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High conductivity in the off-state and low field-effect mobility compared to bulk properties is widely observed in the p-type thin-film transistors of Cu₂O, especially when processed at moderate temperature. This work presents results from in situ conductance measurements at thicknesses from sub-nm to around 250 nm with parallel X-ray photoelectron spectroscopy. An enhanced conductivity at low thickness is explained by the occurrence of Cu(II), which is segregated in the grain boundary and locally causes a conductivity similar to CuO, although the surface of the thick film has Cu₂O stoichiometry. Since grains grow with an increasing film thickness, the effect of an apparent oxygen excess is most pronounced in vicinity to the substrate interface. Electrical properties of Cu₂O grains are at least partially short-circuited by this effect. The study focuses on properties inherent to copper oxide, although interface effects cannot be ruled out. This non-destructive, bottom-up analysis reveals phenomena which are commonly not observable after device fabrication, but clearly dominate electrical properties of polycrystalline thin films.