High-angle annular dark-field imaging of self-assembled Ge islands on Si(0 0 1)

Low-resolution high-angle annular dark-field (HAADF) imaging is applied to the study of coherent Ge islands on a Si(0 0 1) substrate. Experimental HAADF images reveal a complicated pattern for a coherent Ge island under (0 0 1) zone axis conditions due to strain-induced interband scattering between different Bloch-wave branches. This complicated pattern varies with objective aperture size and defocus because of the effect from the depth of field. This suggests that the strain field of a coherent Ge island can be mapped out in 3 dimensions using HAADF imaging. When samples are tilted away from dynamical conditions, image contrast agrees with the predictions from atomic number variation (Z contrast). Therefore, quantitatively compositional analysis is feasible under kinematical imaging conditions when strain contrast is suppressed. Simulations using multi-beam Bloch-wave theory agree well with the experimental images on the complicated strain-induced and through-focus images.