The band bending at Cu/PZT(001) interfaces is investigated by X-ray photoelectron spectroscopy (XPS) for a PZT(001) layer which exhibits initial outwards ferroelectric polarization. Two competitive processes are identified: (a) formation of the Schottky barrier between the ferroelectric and unconnected Cu islands, and (b) coalescence of the Cu islands, realisation of an electrical contact to the ground of the system, inducing the apparent loss of the component of the ferroelectric polarization perpendicular to the sample surface, at least as it manifests in band bending. Three mechanisms are proposed to explain this loss of band bending when a full metal layer connected to ground is formed on the surface: (i) over-compensation of depolarization field in the sub-surface region, (ii) formation of domains with in-plane orientation of the polarization vector and (iii) loss of polarization in the near-surface layers of the ferroelectric due to electrons provided by the metal. These result in a non-monotonous variation of binding energies with the amount of Cu deposited. High resolution transmission electron microscopy and piezoresponse force microscopy confirmed these hypotheses. The XPS data allowed also to derive the surface PZT composition, its evolution with the deposition of copper and the formation of surface compounds.