  We investigate the currently debated issue concerning whether transition
metal substitutions dope carriers in iron based superconductors. From
first-principles calculations of the configuration-averaged spectral function
of BaFe$_2$As$_2$ with disordered Co/Zn substitutions of Fe, important doping
effects are found beyond merely changing the carrier density. While the
chemical potential shifts suggest doping of a large amount of carriers, a
reduction of the coherent carrier density is found due to the loss of spectral
weight. Therefore, none of the change in the Fermi surface, density of states,
or charge distribution can be solely used for counting doped coherent carriers,
let alone presenting the full effects of the disordered substitutions. Our
study highlights the necessity of including disorder effects in the studies of
doped materials in general.
