The effect of barrier form on slope and intercept correction factors for curved emitters: Development of some enabling theory

The work described in this conference poster follows up recent work on the interpretation of Fowler-Nordheim (FN) plots. It puts in place some enabling theory that should allow further development of plot interpretation theory, in the context of the sphere-on-orthogonal-cone (SOC) emitter model. This model is expected to be more suitable, for small-apex-radius emitters, than the spherical-emitter (SPH) model. First, this report shows (as expected) that use of the spherical image-potential-energy formula, rather than the planar formula, appears to make little difference to the values of calculated parameters. Second, values of the exponent n (in the SOC model) are tabulated as a function of internal cone half-angle. Third, an expression is derived for the electrostatic component of electron motive energy, in the SOC model. Finally, the results of a sample calculation are presented. This compares values of the slope correction factor σ for the SPH and SOC models, for emitter-radius values 20 nm and 5 nm. As expected, the results for the two models are similar for 20 nm, but diverge as apex radius decreases.