  Band offsets at semiconductor-oxide interfaces are determined through a
scheme based on hybrid density functionals, which incorporate a fraction
$\alpha$ of Hartree-Fock exchange. For each bulk component, the fraction
$\alpha$ is tuned to reproduce the experimental band gap, and the conduction
and valence band edges are then located with respect to a reference level. The
lineup of the bulk reference levels is determined through an interface
calculation, and shown to be almost independent of the fraction $\alpha$.
Application of this scheme to the Si-SiO$_2$, SiC-SiO$_2$, and Si-HfO$_2$
interfaces yields excellent agreement with experiment.
