Thermoelectric Modeling of the Non-Ohmic Differential Conductance in a Tunnel Junction containing a Pinhole

To test the quality of a tunnel junction, one sometimes fits the bias-dependent differential conductance to a theoretical model, such as Simmons's formula. Recent experimental work by {\AA}kerman and collaborators, however, has demonstrated that a good fit does not necessarily imply a good junction. Modeling the electrical and thermal properties of a tunnel junction containing a pinhole, we extract an effective barrier height and effective barrier width even when as much as 88% of the current flows through the pinhole short rather than tunneling. A good fit of differential conductance to a tunneling form therefore cannot rule out pinhole defects in normal-metal or magnetic tunnel junctions.