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We report on temperature, time, and voltage dependent resistive hysteresis measurements of BaTiO3-ZnO heterostructures grown on (001) Si substrates by pulsed laser deposition. We observe a diodelike behavior and cycling-voltage dependent hysteresis formation under forward bias. We explain these effects with depletion layer formation between the ZnO and BaTiO3 layers, an additional barrier due to the spontaneous polarization of ZnO and the ferroelectric nature of BaTiO3. The disappearance of the resistive hysteresis above the ferroelectric-paraelectric phase transition temperature of BaTiO3 conformed that the hysteresis is related to the ferroelectricity of BaTiO3. Time dependent resistance measurements reveal memory effects.