Nickel (Ni), titanium (Ti), and molybdenum (Mo) 4H-silicon carbide Schottky-barrier diodes (SiC SBDs) were fabricated and used to investigate the relation between forward and reverse currents. Temperature dependence of reverse current follows a theory that includes tunneling in regard to thermionic emission, namely, temperature dependence is weak at low temperature but strong at high temperatures. On the other hand, the reverse currents of the Ni and Mo SBDs are higher than their respective currents calculated from their Schottky barrier heights (SBHs), whereas the reverse current of the Ti SBD agrees well with that calculated from its SBH. The cause of the high reverse currents was investigated from the viewpoints of low barrier patch, Gaussian distribution of barrier height (GD), thin surface barrier, and electron effective mass. The high reverse current of the Ni and Mo SBDs can be explained not in terms of a low-barrier patch, GD, or thin surface barrier but in terms of small effective masses. Investigation of crystal structures at the Schottky interface revealed a large lattice mismatch between the metals (Ni, Ti, or Mo) and SiC for the Ni and Mo SBDs. The small effective mass is possibly attributed to the large lattice mismatch, which might generate transition layers at the Schottky interface. It is concluded from these results that the lattice constant as well as the work function is an important factor in selecting the metal species as the Schottky metal for wide band-gap SBDs, for which tunneling current dominates reverse current.