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The epitaxial growth of multifunctional oxides on semiconductors has opened a pathway to introduce new functionalities to semiconductor device technologies. In particular, the integration of gate materials that enable nonvolatile or hysteretic functionality in field-effect transistors could lead to device technologies that consume less power or allow for novel modalities in computing. Here we present electrical characterization of ultrathin single crystalline SrZr_xTi_1–xO₃ (x = 0.7) films epitaxially grown on a high mobility semiconductor, Ge. Epitaxial films of SrZr_xTi_1–xO₃ exhibit relaxor behavior, characterized by a hysteretic polarization that can modulate the surface potential of Ge. We find that gate layers as thin as 5 nm corresponding to an equivalent-oxide thickness of just 1.0 nm exhibit a ∼2 V hysteretic window in the capacitance–voltage characteristics. The development of hysteretic metal–oxide–semiconductor …