  We show that less than 10% of the barrier area dominates the electron
tunneling in state-of-art Al/AlOx/Al Josephson junctions. They have been
studied by transmission electron microscopy, specifically using atomic
resolution annular dark field (ADF) scanning transmission electron microscopy
(STEM) imaging. The direct observation of the local barrier thickness shows a
Gaussian distribution of the barrier thickness variation along the junction,
from ~1 nm to ~2 nm in the three junctions we studied. We have investigated how
the thickness distribution varies with oxygen pressure (po) and oxidation time
(to) and we find, in agreement with resistance measurements on similar
junctions, that an increased to gives a thicker barrier than an increased po.
