Polarization switching dynamics simulation by using the practical distribution of ferroelectric properties

Abstract

We investigated the internal bias field and coercive field in a typical ferroelectric thin-film capacitor and simulated polarization switching dynamics using Euler's method. The simulation results agreed well with the experimental results and reflected the well-known polarization domain switching model in which the polarization switching occurs on the order of nucleation, growth, and coalescence. The fit parameters (damping parameters affecting the polarization change rate) also followed a certain distribution. When the expected value was used instead of full distribution, the simulation results did not agree well with corresponding experimental results. The simulation results suggested no domain structure in the polarization switching dynamics, indicating that the polarization domain structure was affected by the distribution of the fit parameters. Our results demonstrate the possibility of simulation using realistic distribution of ferroelectric properties.

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“…The switching density 𝜌 SW (V,V r ) was obtained from Equation 1 by fitting the polarization P(V, V r ). [17,20]…”

“…In LGD theory, the free energy is described as a polynomial function of polarization P (Equation 3). [17,18] The coefficients for LGD theory are obtained from the coercive field and the effective field is obtained considering the internal bias field. Then, we have different free energy and assign the values to every point on the grid of x-y plane.…”

“…Kim et al simulated the polarization switching dynamics with a practical distribution of ferroelectric properties by modeling the capacitor as a 2D plane. [17] They assigned the free energy values to every point on the grid of the plane. When the free energy function is changed due to the application of external voltage signal, the polarization distribution starts to change toward new stable state in the ferroelectric film.…”

“…The simulation uses the Landau-Ginzburg-Devonshire (LGD) theory and the Landau-Khalatnikov (L-K) equation. [17][18][19] Coefficients of the free energy function and effective fields were calculated from the local coercive fields E c and the local internal bias fields E bias obtained using the first-order reversal curves (FORCs) method, respectively. [17,20] As several voltage pulses were applied across the HZO thin film one by one, the area of switched polarization gradually widened.…”

“…[17][18][19] Coefficients of the free energy function and effective fields were calculated from the local coercive fields E c and the local internal bias fields E bias obtained using the first-order reversal curves (FORCs) method, respectively. [17,20] As several voltage pulses were applied across the HZO thin film one by one, the area of switched polarization gradually widened. To study the conductance modulation characteristics, we assumed that there was a source electrode, a drain electrode, and a channel layer around the HZO thin film.…”