Band-Structure Effects in the Field-Induced Tunneling of Electrons from Metals

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.