The meshes are refined in the X direction in the Al2O3 layer and close to the Al2O3 │LLZO interface. The number of elements in the X direction in Al2O3 and LLZO layers are 300 and 2300, respectively. Thickness of the Al2O3 and LLZO layers are assumed 5 nm and 1 µm respectively. The modeling of the diffusion with different Al2O3 thicknesses and without Al2O3 are also reported, however, the LLZO thickness (1 µm ) is kept constant. a Calculated, based on atomic ratios (using Zr=2 pfu as fixed point). O contents are estimated from charge balance considerations.