The dominant mechanisms of the reverse leakage current of a Schottky Barrier Diode (SBD) are identified as a function of the electric field and Schottky Barrier Height (SBH) from the analytical formula of the field emission model, the thermionic field emission model, and the barrier lowering model. Further, the reverse characteristics of a 4H-SiC SBD and a Si SBD are examined using the device simulator, where the tunneling process (field emission and thermionic field emission) is considered. The calculated results show that the tunneling current dominates the reverse leakage current of a SiC SBD, while the effect of the tunneling process on the reverse leakage current of a Si SBD is relatively small, because the electric field applied to the metal/semiconductor interface of a Si SBD is much lower than that of a SiC SBD. The trade-off between the leakage current and forward characteristics of a 4H-SiC SBD and a Junction Barrier Schottky Diode (JBS) is examined by device simulations and it is shown that the JBS improve the trade-off.