Influence Of Flexoelectric Effect On Domain Structure And Domain Switching Of Ferroelectric Film

Since the charge-based memories including Flash are currently facing the theoretical and physical limits of downscaling, people have to pay more attention to non-charge-based memories. Owing to excellent anti-radiation, high reading and writing speed, high endurance and non-volatility, etc, ferroelectric memory is considered to be an ideal memory that has the potential to replace the current dominant memories in future. However, several major failure issues including fatigue, retention loss and imprint have severely hindered the full commercialization of them. These macro failure phenomena are essentially determined by the domain structure and switching dynamics in ferroelectric film. Therefore, study of domain structure and domain switching dynamics is an indispensible approach to reveal the failure mechanism of ferroelectric memory.To our knowledge, one of the most important factors that govern the domain behavior is electromechanical coupling, the interaction between electrical and mechanical properties. The coupling between strain and polarization (piezoelectricity) has been studied extensively. Strain engineering, with an appropriate choice of substrate, has been proved to be a useful tool to optimize properties of ferroelectric thin films. Recently, an increasing amount of attention has been paid to a high order electromechanical coupling behavior, flexoelectricity, which describes the generation of an electric field by a strain gradient (the direct flexoelectric effect) or the mechanical response induced by an electric field gradient (the converse flexoelectric effect). Some failure problems were ascribed to the flexoelectric effect, such as imprint, dead layer effect or lowering of permittivity. On the other hand, flexoelectricity also provides opportunities to tune the physical properties of thin films. Because of flexoelectricity, strain gradient generated by mechanical force can switch the polarization in the nanoscale volume of a ferroelectric film. This result opens up a way to switch polarization in ferroelectric thin films using mechanical force and may enable application in which memory bits are written mechanically and read electrically.Remarkable progress has been achieved in the experimental studies of the influence of flexoelectric coupling on the domain structure and polarization switching. However, there are limited theoretical studies relating the effect of flexoelectric coupling on the polarization switching. Our understanding of mechanical stress induced polarization switching is still rather deficient and limited. The weakness of the theoretical research will bring risk and high cost for experimental research. It also will slow down the engineering application of flexoelectricity.Based on above analysis, the main purpose of this paper is to theoretically study the influence of flexoelectric effect on domain structure and domain switching of ferroelectric thin film as well as to find ways to control mechanical stress induced switching. Following are the main results obtained by this paper,1. Theoretical framework for electromechanical coupling of flexoelectric effect on ferroelectric domain evolution is developed based on the phase-field method, Mindlin’s strain gradient theory and finite element method. The strain and polarization distributions in an epitaxial ferroelectric PbTiO3 film are studied. The simulations show that enormous strain gradients are existed in dislocation-free film. Owing to flexoelectricity, the huge strain gradients have a great impact on polarization distribution.(1) The dislocation-free ferroelastically twinned films exhibit intrinsic elastic strain gradients of ～106 m-1 inside c domains and 107-108 m-1 at domain walls, sufficient to produce significant flexoelectric effect.(2) These gradients, observed in both the vertical and the horizontal direction, generate a horizontal flexoelectricity that forces the spontaneous polarization to rotate away from the normal direction in the c domains.(3) The magnitudes of remnant polarizations and coercive field decrease and eventually become zero as the horizontal flexoelectricity increases. A large horizontal flexoelectricity beyond a critical value may lead to the formation of an incommensurate state, which shows antiferroelectric-like double hysteresis loops under a high electric field.2. The effect of flexoelectric coupling on the polarization patterns and polarization switching of a two-dimensional ferroelectric thin film is investigated by using the proposed flexoelectric coupling theoretical framework. The simulations predict that flexoelectric coupling would induce failure-like problems. Different flexocoupling type leads to different failure-like phenomena.(1) The coupling of polarization with longitudinal strain gradient, f11 closely relates to the imprint-like phenomenon of ferroelectric films. But a sufficient large external electric field could eliminate the imprint-like phenomena of the ferroelectric film with larger flexocoupling strength.(2) The coupling of polarization with transverse strain gradient, f12, may result in the loss of ferroelectric properties and the formation of an incommensurate state displaying double hysteresis loops under a high electric field.(3) The coupling of polarization with shear strain gradient, f44, can induce the increasing of coercive field and imprint behaviorComparing the influence capability of f11, f12 and f44 on domains and polarization switching, we have f11> f12>f44 for ferroelectric film. The simulation results indicate that one can significantly improve the ferroelectric properties by reducing the flexoelectricity caused by f11, for example, reducing the longitudinal strain gradient by doping, or controlling the oxygen vacancies in film.3. The influence of local stress on the polarization patterns and polarization switching of a two-dimensional ferroelectric thin film is investigated by using the proposed theoretical framework for electromechanical coupling of flexoelectric effect. The evolution law of domain in ferroelectric film under a local mechanical force is obtained. Also the mechanism of effect of flexoelectricity on the mechanical switching process is obtained.(1) Under increasing mechanical stress, domain in ferroelectric film will experience a process of "beginning with the small angle rotation, then the appearance of 90° domain switching, and then the expansion of area of 90° rotation, and then the appearance of 180° domain switching, and followed by the expansion of area of 180° domain switching, and finally the steady state of domain structure".90° switching arises from the combined effect of the gradient of transverse strain in the thickness and horizontal direction as well as the gradient of out-of-plane strain in the horizontal direction, while 180° switching is attributed to the combined effect of the gradient of transverse strain and out-of-plane strain in the thickness direction.(2) The polarization switching of ferroelectric film under vertical compressive stress shows preference of downward polarization state, which results in a shift of the hysteresis loop, i.e. imprint phenomena. The offset bias of the hysteresis loop is proportional to strain gradient induced flexoelectric bias.(3) Under increasing mechanical stress, the hysteresis loops of ferroelectric film become narrower, and increasingly asymmetric which implies a more serious imprint failure.The study of effect of local stress on polarization patterns and switching of ferroelectric film provides guidelines on controlling the material properties with pure mechanical force, which might be crucial to the application of ferroelectric thin films.4. The effect of misfit strain at the interface on domain structure and switching of ferroelectric film under a local vertical compressive stress is investigated by using the proposed theoretical framework for electromechanical coupling of flexoelectric effect. The simulations show that misfit strain can be used as an effective tool for controlling the mechanical writing process.(1) The mechanical threshold stress for 180° domain switching in PbTiC3 film decreases when the misfit strain changed from -0.038 to 0.021.(2) Under the same mechanical force that far larger than the threshold stress, the size of the newly formed -x2 oriented c domain reduces when the misfit strain changed from -0.038 to 0.021.(3) Under the same mechanical force, the coercivity and remnant polarization of the film reduces when the misfit strain changed from -0.038 to 0.021.