Ferroelectricity, Photorefractive effect, and Perovskite

Ferroelectricity is a spontaneous electric polarization of a material that can be reversed by the application of an external electric field, upon cooling the material below a certain temperature called the Curie temperature. Ferroelectric ceramics were born in the early 1940s with the discovery of the phenomenon of ferroelectricity with high dielectric constant in barium titanate (BaTiO3). Ferroelectric materials have long been used in bulk forms in variety of fields such as ceramic capacitors.

Furthermore, ferroelectric materials in the forms of thin films are essential for variety of devices such as ferroelectric random access memory (FRAM), infrared pyroelectric sensors, transistors, microwave electronics, electro-optic modulators, and in other integrated devices. Among the many classes of ferroelectric materials, the perovskite compounds such as lead lanthanum titanate (PLT) [1], lead zirconate titanate (PZT) [2], lead titanate (PTO) [3], and barium titanate (BTO) [4] have been the most intensively investigated.

Because of the beneficial properties of light such as wide bandwidth and high speed switching, photonic devices have the trend to replace electronic ones when they are available. Photorefractive materials particularly offer many fascinating

possibilities for applications in the development of communication networks and volume holographic memories [5]. The photorefractive effect is a phenomenon whereby the local refraction index is modified by spatial variations of the light intensity. When two coherent rays interfere with each other in a photorefractive material to forms a spatially varying pattern of illumination, charge carriers will be produced in the material and migrate owing to drift or diffusion and space charge separation effects. The resulting electric field from charge separation induces a refractive index change via the electro-optic effect. Owing to the large electro-optic effect present in perovskite materials such as barium titanate, the perovskite compounds are an extremely important group of not only ferroelectric but also photorefractive materials.

Perovskites are a large family of crystalline ceramics that derive their name from a

specific mineral known as perovskite. The parent material, perovskite, was first described in the 1830’s by a geologist Gustav Rove, who named it after the famous Russian mineralogist Count Lev Aleksevich von Perovski. The general formula of perovskite oxides is ABO3 (see Fig. 1.1), which is composed of three distinct chemical elements in the ratio of 1:1:3. Ideal oxide perovskite of the aristotype assumes cubic group Pm3m with atom positions of cation “A” at (1/2, 1/2, 1/2) of Wyckoff position 1a, cation “B” at (0, 0, 0) of Wyckoff position 1b, and anions “O” at

(1/2, 1/2, 0), (1/2, 0, 1/2) and (0, 1/2, 1/2) of Wyckoff position 3d. The cation “A” is usually larger than vation “B” in the perovskite oxide structure and the “A” and “B”

sites are normally occupied by “+2” and “+4” ions, respectively. Conventionally, two types of unit cells with (1) A-cation and (2) B-cation located at center are adopt and often termed the A-cell and B-cell. For type A-cell, the corner-sharing BO6

octahedra where A-cation is located in the cubo- octahedral interstice of coordination number CN=12 is easily visualized. On the other hand, B-cation of CN=6, forming BO6 octahedron with six oxygen ions, is situated at the octahedral interstice. The configurations of two types of unit cells are illustrated schematically in Fig. 1.1(a) for A-cell type and Fig. 1.1(b) for B-cell type [Galasso 1970]. B-cell type unit cell has adopted recently since it clearly represents the BO6 octahedra from whose distortion the ferroelectricity in t-BaTiO3 and other ferroic properties, e.g. ferroelasticity, ferromagnetism are derived. Take cubic-ABO3 (Pm3 m), the 3C-polytype, to exemplify how perovskite structure is constructed is illustrated schematically in Fig.

1.1(c). Its crystal structure designated to E21 using Strukturbreicht symbols may be derived in the way from either α-ReO3 (D09), α-Cu3Au (L12) or CsCl (B2).

When A²⁺ is inserted into D09 at eight corner sites, the structure becomes perovskite B-cell type. Similarly, removing “A” from B-cell type, the structure becomes ReO3

with all A-site vacant. Removing “B” from B-site of B-cell type, the crystal

structure becomes ordered fcc α-Cu3Au (L12). And then, by removing O^2- from B-cell type, the structure perovskite is reduced to ordered bcc CsCl (B2). The atomic structure of perovskite is very sensitive to the alteration in the temperature of Figure 1.1: Schematic illustrations for A-cell and B-cell types of unit cell for cubic-ABO3 and possible alternative ways to derive cubic-ABO3 structure. [Galasso 1970].

the crystal. As the temperature changes, the crystallographic dimensions change and the crystal structures of ABO3 include cubic, tetragonal, orthorhombic, and rhombohedral due to distortion of the BO6 octahedra[6]. According to Landau free energy [Putnis 1992], the phase transition is discontinuous first-order in nature. All of the ferroelectric materials have a transition temperature called the Curie temperature (Tc). When the crystal temperature goes above the Curie temperature, T

> Tc, the elongated crystallographic dimensions allow the B cation to sit at the center of BO6 skeleton. In this case, the crystal structure is cubic with no spontaneous or permanent electric dipole. Therefore, the crystal doesn’t exhibit ferroelectricity.

While for T < Tc, the shrinkage of the octahedral lets the B cation be more energized to move farther from the center of the original octahedron. Shifting of the B cation causes the structure to alter, thus to induce spontaneous electric dipole. As a result, the distorted octahedral are coupled together, and a very large spontaneous polarization can be achieved. This large spontaneous polarization will lead to a large dielectric constant highly sensitive to temperature. It possesses ferroelectricity in this non-cubic crystal structure and is called ferroelectric phase. A ferroelectric crystal undergoes a phase transition from a non-ferroelectric phase to a ferroelectric phase on decreasing the temperature through the Curie point. The structure of perovskite is also sensitive to A cation substitutions [7-9] and the behavior is similar

to the alteration in the temperature of the crystal.