The stability of oxygen vacancies across the Ge-HfO2 interface is studied through semilocal and hybrid density-functional calculations. On the semiconductor side, the formation energies are obtained for substoichiometric GeOx of varying x through the use of a bond-energy model. On the hafnium oxide side, the interface is modeled through bulk models with aligned band structures. Formation energies are compared for different charge states and Fermi energy levels. The oxygen vacancy is found to be most stable in the interfacial germanium oxide layer for both p-type and n-type doping. This favors the formation of substoichiometric GeOx, consistent with experimental observations. (C) 2010 American Institute of Physics. [doi:10.1063/1.3518491]