**1. Introduction**

552 Sintering of Ceramics – New Emerging Techniques

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polycrystalline alumina ceramics by electrophoretic deposition in a strong

The dielectric properties of undoped corundum, α-alumina, of different kinds (single crystal or polycrystalline obtained by solid state sintering) have been the subject of numerous studies concerning, in particular, the breakdown strength and the charging behavior (Haddour et al., 2009; Liebault et al., 2001; Si Ahmed et al., 2005; Suharyanto et al., 2006; Thome et al., 2004; Touzin et al., 2010; Zarbout et al., 2008, 2010). The common feature pointed out by most of these investigations is the conspicuous role played by the microstructure and the impurities. It is also established that the microstructure induced by the sintering process (grain size and porosity) goes concomitantly along with impurities segregation at grain boundaries and/or the development of defects in the lattice (Chiang et al., 1996; Gavrilov et al., 1999; Lagerlöf & Grimes, 1998; Moya et al., 2003). To some extent, for a given composition, these evolutions can be governed by the sintering conditions, for instance the firing cycle in the case of solid state sintering (Chiang et al., 1996).

The breakdown strength is a key parameter for the reliability of dielectrics and in particular of microelectronic insulator components. This parameter is intimately linked to the charging properties as breakdown originates from the enhancement of the density of trapped charges, which stems from the competition between charge trapping and conduction (Blaise & Le Gressus, 1991; Le Gressus et al., 1991; Liebault et al., 2001; Haddour et al., 2009). The charges can be either generated by irradiation or injected through interfaces via an applied voltage. Charge trapping can occur around intrinsic point defects, defects induced by the dissolution of impurities, defects associated with grain boundaries interfaces and dislocations (Kolk & Heasell, 1980). We must also keep in mind that trapping in insulators gives rise to polarization and lattice deformation allowing energy accumulation within the material (Blaise & Le Gressus, 1991; Le Gressus et al., 1991; Stoneham, 1997). As a result, if some critical density of trapped charges (or some critical electric field) is reached, external stresses (thermal, electrical or mechanical) can trigger a collective relaxation process corresponding

Effects of the Microstructure Induced by Sintering on the Dielectric Properties of Alumina 555

Simulation results show that the formation energies of intrinsic point defects in α-alumina are relatively high (Atkinson et al., 2003). They are estimated respectively for Schottky

Extrinsic point defects are entailed by the dissolution of foreign elements. The solubility of an impurity depends mainly on its cation size (generally, small size elements exhibit high solubility). The charge compensating defects accompanying the dissolution of aliovalent impurities (i.e, defects that are required for ensuring the electrical neutrality) are determined not only by their valence (charge) but also by their position (interstitial or substitutional) in

In the case of a cation (M) greater in valence than the host cation (Al3+), the dissolution mode in substitutional position is most likely the cationic vacancy compensation mechanism (Atkinson et al., 2003). Accordingly, for tetravalent cations, in MO2 (such as SiO2 or TiO2),

x '''

This compensation by a cationic vacancy is somewhat corroborated by experiments involving solution of Ti4+ in α-Al2O3 (Mohapatra & Kröger, 1977; Rasmussen & Kingery,

For divalent cations, in MO (such as MgO or CaO), the anionic vacancy compensation of

The interstitial dissolution of monovalent elements, in M2O (such as Na2O or Ag2O), can be governed by a host cationic vacancy compensation mechanism. However, a selfcompensating dissolution mode, involving both interstitial and substitutional positions of

In the case of isovalent elements, in M2O3 (such as Cr2O3 or Y2O3), the dissolution will not create charged defects in the lattice but can induce a stress field due to the misfit arising

As previously pointed out, the formation energies of intrinsic defects are very high in α-alumina. Consequently, a few ppm of impurities will make the concentrations of extrinsic defects higher than those of the intrinsic ones, even at temperatures near the melting point

Isolated point defects can be associated, at appropriate temperature, to form neutral or charged defect clusters. This association leads to a substantial reduction in the solution

xx '

2 Al Al Al 2 3 3 MO 4 Al 3 M V 2 Al O • + ⇔ ++ (4)

Al O Al O 2 3 2 MO 2 Al O 2 M V Al O •• + +⇔ ++ (5)

defects, cation Frenkel and anion Frenkel at 5.15, 5.54 and 7.22 eV.

substitutional ' M , is suggested (Atkinson et al., 2003): Al

M, is also expected (Gontier-Moya et al., 2001).

from the difference in cation radii.

**2.1.3 Point defects association** 

(Kröger, 1984; Lagerlöf & Grimes, 1998).

**2.1.2 Extrinsic point defects** 

the host lattice.

1970).

the dissolution reaction is:

x '' O VO O Oi ⇔ + •• (3)

to a release of stored energy. If the amount of this energy is sufficient, breakdown could set in causing irreversible damages of the material (Blaise & Le Gressus, 1991; Moya & Blaise, 1998; Stoneham, 1997).

It appears that an improvement of the breakdown strength would require that conduction, which tends to decrease density of trapped charges, be favored to some extent without, however, substantially altering the insulating properties. Conduction will also be referred as the ability of the material to spread charges. Therefore, the control of the competition between charge accumulation (trapping) and spreading (conduction), via the fabrication processes, is a key technological concern. The foregoing arguments motivate the need to develop methods for the characterization of charge conduction (conversely charge trapping) and underscore furthermore the importance of controlling the microstructural development during sintering of ceramic insulators. The purpose of this chapter is to provide the physical background for a more comprehensive understanding of the effects of the microstructure (and the various defects) induced by the sintering conditions on charge conduction in alumina. This understanding, which could be generalized to other ceramics, appears as prerequisite for the fabrication of insulators of improved dielectric breakdown strength.
