The Josephson energy E_J is a key parameter governing the properties of transmon superconducting qubits. In Al/AlO_x/Al junctions, E_J is set by electron tunneling through an ultrathin oxide barrier and therefore depends exponentially on the ato
The Josephson energy E_J is a key parameter governing the properties of transmon superconducting qubits. In Al/AlO_x/Al junctions, E_J is set by electron tunneling through an ultrathin oxide barrier and therefore depends exponentially on the atomic structure of the barrier. We compute E_J by first-principles device modeling based on the NEGF-DFT quantum-transport method, comparing a junction with a crystalline Al_2O_3 barrier against ten junctions with melt–quenched amorphous Al_2O_3 barriers of the same thickness. From the Fermi-level transmission and the Ambegaokar–Baratoff relation, we obtain a mean E_J/h of 2.78 GHz for the amorphous ensemble, with a standard deviation of 4.67 GHz, compared with 0.73 GHz for the crystalline reference; individual amorphous values span nearly two orders of magnitude. Scattering-state analysis shows that transport is quantum tunneling and that the variability originates from stoichiometric inhomogeneity of the amorphous oxide: Al-rich, low-barrier regions can connect into percolation-like tunneling pathways that strongly enhance the conductance. A realistic 200\times200 nm^2 junction self-averages over more than 2\times10^4 such microscopic regions. These results establish a quantitative atomistic route from oxide microstructure to the superconducting-circuit energy scale E_J.