Abstract
The equation of motion and thermodynamic Green's function method for describing tunneling processes in normal and Josephson junctions is here adapted to the problem of field emission of electrons from solids. The formal developments lead to an equation for the emission current in terms of both the Fowler-Nordheim quantities and the spectral weight function of the single particle Green's function in the solid. The formal results are examined in detail for some specific examples. In the case when the spectral function is that of a free, non-interacting electron gas, the formal results obtained here reduce to the usual Fowler-Nordheim result for the current and the energy distribution. Expressions are then obtained for the current and energy distribution of field emitted electrons from superconductors. The consequences of these results are discussed. The next example considered here is the emission current characteristics from an electron gas in which collisions between electrons and phonons, electrons, impurities, or imperfections occur. The damping of the electron energy eigenstates, which is present in all real metals, results in new current characteristics. The last example considered here is the problem of resolution limitations in real experiments. The effects of measurement uncertainties on the experimental energy distributions of emitted electrons are easily treated in the present formalism.
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