Scale invariance of a diodelike tunnel junction

TL;DR

This paper demonstrates that the current-voltage characteristics of a diodelike tunnel junction exhibit scale invariance over six orders of magnitude in tip-sample distance, revealing underlying electrostatic singular behavior.

Contribution

It introduces a universal scaling law for the I-V characteristics of a sharp tip tunnel junction, supported by experimental data and realistic barrier simulations.

Findings

All I-V curves collapse onto a single scaling graph.

The scaling exponent is linked to electrostatic singularity at the tip.

Simulations reproduce the observed scaling and deviations.

Abstract

We measure the current vs voltage (I-V) characteristics of a diodelike tunnel junction consisting of a sharp metallic tip placed at a variable distance d from a planar collector and emitting electrons via electric-field assisted emission. All curves collapse onto one single graph when I is plotted as a function of the single scaling variable Vd^{-\lambda}, d being varied from a few mm to a few nm, i.e., by about six orders of magnitude. We provide an argument that finds the exponent {\lambda} within the singular behavior inherent to the electrostatics of a sharp tip. A simulation of the tunneling barrier for a realistic tip reproduces both the scaling behavior and the small but significant deviations from scaling observed experimentally.