  Josephson junctions are the key components used in superconducting qubits for
quantum computing. The advancement of quantum computing is limited by a lack of
stability and reproducibility of qubits which ultimately originates in the
amorphous tunnel barrier of the Josephson junctions and other material
imperfections. Pinholes in the junction have been suggested as one of the
possible contributors to these instabilities, but evidence of their existence
and the effect they might have on transport is unclear. We use molecular
dynamics to create three-dimensional atomistic models to describe Al-AlOx-Al
tunnel junctions, showing that pinholes form when oxidation of the barrier is
incomplete. Following this we use the atomistic model and simulate the
electronic transport properties for tunnel junctions with different barrier
thicknesses using the non-equilibrium Green's function formalism. We observe
that pinholes may contribute to excess quasiparticle current flow in Al-AlOx-Al
tunnel junctions with thinner barriers, and in thicker barriers we observe
weak-points which facilitate leakage currents even when the oxide is
continuous. We find that the disordered nature of the amorphous barrier results
in significant variations in the transport properties. Additionally, we
determine the current-phase relationship for our atomistic structures,
confirming that devices with pinholes and weak-points cause a deviation from
the ideal sinusoidal Josephson relationship.
