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.
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