Resonant tunneling devices are used for ultrahigh-speed applications. In this work, tunnel junctions based on copper metal (Cu) and cuprous oxide (Cu2O) are electrochemically self-assembled from aqueous solution in an oscillating system. The Cu2O layer thickness (L) is tuned from 0.8 to 2.8 nm by simply changing the applied current density. The layered structures show sharp negative differential resistance (NDR) signatures at room temperature in perpendicular transport measurements, and the NDR maximum shifts to higher bias with a 1/L-2 dependence as the Cu2O layer is made thinner. The results are consistent with resonant tunneling from Cu into hole states in the valence band of quantum-confined Cu2O through thin space-charge regions on each side of the Cu2O.