A theoretical model of fatigue in ferroelectric thin-film memories based upon impact ionization (e.g., Ti+4 to Ti+3 conversion in PbZr1−xTixO3), resulting in dendritic growth of oxygen-deficient filaments, is presented. The predictions of spontaneous polarization versus switching cycles Ps(N) are compared with both Monte Carlo simulations for a two-dimensional Ising model and with experimental data on small-grain (40 nm) sol-gel PZT films. Excellent agreement between theory and experiment is obtained. In addition to modeling the Ps(N) curves, the theory developed explains the observed linear proportionality between switching time ts(N) and polarization Ps(N) during fatigue; other models of aging do not account for this. Earlier theories of switching are also extended to include finite grain sizes, surface nucleation, triangular drive pulses, and dipolar forces. Good agreement with sol-gel PZT switching data is obtained.

By combining Auger data on the width of an oxygen depletion layer near the Pt electrodes with a modified Langmuir–Child law for the leakage current: I(V) = aV + bV2, we deduce parameters related to the space-charge density and field in 210-nm-thick PbZr1−xTixO3 memories. The results are compared with the space charge fields inferred by Okazaki (∼10 kV/cm for PZT), which involve measuring the switching speeds ts(E) for positive and negative voltages. Differences in the voltage dependencies of the leakage current are found after fatigue and are related to specific electrochemical processes involving oxygen deposition on electrode surfaces.

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