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An extended Kolmogorov-Avrami-Ishibashi (EKAI) model is proposed, whichrepresents dynamic characteristics in polycrystalline ferroelectric filmsconsisting of grains under time-dependent electric fields. The originalKolmogorov-Avrami-Ishibashi (KAI) model described time-varying polarizationreversal in a single-crystal film under a constant electric field. The fieldand the polarization were directed along the film normal. The polarizationreversal dynamics were represented by a time-evolution function, c(t),regarding the volume fractions of the downward- and upward-polarization domainsunder a constant electric field. In the EKAI model, a grain in apolycrystalline ferroelectric film is indexed by l with an angle theta which isthe angle between the spontaneous polarization Ps and the film normal. The EKAImodel first assumes KAI-like polarization variations under a constant fieldinside the grain whose angle is tilted by theta. The second assumption isconcerned with polarization variation under time-varying electric field. Duringa time period delta_t from t_now to t_next (=t_now+delta_t), the volumefractions of the downward- and upward-polarization domains changes according tothe function c(t) under an electric field at t_now. By combining the derivedpolarization and an electrostatic potential equation across a gate stackedstructure at t_next, an electric field at t_next is derived. Since the electricfield and the volume fractions of the downward and upward domains are known att_next, the calculation at the next delta_t step is possible. This procedure isrepeated, and the EKAI model can simulate time-varying polarization reversalphenomena. Good agreement of the numerical results with the experimentalindicates that the model is appropriate to simulate dynamic characteristics ofFeFETs with polycrystalline ferroelectric films under swept and pulsedgate-voltages.

An extended Kolmogorov-Avrami-Ishibashi (EKAI) model to simulate dynamic  characteristics of polycrystalline-ferroelectric-gate field-effect  transistors