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The epitaxial growth of crystalline oxides on semiconductors provides apathway to introduce new functionalities to semiconductor devices. Key toelectrically coupling crystalline oxides with semiconductors to realizefunctional behavior is controlling the manner in which their bands align atinterfaces. Here we apply principles of band gap engineering traditionally usedat heterojunctions between conventional semiconductors to control the bandoffset between a single crystalline oxide and a semiconductor. Reactivemolecular beam epitaxy is used to realize atomically abrupt and structurallycoherent interfaces between SrZr$_{x}$Ti$_{1-x}$O$_3$ and Ge, in which theband-gap of the former is enhanced with Zr content $x$. We present structuraland electrical characterization of SrZr$_{x}$Ti$_{1-x}$O$_3$-Ge heterojunctionsfor $x$ = 0.2 to 0.75 and demonstrate the band offset can be tuned from type-IIto type-I, with the latter being verified using photoemission measurements. Thetype-I band offset provides a platform to integrate the dielectric,ferroelectric and ferromagnetic functionalities of oxides with semiconductingdevices.

Band-gap engineering at a semiconductor - crystalline oxide interface