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One such experimental technique is Scanning Tunneling Microscopy (STM). In STM, a sharp metallic tip is brought withing a few atoms distance from the sample to be studied. Electrons tunnel from the tip to the sample at a rate dictated by the number of available states for the tunneling process to occur (the density of states, DOS). By scanning the tip across the sample, we can generate an atom-by-atom picture of the density of states acrosss the surface. We can also generate pretty pictures of the surface of materials!
Copper surface
The surface of a single crystal of copper showing
atomic steps, defects and scattering
of electron waves from the step edges





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