Impurity problem, relation to doping, densities of state

The basic motivation is to see what happens when we have a dopant/impurity in a metallic system where the Fermi level cuts through a band. Does the dopant in fact raise the Fermi level? By how much and in what circumstances? The question comes up when creating oxygen vacancies in a metallic oxide, for example an oxygen vacancy in LaNiO3. Clearly, there is a perturbation to the electronic structure around the vacancy site and oxygen vacancies should donate electrons since the oxygen p bands are below the Fermi level. But do they? What if a bound state forms? More generally, even in a semiconductor, does the raising of the Fermi level correspond exactly to the number of electrons being donated? Or does the change in the density of states around the vacancy modify the counting even if a bound state does not form?