Some methods that are provided form a composite dielectric structure on a substrate. A first dielectric layer that includes metal and oxygen is formed on a substrate. A preliminary dielectric layer that includes silicon is formed on the first dielectric layer. A plasma nitriding treatment is performed on the preliminary dielectric layer to change it into a second dielectric layer. The composite dielectric structure includes the second dielectric layer and the first dielectric layer. Other methods form a semiconductor device that includes the composite dielectric structure.