Experimental and theoretical characterization of ferroelectric bismuth titanate, Bi(4)Ti(3)O(12), thin films

Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Electrical Engineering and Computer Science


Prasanta K. Ghosh


permittivity, coercive field, refractive index, scattering, electromagnetism

Subject Categories

Materials Science and Engineering


This thesis is an investigation of fabrication, experimental characterization of ferroelectric bismuth titanate (Bi$\sb4$ Ti$\sb3$ O$\sb{12}$) and theoretical modeling of multicomponent dielectric thin films. Bismuth titanate thin films have been prepared on different substrates by the ion-beam sputtering technique using a Bi(bismuth)-rich Bi$\sb4$Ti$\sb3$O$\sb{12}$ ceramic target. Films were deposited with the substrate temperature ranging from 320$\sp\circ$C to 550$\sp\circ$C and by employing several sputtering gas mixtures. Experimental results show that dielectric and ferroelectric properties of the deposited films strongly depend on the deposition parameters such as target composition, substrate temperature, composition of the sputtering gas mixture and substrate type. Results also indicate that films deposited using O$\sb2$ + Ar (2:3 volume ratio) gas mixture, at 450$\sp\circ$C substrate temperature, have dielectric properties comparable to that of single crystal bismuth titanate. Also, the ferroelectric polarization of as-deposited thin films are improved significantly if the films are annealed under proper conditions. Thin films which are annealed at 600$\sp\circ$C for 30min in an oxygen atmosphere show ferroelectric polarization values comparable to the value of single crystal.

In the theoretical part of this investigation, several models were developed to relate the microstructure of the polycrystalline thin film to some of its properties, such as effective permittivity, ferroelectric polarization, coercive field and refractive index. The permitivity of bismuth titanate thin films was first modeled using an effective medium method which accounts for the shape of grains, distribution of grains, grain boundaries, and the permittivity profile of each grain. In this model, the effect of grain boundaries and the actual shape of the grains were included by replacing each grain by a layered dielectric particle. The polarization of each composite particle was then calculated using both analytical and numerical methods. In the numerical method, an expression for the polarization of each particle, using boundary integral formulation, was developed. Then, the derived integral equations were approximated and solved using the method of moments (MOM). Next, a relatively large ferroelectric coercive field and slightly lower ferroelectric polarization of the bismuth titanate thin films (compared with a single crystal) were theoretically modeled using a simple multilayer capacitor structure.

Finally, a model was developed to characterize the optical transmission and reflection from the polycrytalline thin films using a method which is based on electromagnetic scattering from a doubly periodic array of nonhomogeneous dielectric unit cells. Each cell contains major features of the polycrystalline thin film. A full-wave electromagnetic formulation has been developed in order to find the electric field both within and without the thin film. Using Floquent's theorem the solution of the problem was narrowed down to that of a single unit cell. To solve the problem in each unit cell a numerical method based on hybrid FEM and the boundary element method has been employed. The FEM solution for the problem was then developed using first-order tetrahedral edge elements.


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