The theory of electron tunneling from metals into vacuum is investigated. Certain ambiguous conclusions reached in previous theoretical treatments are reconsidered. It is found that band-structure information is contained in the total energy distribution of field-emitted electrons. The problem of electron tunneling from narrow energy bands with a high density of states, well described in the tight-binding approximation, is treated. Expressions for the tunneling matrix element of electrons in tight-binding $d$ bands tunneling to free-electron states outside the metal are obtained within the field-ionization approximation of Oppenheimer. Calculations are then given for the energy distribution of field-emitted electrons coming from a model of a real metal in which the band structure is a superposition of a free $s$-like band and a tight-binding $d$ band. This is a reasonable qualitative model for the band structure of a noble metal. The relationship between the energy distribution and the band structure is established.

• Received 11 February 1969

DOI:https://doi.org/10.1103/PhysRev.182.416