Kinetics of nanosize ferroelectrics

Abstract

We analyze theoretically the finite-temperature polarization dynamic in displacive-type ferroelectrics. In particular we consider the thermally activated switching time of a single-domain ferroelectric polarization studied by means of the Landau-Khalatnikov equation, extended to capture thermal fluctuations. The results are compared with the switching time formula that follows from the analytical solution of Pauli master equations. In a second step we focus on the phase diagram of a prototypical ferroelectric as described by the temperature-dependent LandauDevonshire model including thermal fluctuations. Our simulations show the emergence of phase instability at reduced sizes which we attribute to thermal fluctuations in the order parameter in the respective phase. We conclude that, along with the temperature-dependent potential coefficients, thermal fluctuations should be taken into account to achieve a comprehensive description of the thermal behavior of reduced-size ferroelectrics. To support our conclusions, we simulated the electric-field activated switching time for a multidomain system and compared the results to the predictions of well-established models such as Kolmogorov-Avrami-Ishibashi.

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

“…If E z > 0, R dn (l) and R up (l) at t = t next are obtained by Equations ( 19) and (20). If E z < 0, R up (l) and R dn (l) at t = t next are obtained by Equations ( 22) and (23). The procedure of this section gives us E z at t = t next .…”

“…Thus, the LK and TDGL equations are not suitable (at least quantitatively). Additions of Gaussian white-noise terms to these equations are necessary for describing the thermal activation steps, and in fact the effect of the noise term was demonstrated for a small segment number case [ 23 ]. However, since the LDG segments should be finer than the domain-wall width and the wall width size is one crystal lattice or a few times of it [ 24 , 25 ], the number of the LDG segments for general objects including polycrystalline films becomes so huge that we cannot make calculations within a realistic time scale.…”

Kramers' escape problem for white noise driven switching in ferroelectrics

“…Since thermal noise has already been studied in a ferroelectric [26], we are using the same model to define the problem at hand . The free energy density F (in J/m 3 ) of the ferroelectric is related to the polarisation P (under the assumption of homogeneous switching) and is given by…”

“…Under the assumption of homogeneous switching, it is possible to use the LGD theory to model the ferroelectric as a single domain and study the escape problem. Etesami et al [26] simulated the TDGL equation to explain the impact of thermal fluctuations in the bistable potential well, enabling switching between the two states. We present the theory and simulations for two applications that emerge from this formalism: True random number generation (TRNG) and stochastic resonance (SR).…”

Electric control of emergent magnonic spin current and dynamic multiferroicity in magnetic insulators at finite temperatures

“…The latter results in the energy contribution E r P r d 3 r. A switching off the electric field the system relaxes to the pure magnetic configuration. Here we did not discuss the dissipation of the ferroelectric energy nor the dynamics of the polarization (as a separate order parameter) and its damping, which was presented in a recent work [36]. We assume that such dissipation related to the fluctuation in the polarization is accounted for by parts of the Gilbert damping.…”