High-Resolution STEM and Related Imaging Techniques
Advances in electron optics have made it possible to form electron beams of sub-nanometer diameters, and these beams have enabled high-resolution imaging methods with incoherent scattering at high angles. The origin of this incoherence is discussed. Some
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High-Resolution STEM and Related Imaging Techniques
12.1 Characteristics of High-Angle Annular Dark-Field Imaging The previous chapter described the technique of HRTEM imaging by phase-contrast imaging, using coherent elastically-scattered electrons. Another high-resolution imaging technique that is now well-established and is becoming increasingly popular is “high-angle annular dark-field,” or HAADF imaging (also called “Z-contrast imaging”). Unlike HRTEM images, HAADF images are formed from incoherent elastically-scattered electrons. As described in Sect. 4.1.2, for incoherent scattering we sum the intensities, I , from individual atoms, rather than the wavefunction amplitudes, ψ (cf., (4.11) and (4.10)). Phase differences and interferences that were central issues for HRTEM imaging are irrelevant for HAADF imaging. Each atom can be considered an independent scatterer because there is no constructive or destructive interference between the phases of wavefunctions emanating from the different atoms. The incoherent images of the HAADF method are interpreted more directly in terms of atom types and positions. High-angle annular dark-field images are acquired in STEM mode, and advances in HAADF imaging have followed advances in nanobeam optics. The images are formed by collecting high-angle (75–150 mrad) elastically-scattered electrons with B. Fultz, J. Howe, Transmission Electron Microscopy and Diffractometry of Materials, Graduate Texts in Physics, DOI 10.1007/978-3-642-29761-8_12, © Springer-Verlag Berlin Heidelberg 2013
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High-Resolution STEM and Related Imaging Techniques
Fig. 12.1 Schematic of an annular detector and EELS spectrometer in a STEM, arranged for HAADF imaging. After [12.1]
an annular dark-field detector (Fig. 12.1). An annular detector captures a large fraction of the high-angle intensity, and is an efficient device for dark-field imaging. The angle of scattering is an order-of-magnitude larger than for typical Bragg diffractions, and the relevant part of the scattering potential is an order-of-magnitude smaller than typical atomic dimensions. The effective size of the atomic scattering potential (typically 0.01–0.03 nm) is also about an order-of-magnitude smaller than the size of the electron beam probe of modern medium-voltage field-emission STEMs (typically 0.15–0.2 nm). A vertical column of atoms can therefore be understood as a very sharp object in the plane of the sample. The image resolution is the convolution of this “δ-function” with the spatial profile of the probe current (see Fig. 12.2), together with any beam broadening that occurs as the electrons propagate through the sample. Owing to the large cross-section for elastic scattering, however, it is possible to use thin specimens to minimize beam broadening. A phenomenon called “electron channeling,” described in Sect. 12.2, also helps to minimize beam broadening. One criterion for the resolution of HAADF imaging is the full-width-halfmaximum of the profile of the probe beam. The objective lens makes an image of the ele
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