Direct observation of the thickness distribution of ultra thin AlO_x barriers in Al/AlO_x/Al Josephson junctions

We have directly measured the thickness distribution of the tunnel barriers in state-of-the-art Al/AlO_x/Al tunnel junctions. From the distribution we can conclude that less than 10% of the junction area dominates the electron tunnelling. The barriers 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 to ∼2 nm. We have investigated how the thickness distribution varies with oxygen pressure ($p_{\text{o}}$) and oxidation time ($t_{\text{o}}$) and we find, in agreement with resistance measurements, that an increased $t_{\text{o}}$ has a larger impact on barrier thickness and its uniformity compared to an increased $p_{\text{o}}$. (paper)