Field-plate (FP)-terminated 4H-SiC Schottky barrier diodes (SBDs) have been fabricated for the first time using sputter-deposited aluminum nitride (AlNx) and hydrogenated AlN (AlNy : H) as high-k dielectrics. The results are compared to that of conventional plasma-enhanced chemical-vapor-deposition (PECVD) silicon dioxide (SiO2)-based FP devices. Extensive electrical and physical characterizations of these dielectrics on 4H-SiC were carried out. 4H-SiC SBDs fabricated using these dielectrics as FPs are investigated in terms of their breakdown voltage (V-B) with respect to dielectric thickness, reverse-bias leakage current, and forward-bias characteristics up to an elevated temperature of 300 degrees C. Our results indicate that a V-B as high as 1750 V, which is more than 80% of the ideal theoretical value, can be achieved using Al-based dielectrics. This constitutes an improvement by more than 600 V, or almost 30% of the ideal theoretical V-B, over conventional oxide-based FP devices fabricated in this paper using PECVD SiO2. We attribute these improvements to the much-reduced electric field enhancement at the Schottky corners as a result of the higher dielectric constants of Al-based dielectrics, which is almost similar to 2.2 times that of SiO2. A net negative charge within the dielectric film also provides additional field relief, while an improvement of about similar to 1.3 times in the effective dielectric strength further contributes to the higher breakdown voltage observed.