Macroscopic Theory of Charged Domain Walls in Ferroelectrics

This thesis consists of a theoretical analysis of charged domain walls in ferroelectrics based on Landau theory and the theory of semiconductors. First, the internal structure of a 180-degree charged domain wall is considered. It is shown that different regimes of screening and different dependences for width of charged domain walls on the temperature and parameters of the system are possible, depending on spontaneous polarization and concentration of carriers in the material. In typical perovskites the screening is provided by a degenerate electron gas in the nonlinear screening regime. The corresponding width of charged domain walls is about one order of magnitude larger than the width of neutral domain walls. The formation energies of "head-to-head" walls in an isolated sample under different regimes of screening are derived, neglecting the poling ability of the surface. In the nonlinear regimes of screening, this energy is equal to the energy necessary for the creation of electron-hole pairs in a sufficient amount to screen the spontaneous polarization, which is proportional to the band gap of the ferroelectric. It is shown that if the poling ability of the surface is large enough, either "head-to-head" or "tail-to-tail" configurations can be energetically favorable in comparison with the monodomain state of the ferroelectric. For the case of a surface with weak poling ability the existence of charged domain walls in bulk ferroelectrics is merely a result of domain-growth kinetics. It is shown that, at large enough sample thicknesses, a charged domain wall can be energetically favorable in comparison to other possible states: a multidomain state with antiparallel domains separated by neutral walls and a state with zero polarization. This size effect provides a possible explanation of the reason for experimental observation of 180-degree charged domain walls in bulk lead titanate but not in barium titanate. The results obtained for the case of an isolated ferroelectric sample are compared with the results for a sample with electrodes. It is shown that a charged domain wall in an electroded sample can either be metastable or stable, depending on the work function difference between the electrodes and the ferroelectric and the poling ability of the surface. The interaction of an electric field with charged domain walls in ferroelectrics is also addressed. A general expression for the force acting per unit area of the a charged domain wall carrying free charge is derived. It is shown that in proper ferroelectrics, the free charge carried by the wall dependeds on the size of the adjacent domains. As a result, it is found that the mobility of such a domain wall (with respect to the applied field) is sensitive to the parameters of the domain pattern containing this wall. The problem of the force acting on a planar charged 180° domain wall normal to the polarization direction in a periodic domain pattern in a proper ferroelectric is solved analytically. It is shown that, in the linear regime under small applied field, the forces acting on walls in such a pattern increase with decreasing wall spacing. The direction of the forces coincides with those for the case of the corresponding neutral walls. At the same time, for large enough wall spacings and large enough fields, these forces can be of the opposite sign. It is shown that the domain pattern under consideration is unstable in a defect-free ferroelectric. The poling of a crystal containing such pattern, stabilized by the pinning pressure, is also considered. It is shown that, except for a special situation, the presence of charge domain walls can make poling more difficult. It is demonstrated that the results obtained are also applicable to "zig-zag" walls under the condition that the "zig-zag" amplitude is much smaller than the domain wall spacing. A mechanism that leads to a strong enhancement of the dielectric and piezoelectric properties in ferroelectrics with increasing density of charged domain walls is proposed. It is demonstrated that an incomplete compensation of bound polarization charge at these walls creates a stable built-in depolarizing field across each domain leading to increased electromechanical response. This model clarifies a long-standing unexplained effect of domain wall density on macroscopic properties of domain engineered ferroelectrics. It is demonstrated that lead-free ferroelectrics like barium titanate with dense patterns of charged domain-walls are expected to have strongly enhanced piezoelectric properties, thus suggesting a new route to high-performance, lead-free ferroelectrics. The problem of the screening of ferroelectric bound charge on a ferroelectric-semiconductor interface is considered. It is shown that the screening ability of the interface can be drastically improved due to the presence of a built-in potential in the semiconductor, which depends on the electron affinities and surface state density and can be controlled by a judicious choice of materials.


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