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.

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describes domain growth in crystals composed of a large number of relatively small grains. If the grain boundaries stop or significantly affect domain wall motion then the observed switching transients will deviate from those predicted by the infinite grain model of Ishibashi and Takagi. The model assumes a constant nucleation rate throughout the switching process and constant domain wall velocity. A t a characteristic time dependent only on the size of the grains and the domain wall velocity the switching current transient changes from its early-time infinite-grain behavior to an exponential decay. The results are compared with Monte Carlo simulations of switching in the two-dimensional Ising model.