| In recent years, with the development of microelectronics and communications, electronic component miniaturization and integration have become the main research direction of today's electronic technology. The donor-doped BaTiO3 semiconductor ceramic materials applied to positive temperature coefficient thermistor (PTCR) and the BaTiO3 Ferroelectric materials applied to multi-layer ceramic capacitors (MLCC) require miniaturization. The electrical properties of BaTiO3-based ceramics will change tremendously with the grain size decreasing to the nanometer size, which directly affects the device performance. In this dissertation, the structure, phase transition, dielectric properties and conductive properties of micro-nano ferroelectric BaTiO3-based ceramics was studied theoretically and quantitatively, based on electrodynamics theory and Landau thermodynamic theory. The main work and results are as follows:Considering the surface effects, a quantitative multishell structure model of the grain size effect of nano-BaTiO3 ceramics is proposed on the basis of Ginsburg-Landau-Devonshire thermodynamic theory. Then the size effect of the structure, the phase transition and the dielectric constant were studied. Further, introducing anisotropy energy, the size effects on the spontaneous polarization, Curie temperature, c/a ratio, electrocaloric, and dielectric properties of BaTiO3 ferroelectric nanoceramics were studied using the two-phase model. It is found that the surface energy increases and the ferroelectric-paraelectric phase boundary moves to the center of the grain with decreasing grain size. With further reducing grain size, ferroelectric phase disappears, leaving only one stable cubic structure. The surface effects lead to the multishell structure in BaTiO3 nanoparticles consisting of a surface paraelectric layer and inner ferroelectric core. The dielectric constant of BaTiO3 ceramics is reduced at room temperature with decreasing grain size. The three temperature dependent dielectric peaks are depressed and diffuse in the nano-BaTiO3 ceramics. The two low dielectric peaks move to higher temperatures, while the higher dielectric peak moves to lower temperature with decreasing grain size. The increased thickness of the surface cubic layer is one of the reasons for the decrease in dielectric constant with decreasing grain size.We have studied a one-dimensional ferroelectric domain model, calculated single-domain critical size and ferroelectric critical size, and analysised the dipole-dipole interaction. Further the three-dimensional ferroelectric domain models have been studied. By introducing a parameterηthe surface charge compensation factor, the long-range Coulomb interaction energy and the domain wall energy incorporated into the Landau-Ginzburg free-energy density, the relationship between ferroelectricity and grain size in nano-BaTiO3 ceramics can be calculated. Then the domain wall motion contribution to the dielectric constant is discussed. The results show that when the grain size reduces to the critical size, long-range Coulomb interaction weaking dramatically results in the instability of the ferroelectric phase. Taking into account the effects of domains, the room temperature dielectric constant of BaTiO3 particles shows a maximum value at some grain size above the ferroelectric critical size.On the basis of Poisson's equation, a three-dimension comprehensive and quantitative model for semiconductive BaTiO3 ceramics was first established, after the migration of the donors, acceptor, electrons and holes has important influence on the grain boundary effect were considered. By setting a differential equation of electron level, Energy band chart was obtained by solving the equation with Runge-Kutta method. The positive temperature coefficient effect of semiconductive BaTiO3 ceramics with different grain sizes and different donors and acceptors doping were computed quantitatively. It was found that the resistivity forms a U-shaped curve with the donor concentration increasing. The resistance jumping shows a maximum at a certain acceptor doping concentration and grain size.The non-linear Current-voltage characteristics of BaTiO3 semiconductor ceramics were studied by the method of tilted energy band and continuous medium seperately at one-dimensional case. The characteristics of the grain boundary were researched. The resistance jumping is reduced with increasing electric field applied; current and voltage relation follows Ohm's law below Curie temperature, and exhibits strong non-linear above Curie temperature; the non-linear coefficient shows a maximum value at temperature the resistivity reaches maximum and with grain size closed to depletion region width. Non-linear current-voltage characteristics indicate that the current-voltage curve is divided into three regions:The results pointed out that current and voltage characteristics divide into there regions:linear region before breakdown field, nonlinear region near breakdown field, and upturn region after breakdown field. As the applied voltage increases, the grain boundary barrier in the nonlinear zone drops drastically. As the grain size decreases, the breakdown field and nonlinear are both inhancedIn short, in this dissertation, our theoretical results about size effects of BaTiO3 ceramics are basically consistent with the experimental data, and explain reasonably the causes of size effect, predict structure and phase transition of nano BaTiO3 ceramics with a smaller grain size. Our theoretical results provide a theoretical basis for the ferroelectric BaTiO3 ceramics miniaturization and integration, and have guiding significance for further study on preparation of high-performance heat-sensitive materials and capacitor materials.
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