Theoretical Total-Energy Distribution of Field-Emitted Electrons

The Fowler-Nordheim equation is derived in terms of total electron energy so as to obtain the total-energy distribution of field-emitted electrons. At 0^∘{}K the new distribution width is less than 1/3 of that obtained from the previous "normal-energy" theory. A surprising mirror-image symmetry is observed between the zero-temperature total-energy field emission and the zero-field normal-energy thermionic emission distributions. The total-energy distribution is also derived for the zero-field thermionic case and this is found to be the mirror image of the normal-energy zero-temperature field emission distribution.The new distribution applies to problems involving the total energy of electrons before and after emission.