A theoretical model of fatigue in ferroelectric thin‐film memories based upon impact ionization (e.g., Ti+4to Ti+3conversion in PbZr1−xTixO3), resulting in dendritic growth of oxygen‐deficient filaments, is presented. The predictions of spontaneous polarization versus switching cyclesPs(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 thePs(N) curves, the theory developed explains the observed linear proportionality between switching timets(N) and polarizationPs(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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