RT Journal Article
SR Electronic
T1 Scaling properties of a non-Fowler–Nordheim tunnelling junction
JF Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science
FD The Royal Society
DO 10.1098/rspa.2013.0795
VO 470
IS 2166
A1 Kyritsakis, A.
A1 Xanthakis, J. P.
A1 Pescia, D.
YR 2014
UL http://rspa.royalsocietypublishing.org/content/470/2166/20130795.abstract
AB We have theoretically explained the experimentally observed scaling properties of the current–voltage (I–V) characteristics of a field-emission tunnelling diode with respect to the tip–anode distance d. All the I–V curves for different d-values collapse onto a single curve by a scaling transformation that keeps the electrical field at a given direction constant for different d. Our proof is applicable to more than just the obvious case where the electrostatic potential varies linearly with the distance from the cathode x (and the Fowler–Nordheim plot is also linear). It applies to any general nonlinear potential encountered in emitting tips of small radii of curvature R. Furthermore, we explain why the scaling property is excellent at d≫R, but deteriorates when d∼R. The scaling property is shown to derive from the simultaneous action of two factors: (i) in a Taylor expansion of the potential in the tunnelling region, the second-order coefficient is found to be proportional to the first-order coefficient and their ratio independent of d. (ii) The angular variation of the electric field is independent of d for d≫R. Deviations from scaling at d∼R are attributed to both the dependence on d of the angular variation of the electrical field and/or the presence of a third-order term.