**6.1 Charge spreading in reference materials (single crystals)**

568 Sintering of Ceramics – New Emerging Techniques

From Eq. 14, we can associate to Q∞(T) the amount of charges Qf(T) that still remain in the irradiated volume, Q∞(T) = Qst – Qf(T). Therefore, the remaining quantity of charges Ql(tp, T)

> ( ) <sup>p</sup> l p st f f

=− − +

Q (t , T) Q Q (T) exp Q (T) (T)

The first term in this expression, which corresponds to the curve of the pause stage in Fig. 8, expresses charge decay under the internal electric field. Generally, the time constant τr can be set equal to ε/γ, where ε is the dielectric permittivity (ε = εrε0) and γ is the electric conductivity of the material (Adamiak, 2003; Cazaux, 2004). The value of τr deduced from Fig. 9 is 82 s giving a conductivity of about 10-14 Ω-1cm-1 which can be expected for this material, in agreement with the experimental value of the resistivity obtained for this

The asymptotic value Q∞ at T = 473 K is reached after only 300 s (Fig. 9). Therefore, one can anticipate that at temperatures within the range of interest (300 − 663 K), the condition for

The measured value of Q∞(T) is the result of detrapping of charges and their subsequent transport under the internal electric field. During this transport, a fraction of the detrapped charges can undergo a retrapping in deeper traps in the irradiated volume and eventually a recombination. The overall effect is a variation of charge distribution in the volume of interest, which affects the electric field. Consequently, since in the considered temperature range the experimental results do not reveal any significant dependence of Qst on temperature, the ratio R(T) = Q∞(T)/Qst can be expressed in terms of the measured currents:

inj

t

 <sup>−</sup> = = <sup>−</sup> 

I (t)dt Q (T) R(T) <sup>Q</sup> I (t)dt

∞

irradiated volume, also characterizes the extent of discharging.

could shed some light on the discharge process.

**to trap or spread charges** 

inj

This experimental parameter, which measures the fraction of charge removed from the

The ratio R(T), which can vary between 0 and 1, corresponds to an evolution from either the dominance of stable charge trapping (low values of R) or of charge spreading (high values of R, with R = 1 for a complete recovery of the uncharged state). The rate at which charges are detrapped depends usually on an attempt escape frequency and an activation energy linked to the trap depth. As a result, one can expect that, the variation of R with temperature

**6. Effect of microstructure induced by sintering on the ability of a dielectric** 

As it will be pointed out, trapping and spreading are intimately linked to the microstructure and defects. Sintering not only leads to the creation of new interfaces but also to important

phenomena such as segregation at grain boundaries and defects association.

<sup>t</sup> st ind <sup>0</sup> first injection

ind <sup>0</sup> second injection

reaching the asymptotic value Q∞(T) are met for the chosen pause time Δt of 900 s.

r t

τ

(15)

(16)

can be obtained from Eqs. 13 and 14:

sample in our laboratory (1.2 1014 Ωcm).

The results of the two types of single crystals are reported in Fig. 10. The values of R in both Pi-Kem and RSA are zero up to 473 K, indicating a perfect stable trapping behavior. Above 473 K, R increases but the enhancement is significant only for Pi-Kem.

Fig. 10. Fraction R of charges removed from the irradiated volume as a function of temperature for the two types of single crystals (Pi-Kem and RSA samples).

In order to interpret these behaviors we can consider the following results:


As mentioned in paragraph 2, the dissolution of silicon into Al2O3, is expected to be compensated by a negatively charged cationic vacancy, ''' VAl (Eq. 4). In this context, the positively charged substitutional silicon Al Si• may act as electron trapping site while the cationic vacancy ''' VAl as hole trap. Upon trapping one electron during irradiation, Al Si• induces a donor level associated to Al Si<sup>×</sup> , which is estimated at 1.59 eV below the edge of the conduction band (Kröger, 1984). With regard to ''' VAl , hole trapping will give an acceptor level (associated to '' VAl ) located at 1.5 eV above the valence band (Kröger, 1984).

Effects of the Microstructure Induced by Sintering on the Dielectric Properties of Alumina 571

Fig. 11. Fraction R of charges removed from the irradiated volume as function of temperature for pure polycrystalline alumina samples of different grain diameters d.

likely responsible for the stable trapping in the bulk.

less efficient in trapping charges.

This agrees with the experimental facts:

large grains is substantially lower.

In the RSA single crystal and pure polycrystalline alumina, silicon is the dominant impurity. Therefore, one can suggest that atomic disorder introduced by grain boundaries gives rise to states closer to the edge of the conduction band than those of Al Si<sup>×</sup> and ''' V , which are most Al

For fine grains (d = 1.7 µm), R spans from 0 (at 300 K) to 45 % (at 663 K) whereas for large grains (d = 4.5 µm) R varies between 15 % (at 300 K) to near complete discharge (about 100 %) above 473 K. One would expect the behaviour of polycrystalline material to tend towards that of single crystals when the grain size increases. However, the reverse is clearly seen. The explanation of this apparent contradiction can be found by considering the distribution of impurities in the polycrystalline samples. We have to bear in mind that the microstructural evolution during the sintering process, with in particular the achievement of a given grain size, is concomitant with segregation to grain boundaries of impurities, which corresponds to a purification of the grain (interpreted as an internal gettering). In fact, the large grain size of 4.5 µm has required both a higher sintering temperature and a longer dwelling time than those used to attain 1.7 µm. Hence, the enhancement of gettering effect in large grain sample may have lowered the concentration of deep traps (such as Al Si<sup>×</sup> and ''' V ) in the bulk. In this assumption, the impurities Al (mainly Si) segregates at grain boundaries where they can be associated to other defects to form clusters, as suggested by positron measurements (cf. paragraph 3), which may be

i. The R values are always higher for the larger grain (for example at 573 K, R = 100 % for d = 4.5 µm and only 22 % for d = 1.7 µm). This means that the density of deep traps in

Accordingly, with such relatively deep trap levels, it is very unlikely that detrapping of charge carriers occurs at the temperatures of our experiments. However, the contribution of the other impurities, such as the ones of smaller valence than the host, cannot be ruled out because trapping depends not only on the defect concentration but also on their specific trapping properties such as the capture cross section of traps which is mainly determined by their charge state. Indeed, the cathodoluminescence spectra have also detected (Jardin et al., 1995) in similar RSA samples (which like ours were annealed at 1773 K during 4 hours) the deep centers Fcation, such as <sup>x</sup> F with an energy level at 4 eV below the edge of the Mg conduction band (Kröger, 1984).

We alternatively tried to shed some more light on the trapping behaviors of single crystals by using the Scanning Electron Microscope Mirror Effect "SEMME" method, which requires net negative charging (Liebault et al., 2003; Vallayer et al. 1999). Thus, we performed electron injection with 30 keV (energy greater than EpII) focused beam and an injected dose of 300 pC followed by a scanning of the sample surface, with low electron beam energy (some hundred of eV). In RSA samples we find a mirror image at 300 K, which remains stable up to about 663 K. In contrast, in Pi-Kem materials no mirror image formation was achievable even at 300 K.

It must be reminded that in the SEMME method the observation of a mirror image, immediately after irradiation, is due to the presence of a sufficiently high concentration of stable traps for electrons. Thus, no mirror image is observed in Pi-Kem samples as they do not contain enough traps. The fact that in RSA the mirror is maintained at high temperatures confirms the presence of deep traps and somewhat supports the assumption, discussed above in point (ii), that stable trapping can be assigned to the defects induced by the dissolution of the dominant silicon impurity.

In contrast with SEMME method, the ICM method can give, during charging, an induced current whatever the trap concentration is. So, the parameter R gives indications on the stability of trapped charges, after a pause Δt, independently of the trap concentration. As a result, at temperatures lower than 573 K, for which trapped charges are stable in RSA and Pi-Kem samples, the R values are very low (R = 0 at room temperature for both kinds of single crystals). Above 573 K, RSA samples have R values lower than those of Pi-Kem. This is a supplementary indication of the existence of deeper traps in RSA, which is one of the requirements for the mirror image formation at high temperatures in the SEMME method.

#### **6.2 Charge spreading in sintered alumina of various microstructures and impurities**

### **6.2.1 Charge spreading in pure sintered alumina**

The values of R(T) for the three polycrystalline alumina pure samples as function of temperature are shown in Fig. 11. The comparison with single crystals (R close to zero up to 573 K) indicates that the presence of grain boundaries makes trapping less stable in polycrystalline alumina (R is substantially above zero). This interpretation agrees with the fact that, with SEMME method, we do not detect any mirror image in the polycrystalline samples.

Accordingly, with such relatively deep trap levels, it is very unlikely that detrapping of charge carriers occurs at the temperatures of our experiments. However, the contribution of the other impurities, such as the ones of smaller valence than the host, cannot be ruled out because trapping depends not only on the defect concentration but also on their specific trapping properties such as the capture cross section of traps which is mainly determined by their charge state. Indeed, the cathodoluminescence spectra have also detected (Jardin et al., 1995) in similar RSA samples (which like ours were annealed at 1773 K during 4 hours) the deep centers Fcation, such as <sup>x</sup> F with an energy level at 4 eV below the edge of the Mg

We alternatively tried to shed some more light on the trapping behaviors of single crystals by using the Scanning Electron Microscope Mirror Effect "SEMME" method, which requires net negative charging (Liebault et al., 2003; Vallayer et al. 1999). Thus, we performed electron injection with 30 keV (energy greater than EpII) focused beam and an injected dose of 300 pC followed by a scanning of the sample surface, with low electron beam energy (some hundred of eV). In RSA samples we find a mirror image at 300 K, which remains stable up to about 663 K. In contrast, in Pi-Kem materials no mirror image formation was

It must be reminded that in the SEMME method the observation of a mirror image, immediately after irradiation, is due to the presence of a sufficiently high concentration of stable traps for electrons. Thus, no mirror image is observed in Pi-Kem samples as they do not contain enough traps. The fact that in RSA the mirror is maintained at high temperatures confirms the presence of deep traps and somewhat supports the assumption, discussed above in point (ii), that stable trapping can be assigned to the defects induced by

In contrast with SEMME method, the ICM method can give, during charging, an induced current whatever the trap concentration is. So, the parameter R gives indications on the stability of trapped charges, after a pause Δt, independently of the trap concentration. As a result, at temperatures lower than 573 K, for which trapped charges are stable in RSA and Pi-Kem samples, the R values are very low (R = 0 at room temperature for both kinds of single crystals). Above 573 K, RSA samples have R values lower than those of Pi-Kem. This is a supplementary indication of the existence of deeper traps in RSA, which is one of the requirements for the mirror image formation at high temperatures in the SEMME

**6.2 Charge spreading in sintered alumina of various microstructures and impurities** 

The values of R(T) for the three polycrystalline alumina pure samples as function of temperature are shown in Fig. 11. The comparison with single crystals (R close to zero up to 573 K) indicates that the presence of grain boundaries makes trapping less stable in polycrystalline alumina (R is substantially above zero). This interpretation agrees with the fact that, with SEMME method, we do not detect any mirror image in the polycrystalline

conduction band (Kröger, 1984).

achievable even at 300 K.

method.

samples.

the dissolution of the dominant silicon impurity.

**6.2.1 Charge spreading in pure sintered alumina** 

Fig. 11. Fraction R of charges removed from the irradiated volume as function of temperature for pure polycrystalline alumina samples of different grain diameters d.

In the RSA single crystal and pure polycrystalline alumina, silicon is the dominant impurity. Therefore, one can suggest that atomic disorder introduced by grain boundaries gives rise to states closer to the edge of the conduction band than those of Al Si<sup>×</sup> and ''' V , which are most Al likely responsible for the stable trapping in the bulk.

For fine grains (d = 1.7 µm), R spans from 0 (at 300 K) to 45 % (at 663 K) whereas for large grains (d = 4.5 µm) R varies between 15 % (at 300 K) to near complete discharge (about 100 %) above 473 K. One would expect the behaviour of polycrystalline material to tend towards that of single crystals when the grain size increases. However, the reverse is clearly seen. The explanation of this apparent contradiction can be found by considering the distribution of impurities in the polycrystalline samples. We have to bear in mind that the microstructural evolution during the sintering process, with in particular the achievement of a given grain size, is concomitant with segregation to grain boundaries of impurities, which corresponds to a purification of the grain (interpreted as an internal gettering). In fact, the large grain size of 4.5 µm has required both a higher sintering temperature and a longer dwelling time than those used to attain 1.7 µm. Hence, the enhancement of gettering effect in large grain sample may have lowered the concentration of deep traps (such as Al Si<sup>×</sup> and ''' V ) in the bulk. In this assumption, the impurities Al (mainly Si) segregates at grain boundaries where they can be associated to other defects to form clusters, as suggested by positron measurements (cf. paragraph 3), which may be less efficient in trapping charges.

This agrees with the experimental facts:

i. The R values are always higher for the larger grain (for example at 573 K, R = 100 % for d = 4.5 µm and only 22 % for d = 1.7 µm). This means that the density of deep traps in large grains is substantially lower.

Effects of the Microstructure Induced by Sintering on the Dielectric Properties of Alumina 573

might be less efficient due to a possible saturation of grain boundaries. In addition, interactions between the various defects generated by the foreign elements are expected (Gavrilov et al., 1999). It must be pointed out that the great variety of impurities and their substantial content make difficult the interpretation of the results due to a possible interference of co-segregation, which is difficult to predict when more than three elements are involved. The actual situation is even more complicated by the fact that segregation leads to the creation of a space charge at grain boundaries (Tiku & Kröger, 1980) with a sign that depends on the segregated impurities, which may interfere with the charging process.

Fig. 13. Fraction R of charges removed from the irradiated volume as a function of temperature for impure polycrystalline alumina samples of different grain diameters d.

trapping sites located within the grain boundary.

results of micrometric grain size materials.

confirms the importance of charge spreading to prevent breakdown.

**6.3 Charge spreading in alumina of sub-micrometric grain size** 

The semi-logarithmic plot of the degree of discharge R versus reciprocal temperature exhibits, as for the pure samples, an Arrhenius type law leading to an activation energy of about 0.12 eV for the smallest grain size sample (d = 1.2 µm) and about 0.28 eV for the largest one (d = 4 µm). These activation energies are an indication of detrapping from

It is worth noting that, at room temperature and in the same impure polycrystalline samples, breakdown strength increases with the grain sizes (Liebault, 1999; Si Ahmed et al., 2005), which is also the case for the fraction of removed charges R. Therefore this correlation

The evolution of the properties with the grain size raises queries about the effect of changing the grain size from micron to nanometer scales. The study of charging properties of nanostructured alumina is beyond the scope of the present chapter. However, there is interest in trying to verify whether they can be obtained by simple extrapolation from the

ii. The foregoing assumption is somewhat confirmed in Fig. 12, where below 573 K the semi-logarithmic plot of R versus reciprocal temperature exhibits an Arrhenius law leading to an activation energy about 0.12 eV whatever the grain size is. This same activation energy means that we are dealing with detrapping from similar trapping sites (i.e., grain boundary traps). The continuous variation in R over a large temperature range, as shown in Fig 11, indicates a detrapping from a density of continuous trapping states rather than from a single trapping level. This aspect characterizes disordered solids in which hopping conduction mechanism can occur with the same order of magnitude of activation energy (Blaise, 2001).

Fig. 12. Semi-logarithmic plot of the ratio R expressing the degree of discharge versus reciprocal temperature for polycrystalline alumina (solid line: linear fit of the data). For T below 573 K, discharging is characterized by the same activation energy (0.12 eV). Above 573 K, a second energy (0.26 eV) in small grains sample arises.

iii. for temperature above 573 K the smallest grain size sample presents a second detrapping zone corresponding to an activation energy of about 0.26 eV (i.e., twice the energy at lower temperature). This fact is a further confirmation of the presence in the smaller grain size of a higher density of deeper traps located within the grain (likely SiAl <sup>×</sup> and ''' V ) in accordance with a less efficient gettering effect. Al

#### **6.2.2 Charge spreading in impure sintered alumina**

The results of the three polycrystalline alumina impure samples are reported in Fig. 13. The comparison of the pure and impure polycrystalline samples reveals a more stable trapping behavior in impure samples in the whole temperature range. Furthermore, two opposite behaviors arise: stable trapping increases with the grain diameter in impure samples (Fig.13) and the contrary is obtained in the pure ones (Fig. 11). In the impure material, the contents of impurities are much higher and expected above the solubility limits. Hence, gettering

ii. The foregoing assumption is somewhat confirmed in Fig. 12, where below 573 K the semi-logarithmic plot of R versus reciprocal temperature exhibits an Arrhenius law leading to an activation energy about 0.12 eV whatever the grain size is. This same activation energy means that we are dealing with detrapping from similar trapping sites (i.e., grain boundary traps). The continuous variation in R over a large temperature range, as shown in Fig 11, indicates a detrapping from a density of continuous trapping states rather than from a single trapping level. This aspect characterizes disordered solids in which hopping conduction mechanism can occur with the same order of

Fig. 12. Semi-logarithmic plot of the ratio R expressing the degree of discharge versus reciprocal temperature for polycrystalline alumina (solid line: linear fit of the data). For T below 573 K, discharging is characterized by the same activation energy (0.12 eV). Above

<sup>×</sup> and ''' V ) in accordance with a less efficient gettering effect. Al

iii. for temperature above 573 K the smallest grain size sample presents a second detrapping zone corresponding to an activation energy of about 0.26 eV (i.e., twice the energy at lower temperature). This fact is a further confirmation of the presence in the smaller grain size of a higher density of deeper traps located within the grain (likely

The results of the three polycrystalline alumina impure samples are reported in Fig. 13. The comparison of the pure and impure polycrystalline samples reveals a more stable trapping behavior in impure samples in the whole temperature range. Furthermore, two opposite behaviors arise: stable trapping increases with the grain diameter in impure samples (Fig.13) and the contrary is obtained in the pure ones (Fig. 11). In the impure material, the contents of impurities are much higher and expected above the solubility limits. Hence, gettering

573 K, a second energy (0.26 eV) in small grains sample arises.

**6.2.2 Charge spreading in impure sintered alumina** 

SiAl

magnitude of activation energy (Blaise, 2001).

might be less efficient due to a possible saturation of grain boundaries. In addition, interactions between the various defects generated by the foreign elements are expected (Gavrilov et al., 1999). It must be pointed out that the great variety of impurities and their substantial content make difficult the interpretation of the results due to a possible interference of co-segregation, which is difficult to predict when more than three elements are involved. The actual situation is even more complicated by the fact that segregation leads to the creation of a space charge at grain boundaries (Tiku & Kröger, 1980) with a sign that depends on the segregated impurities, which may interfere with the charging process.

Fig. 13. Fraction R of charges removed from the irradiated volume as a function of temperature for impure polycrystalline alumina samples of different grain diameters d.

The semi-logarithmic plot of the degree of discharge R versus reciprocal temperature exhibits, as for the pure samples, an Arrhenius type law leading to an activation energy of about 0.12 eV for the smallest grain size sample (d = 1.2 µm) and about 0.28 eV for the largest one (d = 4 µm). These activation energies are an indication of detrapping from trapping sites located within the grain boundary.

It is worth noting that, at room temperature and in the same impure polycrystalline samples, breakdown strength increases with the grain sizes (Liebault, 1999; Si Ahmed et al., 2005), which is also the case for the fraction of removed charges R. Therefore this correlation confirms the importance of charge spreading to prevent breakdown.

#### **6.3 Charge spreading in alumina of sub-micrometric grain size**

The evolution of the properties with the grain size raises queries about the effect of changing the grain size from micron to nanometer scales. The study of charging properties of nanostructured alumina is beyond the scope of the present chapter. However, there is interest in trying to verify whether they can be obtained by simple extrapolation from the results of micrometric grain size materials.

Effects of the Microstructure Induced by Sintering on the Dielectric Properties of Alumina 575

Fig. 15. Fraction R of charges removed from the irradiated volume as a function of temperature for the sub-micrometric and 1.2 µm grain sizes alumina samples.

This chapter provides a method for the characterization of charge trapping and spreading in dielectrics. A quantitative recovery parameters reflecting the relative degree of the two competing processes is accurately derived. The experimental set up makes possible the assessment of the effect of temperature (in the range 300-700 K). The ability of polycrystalline alumina to trap or, conversely, to spread charges depends strongly on the grain size and segregation of impurities at interfaces. The results suggest that the grain boundary interfaces can be associated to shallow traps whereas the defects within the grains to deeper ones. The strong tendency for segregation of the main impurities implies that an internal gettering effect can also intervene. It appears therefore that the control of the microstructural development, during the conventional sintering process, is of importance as it provides ways to influence the insulator properties in technological applications of oxide ceramics, for instance, the breakdown strength. Further investigations dealing with the properties of nanostructured materials, processed by sintering techniques that reduce grain growth, could bring more understanding of the role

The authors are grateful to Dr. Goeuriot D. and Dr. Liébault J. (E.N.S.M.), to Prof. Kortov V.S. (Ural State Technical University) for the supply of some samples. Fruitful discussions with Dr. Bernardini J. (Im2np) and Prof. Fakhfakh Z. (LaMaCoP) were highly appreciated. The first author gratefully acknowledges financial support from the Ministry of Higher

Education and Scientific Research of Tunisia and the French Institute of Cooperation.

**7. Conclusion** 

of interfaces.

**8. Acknowledgments** 

Nanopowders, with grain diameter of about 27 nm, have been synthesized by the gaseous phase method and compacted via magnetic compaction process at Ural State Technical University, Russia (Kortov et al., 2008). Next, sintering of the compacts has been carried out at Institut National des Sciences Appliquées (INSA) of Lyon (France). The sintering temperature of 1473 K (dwelling time 60 min) was reached at a rate of 3 K/min. As expected, with such heating rate, a substantial grain growth occurred (i.e., from 27 to about 100 nm, cf. Fig. 14). Indeed, grain growth could have been reduced by using faster heating rates that are made possible by different sintering techniques such as spark plasma sintering.

Fig. 14. Microstructure of the sub-micrometric grain size of the impure polycrystalline alumina sample after sintering. This picture is the SEM observation of fracture surface. The average grain diameter has grown after sintering to about of 100 nm (the initial particle diameter prior to sintering was about 27 nm).

The overall purity of this material is about the same as the one of impure polycrystalline alumina. In Fig. 15, the fraction R of charges removed from the irradiated volume as a function of temperature is given for the 0.1 and 1.2 µm samples. The manifest difference is the sharp enhancement of R between 600 and 663 K for the 0.1 µm sample (the value of R increases from 30 to 90 %), which contrasts with the continuous behaviour of the other polycrystalline samples. The activation energy that arises from the semi-logarithmic plot of the recovery parameter versus reciprocal temperature in the range 600-663 K is 0.53 eV (Moya et al., 2007). These results are an indication that detrapping occurs, at about 600 K, from a dominant efficient trap having a well-defined energy level in the gap as in the case of silver doped single crystal (Zarbout et al. 2010).

Fig. 15. Fraction R of charges removed from the irradiated volume as a function of temperature for the sub-micrometric and 1.2 µm grain sizes alumina samples.
