The step of depositing the encapsulating material may be performed using a mask plate 80 having an aperture 80′ corresponding to the area of the display substrate to be formed. A size of the aperture 80′ may be selected based on a desired thickness of the side part 20b of the encapsulating layer 20. A projection of an edge of the mask plate 80 surrounding the aperture 80′ on the support substrate 1 is spaced apart from a projection of an edge of the base substrate 10 on the support substrate 1 by a distance d. Optionally, the distance is in a range of 0 μm to approximately 1000 μm, e.g., approximately 1 μm to approximately 1000 μm, approximately 1 μm to approximately 500 μm, approximately 500 μm to approximately 1000 μm, approximately 1 μm to approximately 250 μm, and approximately 1 μm to approximately 100 μm. Optionally, the step of depositing the encapsulating material may be performed using a vapor deposition method, e.g., plasma-enhanced chemical vapor deposition (PECVD).