The region-by-region polarization switching in ferroelectric Pb(Zr,Ti)O-3 thin films sandwiched between Pt electrodes has been directly observed using piezoelectric scanning probe microscopy. A resolution improved by one order-of-magnitude compared to the standard piezoelectric response imaging technique for ferroelectric capacitors was achieved by reducing the top electrode thickness to 10-15 nm through polishing. It was demonstrated that the individually switched regions correspond to single grains or clusters of grains where the grain boundaries act as frontiers limiting the propagation of the switched state. The study of the propagation of the reversed polarization state as a function of voltage applied shows a rather discontinuous growth of the switched areas, the movement of the domain walls being triggered abruptly by different threshold voltages. This result agrees with the earlier proposed nucleation-limited switching model. The observation of the frozen regions that do not switch even at higher voltages provides significant insight into the "bits-failure" problem in submicron ferroelectric capacitors used for nonvolatile memory applications. (C) 2005 American Institute of Physics.