A SiC Schottky barrier diode (SBD) is provided having a substrate and two or more epitaxial layers, including at least a thin, lightly doped N-type top epitaxial layer, and an N-type epitaxial layer on which the topmost epitaxial layer is disposed. Multiple epitaxial layers support the blocking voltage of the diode, and each of the multiple epitaxial layers supports a substantial portion of the blocking voltage. Optimization of the thickness and dopant concentrations of at least the top two epitaxial layers results in reduced capacitance and switching losses, while keeping effects on forward voltage and on-resistance low. Alternatively, the SBD includes a continuously graded N-type doped region whose doping varies from a lighter dopant concentration at the top of the region to a heavier dopant concentration at the bottom.