Scanning tunneling microscopy (STM) is the only tool making it possible to study both the topography and electronic structure of carbon nanosystems in sub-nanometer resolution The interpretation of the STM images of carbon nanosystems is more complicated than in the case of at, single crystalline surfaces. Because of this computer simulation is a helpful tool in understanding the experimental data. In this paper the image formation in STM and the particularities of imaging supported carbon nanosystems are discussed. The tight binding and the wave packet dynamical STM simulation methods are reviewed with applications showing their complementary merits. These methods are simple enough to make feasible in the near future their application to more complex carbon nanosystems like coiled nanotubes and nanotube crossings.
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