Improvement of the Simmons model for tunnel junctions

TL;DR

This paper improves the Simmons model for tunnel junctions by deriving more accurate formulas for tunneling current and conductance, aligning better with quantum approximations and fitting experimental data more precisely.

Contribution

The authors introduce enhanced analytical formulas for the Simmons model, improving accuracy at finite voltage and temperature, and demonstrate practical fitting to experimental data.

Findings

New formulas closely match WKB approximation.

Fitted data shows significant differences from original Simmons model.

Enhanced model provides more accurate barrier parameter estimates.

Abstract

The Simmons model is a well-known and widely used model for the elastic tunneling current of a metallic tunnel junction, and fitting it to electrical measurements can be used to estimate thicknesses and heights of the tunnel barriers. We present here an improvement of the Simmons model, deriving new more accurate analytical formulas for the tunneling current density and conductance at finite voltage and temperature. We demonstrate that our conductance-voltage formulas are much closer to the Wentzel-Kramers-Brillouin approximation than the Simmons model and its commonly used simplified parabolic approximation. In addition, we demonstrate the practical use of our model, by fitting it to experimental tunnel junction conductance-voltage data and showing a sizeable difference from the Simmons model.