A capacitor dielectric structure of a deep trench capacitor for a DRAM cell is disclosed. A semiconductor silicon substrate is provided with a deep trench. Silicon nitride deposition is used to form a silicon nitride layer on the sidewall and bottom of the deep trench. An oxynitride process with wet oxidation and N2O reactive gas is used to form an oxynitride layer on the silicon nitride layer. A post oxynitride growth annealing is performed on the oxynitride layer.