A hybrid permeation barrier having two complementary layers is disclosed. The barrier includes a first layer with a relatively high stress-thickness in the range of −1000 MPa-μm to −200 MPa-μm and a second layer with a relatively low stress-thickness in the range −150 MPa-μm to 300 MPa-μm. The second layer compensates for the stress caused by the first, thereby allowing for a barrier that provides good permeation without causing failure of the device due to delamination.