vacuum potential. Higher field or lower work function → thinner barrier → exponentially more tunnelling current.
Key distinction from thermionic emission: this is a quantum mechanical process that works even at room temperature — it depends on field strength, not temperature.