Phase Transition Temperature of Ferroelectric Thin Film Evaluated by Four-state Potts Model
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Phase Transition Temperature of Ferroelectric Thin Film Evaluated by Four-state Potts Model W. Y. Winnie Chung and V. C. Lo Department of Applied Physics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China ABSTRACT An epitaxial ferroelectric thin film can be modeled by a two-dimensional array of dipoles. The orientation of each dipole is assigned to one of the four possible states which are mutually perpendicular to each other. Consequently, the whole film can be divided into domains with both 90° and 180° domain walls. The dominant switching mechanism for individual dipole is implemented by a 90° rotation. Two different conditions have been considered. For the first one (model A), every dipole inside the film is allowed to rotate, provided that it is thermally activated. For the second (model B), only the dipole rotation is restricted to those at the domain walls. The phase transition temperatures under these two models have been evaluated. Furthermore, the effects of sample size and boundary condition are discussed. INTRODUCTION Ferroelectric thin films have drawn a lot of attention for their potential applications in memory, smart systems and microelectromechanical devices. Due to the demand of miniaturization in microelectronics systems, the study on various size effects is vitally important. Landau thermodynamic theory has provided theoretical framework for various ferroelectric properties of materials with great success. However, it is a macroscopic theory that only macroscopic behaviors can be tackled while the detailed switching mechanism might have been overlooked. The study of phase transition temperature of ferroelectric thin films has been published extensively in literature. Most of them were based on Landau’s free energy approach. In particular, the effects of size, electrode/film interface and composition on phase transition temperature have been studied. However, only a few of them have discussed the effect of domain configuration on phase transition temperature. The former was found to be important in the design of electromechanical systems. In this paper, we present the evaluation of phase transition temperature of a two-dimensional ferroelectric system using four-state Potts model. In this approach, the description on the switching of individual dipoles as well as the role of domain walls are provided.
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The formulation of the model and assumptions are described in the next section. The computational results under different boundary conditions and switching conditions will be presented in Results and Discussion. MODELING AND SIMULATION The q-state Potts model is a generalization of Ising model with q metastable states instead of two. This approach has been used to simulate ferroelectric properties in recent years [1-4]. Liu et al. [2] have demonstrated that Potts model is much better than Ising model in tackling multi-domain ferroelectrics. It has also been found that 90° domain walls are dominant in perovskite-type ferroelectric materials. Cons
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