An electronic device may have components such as a display, a camera, a button, and other electrical components. A transparent crystalline member such as a layer of aluminum oxide, zirconium oxide, or other crystalline dielectric structure may overlap an electrical component and may serve as a display cover layer, button cover member, or window member. An annealed adhesion layer such as an annealed inorganic layer may be formed on a crystalline dielectric member. The annealed adhesion layer may help adhere an oleophobic coating to the transparent crystalline member.