An extended Kolmogorov-Avrami-Ishibashi (EKAI) model to simulate dynamic characteristics of polycrystalline-ferroelectric-gate field-effect transistors
Abstract
An extended Kolmogorov-Avrami-Ishibashi (EKAI) model is proposed, which represents dynamic characteristics in polycrystalline ferroelectric films consisting of grains under time-dependent electric fields. The original Kolmogorov-Avrami-Ishibashi (KAI) model described time-varying polarization reversal in a single-crystal film under a constant electric field. The field and the polarization were directed along the film normal. The polarization reversal dynamics were represented by a time-evolution function, c(t), regarding the volume fractions of the downward- and upward-polarization domains under a constant electric field. In the EKAI model, a grain in a polycrystalline ferroelectric film is indexed by l with an angle theta which is the angle between the spontaneous polarization Ps and the film normal. The EKAI model first assumes KAI-like polarization variations under a constant field inside the grain whose angle is tilted by theta. The second assumption is concerned with polarization variation under time-varying electric field. During a time period deltat from tnow to tnext (=tnow+deltat), the volume fractions of the downward- and upward-polarization domains changes according to the function c(t) under an electric field at tnow. By combining the derived polarization and an electrostatic potential equation across a gate stacked structure at tnext, an electric field at tnext is derived. Since the electric field and the volume fractions of the downward and upward domains are known at tnext, the calculation at the next deltat step is possible. This procedure is repeated, and the EKAI model can simulate time-varying polarization reversal phenomena. Good agreement of the numerical results with the experimental indicates that the model is appropriate to simulate dynamic characteristics of FeFETs with polycrystalline ferroelectric films under swept and pulsed gate-voltages.
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