화학공학소재연구정보센터
Journal of Vacuum Science & Technology B, Vol.28, No.6, 1326-1329, 2010
Simple derivation of the formula for Sommerfeld supply density used in electron-emission physics and limitations on its use
In a free-electron model, an electron crossing a mathematical plane inside a conductor can be characterized by the energy components associated with its motion normal and parallel to the plane. These components define a two-dimensional "energy-space." The "supply density" is defined as the electron current crossing the plane, per unit area of the plane, per unit area in energy-space, when the relevant electron states are fully occupied. For a bulk free-electron conductor, the supply density is the same at all points in energy-space and has been called the "Sommerfeld supply density" (z(S)). This is given by z(S)=4 pi em(e)/h(P)(3), where e is the elementary positive charge, m(e) is the electron mass, and h(P) is Planck's constant. This result is often a convenient starting point for developing basic theories of electron emission. A simple proof of it is recorded here. For small electron emitters, it can be a poor approximation to assume that the supply density is constant in energy-space. Consequently, if an emitter is sufficiently small, then the emission will not be well described by the usual basic emission equations. Criteria for assessing what counts as "sufficiently small" are discussed. (C) 2010 American Vacuum Society. [DOI: 10.1116/1.3501118]