A substrate includes a ceramic core, a first adhesion layer, a barrier layer, and a second adhesion layer. The first adhesion layer encapsulates the ceramic core and includes silicon oxynitride, wherein the atomic number ratio of oxygen to nitrogen in silicon oxynitride of the first adhesion layer has a first ratio. The barrier layer encapsulates the first adhesion layer and includes silicon oxynitride, wherein the atomic number ratio of oxygen to nitrogen in silicon oxynitride of the barrier layer has a second ratio that is different from the first ratio. The second adhesion layer encapsulates the barrier layer and includes silicon oxynitride, wherein the atomic number ratio of oxygen to nitrogen in silicon oxynitride of the second adhesion layer has a third ratio that is different from the second ratio.