The tunnel microscope probes the electrons of a material by quantum tunneling effect.
As a consequence of the migration of electrons, is the tunnel microscope "destroying" a bit the material, by removing electrons ?
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All microscopes damage the material in some way.
Most of the damage is associated with setting up the specimen. e.g. some methods require the specimen to be in vacuum, and even light microscopes require it to be held still which is hard to do non-invasively. Tunnel microscopes require electric fields which may damage some samples. Compared to these sorts of issues, I think the tiny currents involved in the tunnel effect itself have little effect on most samples, but of course there will be exceptions.