The optimization of the Schottky barrier height (SBH) and the maximum electric fields at the interface of a 4H-SiC Schottky barrier diode (SBD) is discussed, considering the reverse leakage current due to tunneling process. We first show that the reverse characteristics of a Ti/4H-SiC SBD are well described by the tunneling theory. Based on the tunneling theory, we show that the maximum electric field decreases as the Schottky barrier height decreases, and becomes smaller than the avalanche breakdown field of SiC. The on-state voltage as a function of the SBH is calculated, considering the specification of a leakage current. The calculated results show that the optimum SBH for a 4H-SiC SBD of 600V class is 0.9eV and that of 2000V class is 1.2eV.