Conditions for direct structure imaging in silicon carbide polytypes

The conditions appropriate for direct structure imaging of silicon carbide polytypes in the high-resolution electron microscope have been investigated. Weak-phase-object calculations confirm that a resolution of better than 2.5 Å is necessary before polytypic stacking sequences can be identified directly. Furthermore, resolutions closely approaching 1 Å are required to resolve projected pairs of Si-C atoms, and considerably better than 1 Å is necessary to differentiate between the two species. Extensive multi-slice calculations, based on both current and projected electron-optical characteristics, show that polytype stacking should be recognizable at 500 kV up to thicknesses of 45-75 Å, but not at 100 kV, except possibly at the 'reversed' Scherzer defocus position with extremely coherent illumination. The occurrence of Fourier images complicates recognition of the correct objective-lens defocus particularly for thin crystals of the 3C polytype. In thicker-crystal regions (≥ 100 Å), where linear image contributions are small, mutual interference between diffracted beams results generally in polytype images of apparently improved resolution and, at specific thickness and defocus values, leads to images of 3C resembling the 'atom-pair' configuration. The latter are then explained by consideration of the image amplitude and intensity spectra. Finally, the problems of recovering specimen structure from crystals of intermediate thickness, as well as some of the factors affecting any quantitative experimental studies, are briefly discussed.