Resolution limits in annular dark field STEM

Abstract

Recent experiments have provided high-resolution annular dark field atom structure images of zone axis crystalline samples. This paper reviews steps towards assessment of such images using simulation and quantitative experiments. Work reviewed includes a power spectral analysis of thin amorphous carbon film images to determine the spherical aberration coefficient C s and to calibrate the defocus Δ f. Agreement with experiment provides evidence of the validity of a “frozen phonon” algorithm for simulation of energy-filtered convergent beam electron diffraction that is then extended to image simulation. For both silicon and indium phosphide the simulations are in good agreement with the incoherent imaging model. Experiments with indium phosphide also support the validity of the incoherent imaging model for zone-axis crystals. Limits of resolution in ADF-STEM for zone-axis-oriented crystals are therefore given by the contrast transfer function of the incoherent imaging model. For a polepiece with C s=0.7 mm at 100 kV, this corresponds to a resolution limit of 1.8 Å at a contrast level of 5% at Scherzer settings. A somewhat larger aperture at larger defocus settings enhances the contrast spatial frequencies close to the resolution limit while decreasing contrast for spatial frequencies further away.