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With a large-area field electron emitter, when an individual post-likeemitter is sufficiently resistive, and current through it sufficiently large,then voltage loss occurs along it. This Letter provides a simple analytical andconceptual demonstration that this voltage loss is directly and inextricablylinked to a reduction in the field enhancement factor (FEF) at the post apex. Aformula relating apex-FEF reduction to this voltage loss was obtained in thepaper by E. Minoux, O. Groening, K. B. K. Teo, S. H. Dalal, L. Gangloff, J.-P.Schnell, L. Hudanski, I. Y. Y. Bu., P. Vincent, P. Legagneux, G. A. J.Amaratunga, and W. I. Milne [Nano Lett. 5, 2135 (2005)], by fitting tonumerical results from a Laplace solver. This Letter derives the same formulaanalytically, by using a "floating sphere" model. The analytical proof bringsout the underlying physics more clearly, and shows that the effect is a generalphenomenon, related to reduction in the magnitude of the surface charge in themost protruding parts of an emitter. Voltage-dependent FEF-reduction is onecause of "saturation" in Fowler-Nordheim plots. Another is a voltage-dividereffect, due to measurement-circuit resistance. An integrated theory of botheffects is presented. Both together, or either by itself, can cause saturation.Experimentally, if saturation occurs but voltage loss is small (< 20 V, say),then saturation is more probably due to FEF-reduction than voltage division. Inthis case, existing treatments of electrostatic interaction ("shielding")between closely spaced emitters may need modification. Other putative causes ofsaturation exist, so the present theory is a partial story. Its extension seemspossible, and could lead to a more general physical understanding of the causesof FN-plot saturation.

Field emission: the theoretical link between voltage loss, reduction in field enhancement factor, and Fowler-Nordheim-plot saturation