  Using angle-resolved photoemission spectroscopy (ARPES), we studied the
effect of the impurity potential on the electronic structure of
FeTe$_{0.5}$Se$_{0.5}$ superconductor by substituting 10\% of Ni for Fe which
leads to an electron doping of the system. We could resolve three hole pockets
near the zone center and an electron pocket near the zone corner in the case of
FeTe$_{0.5}$Se$_{0.5}$, whereas only two hole pockets near the zone center and
an electron pocket near the zone corner are resolved in the case of
Fe$_{0.9}$Ni$_{0.1}$Te$_{0.5}$Se$_{0.5}$, suggesting that the hole pocket
having predominantly the $xy$ orbital character is very sensitive to the
impurity scattering. Upon electron doping, the size of the hole pockets
decrease and the size of the electron pockets increase as compared to the host
compound. However, the observed changes in the size of the electron and hole
pockets are not consistent with the rigid-band model. Moreover, the effective
mass of the hole pockets is reduced near the zone center and of the electron
pockets is increased near the zone corner in the doped
Fe$_{0.9}$Ni$_{0.1}$Te$_{0.5}$Se$_{0.5}$ as compared to FeTe$_{0.5}$Se$_{0.5}$.
We refer these observations to the changes of the spectral function due to the
effect of the impurity potential of the dopants.
