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In order to examine to what extent the rigid-band-like electron dopingscenario is applicable to the transition metal-substituted Fe-basedsuperconductors, we have performed angle-resolved photoemission spectroscopystudies of Ba(Fe$_{1-x}$Ni$_{x}$)$_2$As$_2$ (Ni-122) andBa(Fe$_{1-x}$Cu$_{x}$)$_2$As$_2$ (Cu-122), and compared the results withBa(Fe$_{1-x}$Co$_x$)$_2$As$_2$ (Co-122). We find that Ni 3$\it{d}$-derivedfeatures are formed below the Fe 3$\it{d}$ band and that Cu 3$\it{d}$-derivedones further below it. The electron and hole Fermi surface (FS) volumes arefound to increase and decrease with substitution, respectively, qualitativelyconsistent with the rigid-band model. However, the total extra electron numberestimated from the FS volumes (the total electron FS volume minus the totalhole FS volume) is found to decrease in going from Co-, Ni-, to Cu-122 for afixed nominal extra electron number, that is, the number of electrons thatparticipate in the formation of FS decreases with increasing impuritypotential. We find that the N$\acute{\rm{e}}$el temperature $T_{\rm{N}}$ andthe critical temperature $T_{\it{c}}$ maximum are determined by the FS volumesrather than the nominal extra electron concentration nor the substituted atomconcentration.

Dependence of carrier doping on the impurity potential in transition-metal-substituted FeAs-based superconductors