Comparison between Simmons's Equations and Quantum Tunneling Experimental Results in A Thin Film

The theoretical predictions of J.G. Simmons's equations are compared with quantum tunneling experimental results and a discrepancy is found at bias voltage $V_{b}=U$/$e$, where U is the barrier's potential height and e is the electron charge. Specifically, he divided the bias voltage into 2 regions: $V_{b} \quad < \quad U$/$e$ and $V_{b} \quad > \quad U$/$e$, and the I -- V characteristics are different in these two regions. The derived equations show a kink on differential conductance d$I$/d$V$ vs. $V_{b}$ at $V_{b}=U$/$e$, because starts at this bias the thickness of the insulation film decreases with $V_{b}$ in addition to the lowering of the barrier's average height. Therefore, the differential conductance decreases more rapidly in the region $V_{b} \quad > \quad U$/$e$ than in the region $V_{b} \quad < \quad U$/$e$. However, in tunneling experiment in which Pt is used as conductor and solid neon as insulator, we have not observed such kink even the bias was increased to 4 volts. Our speculation is either 1) there should not be a kink on conductance at $V_{b}=U$/$e$ so Simmons's equations need to be modified; 2) the kink should exist but bias voltage is not high enough to observe it in the experiments.