In a method of manufacturing a dielectric structure, after a first dielectric layer is formed on a substrate by using a metal oxide doped with silicon, the substrate is placed on a susceptor of a chamber. By treating the first dielectric layer with a plasma in controlling a voltage difference between the susceptor and a ground, a second dielectric layer is formed on the first dielectric layer. The second dielectric layer including a metal oxynitride doped with silicon having enough content of nitrogen is formed on the first dielectric layer. Therefore, dielectric properties of the dielectric structure comprising the first and the second dielectric layers can be improved and a leakage current can be greatly decreased. By adapting the dielectric structure to a gate insulation layer and/or to a dielectric layer of a capacitor or of a non-volatile semiconductor memory device, capacitances and electrical properties can be improved.