Field emission

The field emission of electrons from a cold metallic cathode in the presence of a large surface electrical field was first reported by Wood (1899). Classical theory fails completely to describe field emission and it is to quantum mechanics that one must turn. Quantum mechanics were first applied to the field emission of electrons from a metal by Fowler & Nordheim (1928).

A simplified view of their result may be obtained by considering a potential energy diagram for electrons in a metal and the adjoining vacuum, in the presence and absence of an external electric field, fig. 6.1. The energy of the highest filled level in the metal, measured from the potential minimum in the metal, is called the Fermi energy EF, and is equal to the chemical potential of electrons in the metal. The energy difference between the Fermi level and the potential energy of electrons in the vacuum is the thermionic work function φ. (A more complete discussion of this is to be found in section 7.2.) The number of quantum states near the top of the Fermi sea is much larger than near the bottom, so that most electrons can be considered to be accommodated in energy levels near EF, and tunnelling can be assumed to take place largely from the Fermi level.