Fowler Nordheim relation

The exponential represents the probability of an electron escaping into the field on colliding with the core potential. It has the form familiar from the Fowler-Nordheim relation [Eq. (30)], with the ionization potential replacing the work function as a measure of barrier height. The frequency of collisions with the core potential is given by the preexponential factor. At a field of 2 volts/A, this amounts to 0.51 x 1016 sec-1, compared with 0.66 x 1018 sec-1 for the Bohr frequency, yielding a rate constant kp = 2.12 x 107sec-1. 

Electrons escape from the material by tunnelling through a potential barrier at the surface which has been reduced in thickness to about 1.5 nm by the applied field, Figure 2. If the solid is assumed to contain free electrons which obey Fermi-Dirac statistics, the current density J of field emitted electrons is simply related to the applied field Fand work function cf) by the Fowler-Nordheim (FN) equation... 

The escape of electrons from traps by tunneling bears the same relation to the Poole-Frenkel theory as does the Fowler-Nordheim theory to the Schottky theory. It gives a law similar to the Fowler-Nordheim law. 

To study charge injection mechanisms, we have tried to fit Richardson-Schottky thermionic emission and Fowler-Nordheim tunnelling mechanisms. We have found that under forward bias, the temperature-independent Fowler-Nordheim (FN) tunnelling mechanism is applicable, which presumes tunnelling of charge carriers directly into the bands of the semiconductor. According to the model, the current density J) is related to the applied field F) as [11,12] ... 

Fowler and Nordheim showed that if the applied field is high enough, the work function is decreased even more and the potential barrier becomes so narrow that quantum mechanical tunneling can occur. The current-field dependence is represented by the relation... 

---