A classical implementation of the field plate technique is the oxide ramp termination. This paper presents improvements of the breakdown voltage for both SiC JBDs and SBDs, obtained by using high-k dielectrics. A study regarding the influence of the dielectric permittivity and thickness on the off-state performances of the diodes is included. It is shown that Si3N4 is to be preferred to SiO2 for the dielectric ramp. Termination efficiencies up to 96% are reported.