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High quality Nb-based superconductor-insulatorsuperconductor (SIS) junctions with Al oxide (AlOx) tunnel barriers grown from Al overlayers are widely reported in the literature. However, the thin barriers required for high critical current density (Jc) junctions exhibit defects that result in significant subgap leakage current that is detrimental for many applications. High quality, high-Jc junctions can be realized with AlNx barriers, but control of Jc is more difficult than with AlOx. It is therefore of interest to study the growth of thin AlOx barriers with the ultimate goal of achieving high quality, high-Jc AlOx junctions. In this work, 100% O2 and 2% O2 in Ar gas mixtures are used both statically and dynamically to grow AlOx tunnel barriers over a large range of oxygen exposures. In situ ellipsometry is used for the first time to extensively measure AlOx tunnel barrier growth in real time, revealing a number of unexpected patterns. Finally, a set of test junction wafers was fabricated that exhibited the well-known dependence of Jc on oxygen exposure (E) in order to further validate the experimental setup.