# An Extended Kolmogorov–Avrami–Ishibashi (EKAI) Model to Simulate Dynamic Characteristics of Polycrystalline-Ferroelectric-Gate Field-Effect Transistors

## TL;DR

This paper introduces a physics-based model to simulate polarization switching in ferroelectric polycrystalline films used in FeFETs, aligning well with experimental results.

## Contribution

The paper proposes an extended Kolmogorov–Avrami–Ishibashi (EKAI) model for dynamic polarization switching in polycrystalline ferroelectric films.

## Key findings

- The EKAI model accurately describes polarization domain nucleation and wall propagation under time-dependent electric fields.
- Switching time scales follow an exponential dependence on the electric field and grain orientation angle θ.
- The model explains the broad switching time distribution observed in FeFETs without assuming non-physical functions.

## Abstract

A physics-based model on polarization switching in ferroelectric polycrystalline films is proposed. The calculation results by the model agree well with experimental results regarding dynamic operations of ferroelectric-gate field-effect transistors (FeFETs). In the model, an angle θ for each grain in the ferroelectric polycrystal is defined, where θ is the angle between the spontaneous polarization and the film normal direction. Under a constant electric field for a single-crystal film with θ = 0, phenomena regarding polarization domain nucleation and wall propagation are well described by the Kolmogorov–Avrami–Ishibashi theory. Since the electric fields are time-dependent in FeFET operations and the θ values are distributed in the polycrystalline film, the model in this paper forms an extended Kolmogorov–Avrami–Ishibashi (EKAI) model. Under a low electric field, the nucleation and domain propagation proceed according to thermally activated processes, meaning that switching the time scale of a grain with the angle θ is proportional to an exponential form as exp(const./Ezcosθ) [Ez: the film-normal electric field]. Wide θ distribution makes the time response quite broad even on the logarithmic scale, which relates well with the broad switching time experimentally shown by FeFETs. The EKAI model is physics based and need not assume non-physical distribution functions in it.