  We test the consistency with which Simmons' model can predict the local
current density obtained for flat metal-vacuum-metal junctions. The image
potential energy used in Simmons' original papers had a missing factor of 1/2.
Besides this technical issue, Simmons' model relies on a mean-barrier
approximation for electron transmission through the potential-energy barrier
between the metals. In order to test Simmons' expression for the local current
density when the correct image potential energy is included, we compare the
results of this expression with those provided by a transfer-matrix technique.
This technique is known to provide numerically exact solutions of Schrodinger's
equation for this barrier model. We also consider the current densities
provided by a numerical integration of the transmission probability obtained
with the WKB approximation and Simmons' mean-barrier approximation. The
comparison between these different models shows that Simmons' expression for
the local current density actually provides results that are in good agreement
with those provided by the transfer-matrix technique, for a range of conditions
of practical interest. We show that Simmons' model provides good results in the
linear and field-emission regimes of current density versus voltage plots. It
loses its applicability when the top of the potential-energy barrier drops
below the Fermi level of the emitting metal.
