Field emission: New theory for the derivation of emission area from a Fowler-Nordheim plot

This article takes a fresh look at the theoretical basis of methods for deriving emission area from the intercept of a Fowler-Nordheim (FN) plot. It sharpens the concepts involved, by defining a generalized FN equation, an intercept correction factor, and an emission-area extraction function. Some new general formulas are introduced. An improved version of the Charbonnier and Martin (CM) [F. M. Charbonnier and E. E. Martin, J. Appl. Phys. 33, 1897(1962)] method for extracting emission area is discussed; this is numerically illustrated using formulas developed within the framework Of Murphy and Good's 1956 [E. L. Murphy and R. H. Good, Phys. Rev. 102, 1464 (1956)] treatment of the theory of cold field emission from metals at zero temperature. It is shown that uncertainties were underestimated in the methods introduced by CM and by Spindt and colleagues, [C. A; Spindt ct al., J. Appl. Phys. 47, 5248 (1976)] but-can be reduced by iterating the new method. :Strictly, the numerical results presented apply only to field emission from materials that are, or behave like, metals. The numerical results are not exact in any absolute sense, but they are precise within the context of the formulation of FN theory: normally used; in technological contexts; further, they have been derived within the context of higher-level formulas of general validity, and are considered to be a:well-defined and useful step towards future developments. Opportunity is taken to present the usual 1956 version of the FN equation:in modern notation, employing quantity algebra, rmks equations, and precise up-to-date values of the relevant universal constants, and to give an equation that identifies the onset of field-induced ballistic emission. (C) 1999 American Vacuum Society. [S0734-211X(99)09202-1].