  We study from first principles the transport properties of Al/AlOx/Al tunnel
junctions. On this basis, we analyze the reliability of two analytical models
for the conductance, namely the trapezoid potential barrier model and a
tight-binding model. Our findings show that (i) the interface width used in the
models is determined by the electronic density profile, and it is shorter than
the width one expects from the atomic arrangements; (ii) the effective mass},
found to be about on third of the free electron mass, can be determined from
the oxide band-structure calculations, and (iii) the barrier height is given by
one fourth of the bandgap in the oxide, which explains the apparently small
values found for these junctions experimentally.
