Scaling theory of electric-field-assisted tunnelling

Abstract

Recent experiments report the current (I) versus voltage (V) characteristics of a tunnel junction consisting of a metallic tip placed at a distance d from a planar electrode, d varying over six orders of magnitude, from few nanometres to few millimetres. In the ‘electric-field-assisted’ (or ‘field emission’) regime, as opposed to the direct tunnelling regime used in conventional scanning tunnelling microscopy, all I–V curves are found to collapse onto one single graph when d is suitably rescaled, suggesting that the current I=I(V,d) is in reality a generalized homogeneous function of one single variable, i.e. I=Ifalse(V⋅d−λfalse), where λ being some characteristic exponent and Ifalse(xfalse) being a scaling function. In this paper, we provide a comprehensive explanation—based on analytical arguments, numerical simulations and further experimental results—for the scaling behaviour that we show to emerge for a variety of tip–plane geometries and thus seems to be a general feature of electric-field-assisted tunnelling.

Improving the topografiner technology down to nanometer spatial resolution

“…The preset current value depends on the junction quality and can vary from 100 nA up to 400 nA. An exhaustive study of the tip-sample junction can be found in [3].…”

“…To this end, we revisited the Russel Young topografiner [2]. We dubbed this new technique Near Field-Emission Scanning Electron Microscopy (NFESEM) [3], [4]. In NFESEM low-energy electrons are emitted from a polycrystalline tungsten tip via electric-field-assisted tunneling.…”