  Chemical substitution plays a key role in controlling the electronic and
magnetic properties of complex materials. For instance, in EuO, carrier doping
can induce a spin-polarized metallic state, colossal magnetoresistance, and
significantly enhance the Curie temperature. Here, we employ a combination of
molecular-beam epitaxy, angle-resolved photoemission spectroscopy, and an
effective model calculation to investigate and understand how semi-localized
states evolve in lightly electron doped Eu$_{1-x}$Gd$_{x}$O above the
ferromagnetic Curie temperature. Our studies reveal a characteristic length
scale for the spatial extent of the donor wavefunctions which remains constant
as a function of doping, consistent with recent tunneling studies of doped EuO.
Our work sheds light on the nature of the semiconductor-to-metal transition in
Eu$_{1-x}$Gd$_{x}$O and should be generally applicable for doped complex
oxides.
