  We report first-principles density-functional pseudopotential calculations on
the atomic structures, electronic properties, and band offsets of BaO/BaTiO$_3$
and SrO/SrTiO$_3$ nanosized heterojunctions grown on top of a silicon
substrate. The density of states at the junction does not reveal any electronic
induced interface states. A dominant perovskite character is found at the
interface layer. The tunability of the band offset with the strain conditions
imposed by the substrate is studied. Using previously reported theoretical data
available for Si/SrO, Si/BaO and BaTiO$_{3}$/SrRuO$_{3}$ interfaces we
extrapolate a value for the band alignments along the whole gate stacks of
technological interest: Si/SrO/SrTiO$_3$ and Si/BaO/BaTiO$_3$/SrRuO$_3$
heterostructures.
