Hundreds of current-voltage (I-V) measurements of Ni, Pt and Ti Schottky diodes on 4H-SiC were conducted at low applied voltages. The SiC substrates contained homoepitaxial layers grown by either chemical vapor deposition or sublimation. While near-ideal contacts were fabricated on all samples, a significant percentage of diodes (~7%-50% depending on the epitaxial growth method and the diode size) displayed a non-ideal, or inhomogeneous, barrier height. These 'non-ideal' diodes occurred regardless of growth technique, pre-deposition cleaning method, or contact metal. In concurrence with our earlier reports in which the non-ideal diodes were modeled as two Schottky barriers in parallel, the lower of the two Schottky barriers, when present, was predominantly centered at one of the three values: ~0.60, 0.85 or 1.05 eV. The sources of these non-idealities were investigated using electron-beam-induced current (EBIC) and deep-level transient spectroscopy (DLTS) to determine the nature and energy levels of the defects. DLTS revealed a defect level that corresponds with the low- (non-ideal) barrier height, at ~0.60 eV. It was also observed that the I-V characteristics tended to degrade with increasing deep-level concentration and that inhomogeneous diodes tended to contain defect clusters. Based on the results, it is proposed that inhomogeneities, in the form of one or more low-barrier height regions within a high-barrier height diode, are caused by defect clusters that locally pin the Fermi level.