Physics Department, University of Wisconsin, Madison, WI, USA (1999)
The simplicity of the two models examined above in some detail implies that this list of possible improvements should be fairly long and by no means exhaustive. A more realistic representation of the vacuum barrier would be the first obvious next step. To start, one could use the actual formula for the tunneling probability through a triangular barrier, rather than the "average" square one used in the above discussion. Next step would be the inclusion of the image charge effects, long recognized6 to be important for tunneling. Generally the introduction of image charge potentials amounts to smoothening of all the "sharp" features of the barrier potential.
Another interesting effect to consider, would be the voltage drop in the insulator. In the two models examined, it was set to zero, but in fact it is probably not. As suggested in Fig. 1, one would expect to have some voltage drop in the insulator, when tunneling through it (i.e. for biases within the gap). That drop is expected to be smaller than the one in the vacuum, because of the large dielectric constants of insulators (e.g., ε = 7 for CaF_{2}). Once electrons start passing through the conduction band of the insulator, the voltage drop will probably become negligible, however one still may ask whether some effect will be left in the first atomic layer.
For an even more realistic consideration, one would need to solve a 3-dimensional, rather than a planar problem. The framework for performing such calculations has not been established sufficiently well though, so at this point both the modeling and the interpretation of these models are far from being straightforward.