  We establish in a combination of ab initio theory and experiments that the
tunneling process in scanning tunneling microscopy/spectroscopy on the A-122
iron pnictide superconductors - in this case BaFe$_{2-x}$Co$_x$As$_2$ - involve
a strong adatom filtering of the differential conductance from the near-EF Fe3d
states, which in turn originates from the top-most sub-surface Fe layer of the
crystal. The calculations show that the dominance of surface Ba-related
tunneling pathways leaves fingerprints found in the experimental differential
conductance data, including large particle-hole asymmetry and an
energy-dependent contrast inversion.
