Switching dynamics in ferroelectric P(VDF-TrFE) thin films

Dong Zhao (赵冬), Ilias Katsouras, Kamal Asadi, Paul W. M. Blom, and Dago M. de Leeuw

Phys. Rev. B 92, 214115 – Published 28 December 2015

Abstract

Switching, i.e., polarization reversal, of ferroelectric P(VDF-TrFE) thin films has been investigated in a wide range of applied electric field and temperature. The measured polarization transients can be quantitatively described by a compressed exponential function as originally formulated by Kolmogorov, Avrami, and Ishibashi (the KAI model). The phenomenological parameters switching time and Avrami index are related to the velocity and morphology of the domain walls, respectively. We show that the switching time depends exponentially on the electric field as described by the Merz law. The experimentally obtained Avrami index is independent of temperature but decreases with applied electric field from 1.55 at low field to 1.0 at 300 MV/m, indicative of an out-of-equilibrium dynamics of the growing domains. Using a random walk model we demonstrate that the observed switching dynamics is in agreement with a domain growth mechanism where domains are circular at low electric field with few nucleation sites, whereas at high field irregular entangled domains are formed. The density of nucleation sites is extracted as $1.5 %$ of the monomeric units in this work. Switching transients on capacitors where the nuclei density has been artificially increased exhibit one-dimensional-like growth, as predicted by our model.

Received 7 October 2015

DOI:https://doi.org/10.1103/PhysRevB.92.214115

Authors & Affiliations

Dong Zhao (赵冬)^1,*, Ilias Katsouras^1,2, Kamal Asadi¹, Paul W. M. Blom¹, and Dago M. de Leeuw^1,†

¹Max-Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
²Holst Centre, High Tech Campus 31, 5656AE Eindhoven, The Netherlands

^*zhaod@mpip-mainz.mpg.de
^†deleeuw@mpip-mainz.mpg.de

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Vol. 92, Iss. 21 — 1 December 2015

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Images

Figure 1
(a) A photograph of the finished capacitor array. The layout consists of discrete photolithographically defined Ti/Au bottom contacts with evaporated common Au top electrodes. The device area varies from $0.059 m m^{2}$ to $1.38 m m^{2}$ . A schematic representation of the comprising capacitors' layout and the chemical structure of P(VDF-TrFE) are indicated. The thickness of the ferroelectric layer is about 500 nm. (b) Typical example of a measured polarization transient. After fully polarizing the capacitor to $- P_{r}$ and shortening the contacts for 10 s, a positive square pulse is applied. The blue dots present the total change of the charge on the reference capacitor after the first pulse. The measurement is repeated using a second positive square pulse. The green dots represent the nonswitching dielectric contribution. The black dots are obtained by subtracting the two transients and represent the net polarization. The inset shows a schematic representation of the Sawyer-Tower circuit used.
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Figure 2
(a) Typical polarization transients measured at room temperature at electric field between 60 and 120 MV/m. (b) Typical polarization transients measured at an electric field of 80 MV/m at temperatures between 253 and 333 K. The solid lines are fits to the compressed exponential function of Eq. (3). (c) Extracted value of the Avrami index presented as a function of applied electric field between 50 and 300 MV/m at temperatures between 193 and 333 K. The value is independent of temperature and monotonically decreases with applied electric field from 1.55 at low fields to 1.0 at 300 MV/m. The dashed line is a guide to the eye. (d) The measured remanent polarization $P_{r}$ as a function of electric field at temperatures between 19 and 333 K.
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Figure 3
(a) The characteristic switching time $t_{0}$ as a function of reciprocal applied electric field. The lines are fits according to Eq. (4), extrapolated to zero reciprocal electric field. (b) Domain-wall velocity at room temperature as a function of reciprocal electric field. The black line is estimated assuming a velocity equal to the P(VDF-TrFE) lattice constant of 0.25 nm over the switching time. The dots are reported experimental values extracted from PFM measurements on growing domains [27]. (c) The activation field as a function of reciprocal temperature. The blue symbols represent the values extracted from the fit of the data in (a) using Eq. (4). The green symbols represent the values reported in Ref. [13]. The solid line is a linear fit through the origin. (d) Coercive field measured at 100 Hz as a function of activation field. The red line is a linear fit through the origin. The black dashed line represents the coercive field obtained from the iteratively calculated hysteresis loops using Eq. (7).
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Figure 4
Calculated domain morphology as a function of nuclei density $ρ_{nuclei}$ and perturbation strength $N$ . The morphology is presented for a normalized polarization of about 35%. Black areas represent flipped dipoles. The corresponding calculated Avrami indices are presented in Fig. 5.
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Figure 5
(a),(b) Values of the fitting parameters $n^{'}$ and $τ_{0}$ as extracted from the calculated normalized polarization as a function of cumulative number of random walks using Eq. (8). $τ_{0}$ is the number of cumulative random walks needed to reach 63% polarization reversal, normalized to the number of lattice sites. The values of $n^{'}$ and $τ_{0}$ are presented as functions of the perturbation strength $N$ and of the nuclei density $ρ_{nuclei}$ . The density of nucleation sites has been varied between $10^{- 6}$ and $2 \times 10^{- 1}$ . The corresponding calculated domain morphologies are presented in Fig. 4.
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Figure 6
Polarization transients measured at room temperature at an electric field of 80 MV/m of a depolarized and of a fully polarized ferroelectric P(VDF-TrFE) capacitor. The depolarized capacitor switches from the initial polarization of 0 to $+ P_{r}$ (blue dots). The fully polarized capacitor switches from $- P_{r}$ to $+ P_{r}$ (green dots). The solid red lines are fits to the data using Eq. (3) with $n$ equal to 1 and 1.5, respectively.
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