Dielectric permittivity perovskites

The compositions of most dielectric materials used for ceramic capacitors are based on ferroelectric barium titanate. As discussed in detail in Pragraph 1.3 the permittivity of ferroelectric perovskites shows marked changes with temperature, particularly close to the phase transition. From the device point of view a high dielectric permittivity with stable properties over a wide temperature range is required. There are various specifications which have to be fulfilled (e.g. X7R AC/C(T = 25°C) < 0.15 in a range between -55°C and 125°C). 

The first ingredient can be taken for granted, since rl behavior in these materials does not occur in the absence of disorder. The third ingredient is also an experimental fact in that RL behavior occurs in ABO3 oxides with very large dielectric permittivity. The second ingredient is manifested in many experimental observations common to all perovskite rls, as will be discussed later. 

Isovalent substitutions where Sr " and Ca substitute for Pb in the perovskite structure. The Sr substitution lowers the Curie temperature (ferroelectric-paraelec-tric transition temperature), thus raising the room temperature dielectric permittivity. 

The sharpening of the dielectric permittivity peak that occurs between Figure 6.18a and b can be considered to be part of a continuum leading to classical ferroelectric behaviour (Figure 6.18c). This trend is often clear when solid solutions of perovskite phases are examined. For exanple, solid solutions between BaTiOj and the relaxor ferroelectric BiFeOj show an evolution from the classical sharp peak for BaTiOj to a characteristic relaxor peak with a sharp low-temperature margin as the BiFeOj content increases until a broad relaxor peak appears at highest concentrations. 

In conclusion, complex perovskite relaxor ceramics are characterized by a very diffuse range of the ferroelectric-paraelectric OD phase transition, owing to nano-scopic compositional fluctuations. The minimum domain size that stiU sustains cooperative phenomena leading to ferroelectric behavior is the so-called Kiinzig region (Kanzig, 1951), and is on the order of 10 to lOOnm in PMN. In contrast to normal ferroelectric ceramics, relaxor ceramics show a frequency dependence of the dielectric permittivity as well as the dielectric loss tangent, which presumably is caused by the locally disordered structure that creates shallow, multipotential wells. 

Figure 8.20a shows the temperature variation of the dielectric permittivity of undoped BNT samples (curves a-c), as well as of BNT doped with 1 at% La (curve d) and 2at% La (curve e), aU sintered at 1000 C. For this, the measurement frequency was lOkHz. The dielectric permittivihes of the undoped samples varied approximately Hnearly with temperature, and hence followed the Curie-Weiss law. The low values of dielectric permittivity, and their near-linear variation with temperature, could be assigned to the deviation from the ferroelectric perovskite composihon, and the increasing presence of paraelectric contributions from the decomposition products that cause an increase in electrical conductivity. On the other hand, in concurrence with the diffuse OD phase transition from the antiferroelectric to the paraelectric phase at Tq, the dielectric permittivity of the La-doped samples reached a maximum at 350 °C. The dielectric permittivity of BNT doped with lanthanum was more than twice that of undoped BNT, and was larger for lat% La (-2300) than for 2at% La (-2000). The lower value at a higher La concentration was presumed to be related to the superposition of an increasing deformation of the rhombohedral lattice of BNT towards a (pseudo)... 

However, not only the crystal structure of the film is affected by the stresses of the film, but also electrical properties are altered. Figure 27.17 shows the variation of the dielectric permittivity with temperature for the films of Table 27.5. A change in the transition temperature of the perovskite film is observed as tensile stresses are increased [54]. 

Another important group of oxide materials with a very low electrical conductivity is the oxide dielectrics. A number of these are based upon the perovskites, MXO3 or M0 X02. The archetype of these materials is BaTiC>3, which has a high dielectric constant, or relative permittivity to vacuum, the value at room temperature being 1600, and commercial use is made of the isostructural PbTi(>3 and ZrTi03 which form solid solutions, the PZT dielectrics. These materials lose their dielectric properties as the temperature... 

In contrast to dielectric losses permittivity is not, in general, sensitive to small amounts of impurities and for homogeneous dielectrics values can be calculated as described in Section 2.7.1, and the various mixture rules allow good estimates to be made for multiphase dielectrics. For Ba- and Sr-based dielectrics having the perovskite structure the variation of permittivity with temperature, which determines rf (see Eq. (5.37)), can be correlated with the tolerance factor t (see Section 2.7.3) [13] providing guidance for tailoring ceramics to have xf = 0. 

Technically useful properties of such perovskite ceramics are their high permittivities (relative dielectric constants), the semiconductor properties of certain chemical compositions and their piezoelectric properties. 

Perovskites are vital circuit elements for many electronic purposes, from simple capacitors to dielectric resonators used in mobile phones, satellite communications, TV broadcasting and so on. The dielectric properties of bulk perovskites arise from the presence of polarisable constituents in the crystal. These include cation displacements, octahedral tilting and distortions as well as any defects present, such as grain boundaries and various point defects. The relative permittivity is the basic parameter describing a dielectric. In a static electric field this is written as (Table 6.1) but in varying electric fields is replaced by the complex relative permittivity, - is", which is a function of the frequency of the apphed electric field. 

Figure 6.3 Dielectric properties of ceramic perovskites (a) the relative permittivity and (b) the loss tangent of Stg EUgg SnO g and StgggEUgggSnOg gg as a function of temperature (c) the relative permittivity of the hexagonal 8H perovskite BagLigWJD g as a function of sintering temperature...

Chapterb- The perovskite family of materials is of considerable technological importance for its excellent temperature stable microwave properties for dielectric resonator based filters, oscillators and antenna applications. In this chapter author review the preparation, characterization and the microwave dielectric properties of Ca[(Lii/3A2/3)i-xMx]03.5 [A=Nb, Ta and M=Ti, Zr, Sn] dielectric ceramics. This family of perovskite materials shows relative permittivity in the range 20 to 56 with a quality factor up to 45000 GHz and temperature coefficient of resonant frequency (xf) in the range from -21 to +83 ppm/°C. The Xf can be tailored by adjusting the titanium content. The sintering temperature can be lowered below 950 °C to suit LTCC by the addition of low melting glasses. 

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