Scale invariance of a diodelike tunnel junction

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 $V{d}^{\ensuremath{-}\ensuremath{\lambda}}$, $d$ 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 $\ensuremath{\lambda}$ 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.