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Over the last three decades the scanning tunnelling microscope (STM) has been one of the key instruments in the study of the atomic and electronic structure of surfaces. This chapter discusses the most important aspects of the technique. It starts with a brief overview of the invention of the STM and its subsequent evolution, followed by sections on the basic STM operating principles and how the tunnelling interaction between the fine scanning tip and the surface can lead to atomic-resolution images of crystal surfaces of metals and semiconductors. The next section describes examples of STM imaging of surface nanostructures such as Ge nanocrystals on a Si surface, SrTiO3 and MoS2 nanostructures, as well as fullerene clusters. This is followed by a discussion of atomic-scale lithography with the STM, including illustrations of the wave-like nature of quantum mechanical interactions seen in quantum corrals. The STM is not only sensitive to atomic-scale topography, but also to the local electronic surface states. This is described via the imaging of dopant atoms and TiO2 surfaces, and the theme is further developed in the section on tunnelling spectroscopy where the density of electronic states in a window of a few eV either side of the Fermi energy can be measured. The next section covers some common imaging artefacts that arise when the scanning tip is not perfect, and this is followed by a brief conclusion and outlook

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