  Aluminium oxide (AlO$_\mathrm{x}$) tunnel junctions are important components
in a range of nanoelectric devices including superconducting qubits where they
can be used as Josephson junctions. While many improvements in the
reproducibility and reliability of qubits have been made possible through new
circuit designs, there are still knowledge gaps in the relevant materials
science. A better understanding of how fabrication conditions affect the
density, uniformity, and elemental composition of the oxide barrier may lead to
the development of lower noise and more reliable nanoelectronics and quantum
computers. In this paper we use molecular dynamics to develop models of
Al-AlO$_\mathrm{x}$-Al junctions by iteratively growing the structures with
sequential calculations. With this approach we can see how the surface oxide
grows and changes during the oxidation simulation. Dynamic processes such as
the evolution of a charge gradient across the oxide, the formation of holes in
the oxide layer, and changes between amorphous and semi-crystalline phases are
observed. Our results are widely in agreement with previous work including
reported oxide densities, self-limiting of the oxidation, and increased
crystallinity as the simulation temperature is raised. The encapsulation of the
oxide with metal evaporation is also studied atom by atom. Low density regions
at the metal-oxide interfaces are a common feature in the final junction
structures which persists for different oxidation parameters, empirical
potentials, and crystal orientations of the aluminium substrate.
