Relationships among the physical parameters required to give a linear relation between slope and intercept of Fowler–Nordheim plots

For field emitters with a given surface condition, but different apex radii, there exists an empirical linear relationship between the slopes and intercepts of their Fowler–Nordheim plots. This behavior is quite different from that predicted by the theory with the assumption of a smooth surface. We have already characterized the possible reasons for this discrepancy; one possibility is that the emission area rapidly increases with increase in the apex radius. The previous report (Jpn. J. Appl. Phys. Part II 32 (1993) L342), however, showed a curved relation between the slope and the intercept of Fowler–Nordheim plots. In the present article, we try to extract the relationship between the emission area and the apex radius needed in order to give a linear relationship between slope and intercept of the F–N plots. As an additional result of the present analysis, the change in work function of the field emitting surface is demonstrated.