High-Resolution Image Simulation of a Tilted Crystal

Most high resolution images are not directly interpretable but must be compared with simulations based on model atomic structures and appropriate imaging conditions. Typically, the only parameters that are adjusted, in addition to the structure models, are crystal thickness and microscope defocus. Small tilts of the crystal away from the exact zone axis have only rarely been considered. It is shown here that, in the analysis of an image of a silicon twin intersection, the crystal tilt could be accurately estimated and satisfactorily included in the simulations.The micrograph shown in figure 1 was taken as part of an HREM study of indentation-induced hexagonal silicon. In this instance, the intersection of two twins on different habit planes has driven the silicon into hexagonal stacking. However, in order to confirm this observation, and in order to investigate other defects in the region, it has been necessary to simulate the image taking into account the very apparent crystal tilt. The inability to orientate the specimen at the exact [110] zone was influenced by i) the buckling of the specimen caused by strains at twin intersections, ii) the absence of Kikuchi lines or a clearly visible Laue circle in the diffraction pattern of the thin specimen and iii) the avoidance of radiation damage (which had marked effects on images taken a few minutes later following attempts to realign the crystal.) The direction of the crystal tilt was estimated by observing which of the {111} planes remained close to edge-on to the beam and hence strongly imaged. Further refinement of the direction and magnitude of the tilt was done by comparing simulated images to experimental images in a through-focal series. The presence of three different orientations of the silicon lattice aided the unambiguous determination of the tilt. The final estimate of a 0.8° tilt in the 200Å thick specimen gives atomic columns a projected width of about 3Å.