The correlation between barrier inhomogeneities of 4H-SiC Schottky barrier diodes (SBDs) and surface defects and traps for SBDs fabricated with and without chemical-mechanical polishing (CMP) is investigated. 60% of the barrier inhomogeneities of SBDs with invisible surface defects are eliminated when CMP is applied in the refabrication. About 40% of SBDs with carrots inside the active areas exhibit double barriers without using CMP. This excludes that carrots are a cause of barrier inhomogeneities. However, none of the barrier inhomogeneities of the SBDs with carrots can be eliminated by using CMP. Most barrier inhomogeneities of SBDs with various surface defects inside the active areas can be improved by CMP. The difference between the high and low barrier heights of an SBD with CMP was reduced to about 0.02-0.06 eV. Therefore, the leakage current induced by barrier inhomogeneities is also reduced by CMP. Moreover, SBDs with a resistive termination extension (RTE) have a higher barrier height than SBDs without RTE, and there is no direct evidence to show that the inclusion of RTE can induce barrier inhomogeneities.