The crystalline quality of heteroepitaxial (100) and (111) Si layers on spinel or sapphire substrates has been investigated using ion channeling and electron microscopy. Ion channeling and backscattering give the depth profile of the density of imperfections, and electron microscopy is used to determine the nature of the imperfections as well as give an additional determination of their density. Transmission electron microscopy indicates that stacking faults and microtwins are the dominant types of imperfections in the layers, and these defects are interpreted to be the primary source of scattering centers for the channeled ions. Both channeling and scanning electron microscopy measurements indicate that the density of imperfections decreases with increasing distance from the interface. At equal distances from the interface a lower density of imperfections was observed in the Si layer for (111) Si/spinel and (100) Si/sapphire as compared to (100) Si/spinel. Large differences in the rate of decrease of the density of imperfections were observed for (100) Si/sapphire from different suppliers. The interpretation of the influence of the fault planes on channeling has been achieved by modeling the scattering by these defects. Semiquantitative correlations of scattering center densities from electron microscopy and channeling measurements indicate higher absolute densities for the channeling results, while relative densities determined at various depths by these two techniques are in agreement.