title: 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 distancedfrom a planar electrode,dvarying 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, allI-Vcurves are found to collapse onto one single graph whendis suitably rescaled, suggesting that the currentI=I(V,d) is in reality a generalized homogeneous function of one single variable, i.e. [Formula: see text], where λ being some characteristic exponent and [Formula: see text] 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.
authors.affiliation: Department of Chemistry , University of Cambridge , Lensfield Road, Cambridge CB2 1EW, UK.
authors.forename: Thomas C T
authors.initials: TC
authors.lastname: Michaels
authors.affiliation: Laboratory for Solid State Physics , ETH Zurich , Zurich 8093, Switzerland.
authors.forename: H
authors.initials: H
authors.lastname: Cabrera
authors.affiliation: Laboratory for Solid State Physics , ETH Zurich , Zurich 8093, Switzerland.
authors.forename: D A
authors.initials: DA
authors.lastname: Zanin
authors.affiliation: Laboratory for Solid State Physics , ETH Zurich , Zurich 8093, Switzerland.
authors.forename: L
authors.initials: L
authors.lastname: De Pietro
authors.affiliation: Laboratory for Solid State Physics , ETH Zurich , Zurich 8093, Switzerland.
authors.forename: U
authors.initials: U
authors.lastname: Ramsperger
authors.affiliation: Laboratory for Solid State Physics , ETH Zurich , Zurich 8093, Switzerland.
authors.forename: A
authors.initials: A
authors.lastname: Vindigni
authors.affiliation: Laboratory for Solid State Physics , ETH Zurich , Zurich 8093, Switzerland.
authors.forename: D
authors.initials: D
authors.lastname: Pescia
keywords: Fowler–Nordheim tunnelling; electron microscopy; scaling