The origin of power laws in electric field assisted tunneling

We have measured the voltage vs distance V - d characteristics at constant current I of a tunnel junction consisting of an electron emitting sharp tip placed at a variable distance d from a planar anode. At sufficiently large distances, i.e. in the regime of electric field assisted quantum tunneling, the V - d characteristics for different currents follow approximately a power law V ∝ d^λ, the exponent λ being independent of the current. Here we compare and discuss the origin of the observed power law and the measured value of λ in terms of electrostatic properties of the tip-plane junction, taking the geometry of the tip as a hyperboloid of revolution.