**3.3.2 Spectra analysis**

The experimental spectra were fitted via a LTV.9 program (Kansy, 1996), in which a three-state trapping model was introduced into the source code (Krause-Rehberg & Leipner, 1999).

In the case of single crystal Pi-Kem, the spectra analysis reduces to only one lifetime component (τb = 117 ± 1 ps) associated with reasonable confidence to annihilation in bulk free defects. The quite high intensity of this component, (98.4 ± 1.6) %, appears as an unequivocal justification of the absence of discernable defects that are able to trap positrons (e.g., dislocations, negatively charged vacancies, neutral complexes). This result is also interpreted as a confirmation of the very low impurity content, which therefore justifies its choice as reference material for assessing the effects of both the microstructure achieved by the sintering process and the impurity content. For the sintered samples, three lifetime components were deduced. The shortest lifetime (τb = 122 ± 4 ps) was attributed to annihilation in the bulk free defects as it is very close to the one of the reference material, the intermediate (τg = 137 ± 2 ps) to trapping in defects within the grains and the longest (τgb = 397 ± 22 ps) to trapping in clusters located at grain boundaries.

Since Silicon is the main impurity in sintered samples, the possible defects felt by positrons within the grains are isolated vacancies ''' V and Al ''' '' Al Al (Si :V ) • , ''' ' Al Al (2Si :V ) • , ''' x Al Al (3Si :V ) • clusters. However, the neutral cluster ''' x Al Al (3Si :V ) • is more likely than the others due to the sintering temperatures and dwelling times (Lagerlöf & Grimes, 1998). In any case, the positron lifetime in all these defects is expected to have about the same value (τg = 137 ± 2 ps) because it is primarily determined by ''' V (Moya et al., 2003). The nature of clusters at Al grain boundaries is more difficult to ascertain because of the competition between all impurities for the segregation sites. However, one can speculate that the lifetime of about 400 ps (τgb = 397 ± 22 ps) reflects positron trapping in neutral or negatively charged clusters of charge compensating native vacancies ''' V and Al VO •• , which are induced by the impurities that have the strongest tendency for segregation, for instance SiO2, MgO and CaO. In particular, VO •• could stem from the dissolution of CaO (Eq. 5), which, incidentally displays by far the highest enrichment ratio, about 1300 (Dörre & Hübner, 1984).

Effects of the Microstructure Induced by Sintering on the Dielectric Properties of Alumina 561

Furthermore, the injection time, tinj (ranging from 10-3 to 1 s), is adjusted by the Electron Beam Blanking Unit "EBBU" using a function generator, allowing the turns off on the spot over the specimen surface with no electron track outside the investigated area when the

The metallic sample holder is attached to a cooling-heating stage (temperature range 93 − 673 K). Hence, in situ thermal sample cleaning under vacuum (at T = 663 K during 180 minutes) and sample characterization at different temperatures are possible. Prior to electron irradiations, after the cooling that follows the cleaning step, the sample is held during 180 minutes at the testing temperature, so that the thermal equilibrium between the

The ICM method is based on the measurement of the current Iind, produced by the variation of the induced charges Qind (in the sample holder) due to the trapped charges in the sample Qt (Liebault et al., 2001, 2003; Song et al., 1996). Since the influence coefficient in our experimental set up is close to one (Zarbout et al., 2008), the amount of the net trapped

The improvement brought to the ICM method consists in the concurrent measurement of Iind and the total secondary electron current Iσ due to the sole electrons emitted by the sample. For this purpose, as shown in Fig. 3, the SEM is specially equipped with a secondary electron low-noise collector located under the objective lens just above the sample. A biased voltage of 100 V is applied to it in order to collect all the electrons escaping from the sample surface.

During charge injection, the currents, Iσ and Iind, are simultaneously amplified (Keithley 428) and observed on an oscilloscope (HP 54600B) where the material response is displayed after a short lag time. The primary current beam Ip (which is adjusted in a Faraday cage) and the current Iσ are always positive whereas Iind can be positive or negative depending on the Secondary Electron Emission "SEE" yield σ, which is equal to Iσ/Ip. Then if Iσ is higher than Ip (σ > 1), the sample charges positively and Iind is negative. In the other case (σ < 1), the sample charges negatively and Iind is positive. The general variation of σ with Ep is shown in Fig. 4.

Fig. 4. Schematic evolution of the SEE yield σ with primary beam energy Ep for uncharged

**EpI EpII Ep** 

t

t ind ind <sup>0</sup> Q (t) Q (t) I (t) dt =− =− (7)

beam is blanked.

charges is given by:

insulator materials.

**σ**

**1** 

sample and the metallic holder is approached.

**4.2 The improved Induced Current Measurement method** 
