Nuclear Instruments and Methods in Physics Research B 286 (2012) 124–128
Contents lists available at SciVerse ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Lattice damage and nanohardness in 6H–SiC implanted with multiple-energy Xe ions J.J. Li a,b, C.H. Zhang a,⇑, C.L. Xu a,b, X.J. Jia a,b, Y. Song a, J.Y. Li a, Y.F. Jin a a b
Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China Graduate University of Chinese Academy of Sciences, Beijing 100049, China
a r t i c l e
i n f o
Article history: Received 13 August 2011 Received in revised form 18 November 2011 Available online 27 November 2011 Keywords: 6H–SiC Xe ions Irradiation HRXRD Nanoindentation
a b s t r a c t Specimens of 6H–SiC were implanted with Xe ions with multiple kinetic energies at room temperature to obtain nearly uniform Xe concentrations of 7.5, 30, 150 at. ppm, respectively, and were subsequently thermally annealed under high vacuum. The lattice damage and nanohardness of specimens were studied with high resolution X-ray diffraction spectrometry and nanoindentation measurements. In the low dose specimen (7.5 at. ppm), the occurrence of a plateau (with sub-peaks) at low angle side of the SiC (0 0 0 1 2) peak suggests a strain gradient in the direction normal to the specimen surface. Upon subsequent thermal annealing the strain relaxes gradually. The relaxation activation energy of the strain was estimated with Arrhenius law. For the specimens implanted to 30 and 150 at. ppm Xe, the disappearance of the plateau or peak indicates that the implanted region has been amorphized. However, a satellite peak near the main peak reappears after the thermal annealing. In addition, the main peak broadens toward high angle side after the annealing as the result of a shrinkage of crystal lattice. The nanohardness value of the specimen implanted to 7.5 at. ppm exceeds that of virgin SiC, whereas it is opposite for the case of 30 and 150 at. ppm implantation due to the formation of amorphous regions. Changes of nanohardness with thermal annealing temperature were studied. Underlying mechanisms were discussed. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Silicon carbide (SiC) possesses outstanding physical and mechanical properties that make it very promising for applications in semiconductors, advanced nuclear reactors and nuclear waste technology [1–3]. In the semiconductor applications, damage in crystals can be inevitably produced due to ion implantation which is used for dopant incorporation in electronic device fabrication. For the applications in nuclear power industry, defects can be accumulated in materials due to irradiation of energetic particles like neutrons, alpha particles and fission products including heavy inert-gas ions [4]. The accumulation of radiation damage leads to degradation of the material, and needs a full understanding for the sake of safety and reliability of nuclear power systems. In the past decades extensive effort has been devoted to the study of lattice damage and mechanical changes in irradiated SiC with neutron and various ions, and significant results have been obtained. Previous studies have shown that the strain induced by He ion implantation in SiC is strongly localized along the direction perpendicular to the implanted surface [5], causing the lattice to expand. For elevated temperature He ion implants, amorphization ⇑ Corresponding author. Tel.: +86 931 4969036; fax: +86 931 4969201. E-mail address:
[email protected] (C.H. Zhang). 0168-583X/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2011.11.034
of the crystal can be avoided due to dynamical annealing, and the strain profiles show thermally activated saturation in the near-surface region indicating that a threshold concentration of defects is reached [6,7], whereas the strain profiles also show that defect accumulation occurs near the damage peak [7]. Recently it has been demonstrated that in extended surface region both the accumulation of interstitial atoms drifted to the deeper damaged region and the recombination of point defects are enhanced by strain gradient and temperature, resulting in the nearly constant strain that levels off at sufficient fluence [8]. Further researches reveal that the strain profile is proportional to the nuclear energy loss when the implanted helium concentration is lower than 5%, while at higher concentrations the strain profile follows the energy loss profile only in the near surface region and the helium concentration profile in the highly damaged zone [9]. In addition, a volumetric contraction of the unit cell is observed at extremely low doses, resulting from the irradiation-induced vacancies and possible formation of antisite defects [10]. Indeed, theoretical calculations indicate that the CSi antisite may induce a shrinkage of the cell, and yet confirm that all other defects cause the cell to expand, especially interstitial-type defects [11]. Making clear the formation and evolution of lattice disorder promotes the understanding of the contribution of defects to the swelling which is a wellknown irradiation-induced phenomenon for SiC. Moreover,
125
J.J. Li et al. / Nuclear Instruments and Methods in Physics Research B 286 (2012) 124–128 10
0.12
0.10
8
0.08 6 0.06 4 0.04 2
0.02
0
0.00 0
500
1000
Specimens used for the work were cut from a 6H–SiC (0 0 0 1) bulk single crystal wafer (267 lm thick, research standard, n-type, supplied by Cree Research Inc.). The irradiation of the specimens were carried out with multiple-energy 129Xe29+ ions at ambient temperature in a terminal of the 320 kV High-voltage Experimental Platform equipped with an electron cyclotron resonance (ECR) ion source in the Institute of Modern Physics, Lanzhou. Six successively decreasing energies (8.0, 7.0, 6.0, 5.0, 4.0, 3.3 MeV) of Xe ions were adopted to obtain three nearly uniform Xe concentrations, corresponding to 7.5, 30, 150 at. ppm, respectively, according to SRIM calculation [13], in the depth region between 850 and 1800 nm. Details of the schedule to achieve the ion implantation are described in Table 1, and estimated depth profiles of Xe concentration and damage level (dpa) corresponding to a Xe concentration of 7.5 at. ppm are shown in Fig. 1. The beam current was limited to 4 lA cm 2 to avoid sample heating effect. After irradiation, each specimen was cut into four pieces, three of which were subsequently thermally annealed at temperatures of 773, 1073 and 1373 K, respectively, for 30 min in a high vacuum (10 4 Pa). HRXRD measurements were conducted with a high resolution X-ray diffractometer with four-circle geometry (Bruker D8 Discovery, resolution 60.005). The x-2h scans were performed at the 6H– SiC (0 0 0 1 2) pole. Nanoindentation experiments were carried out at room temperature using a diamond Berkovich indenter (triangu-
2000
2500
Fig. 1. Depth profiles of Xe concentration and damage level (dpa) corresponding to Xe concentration of 7.5 at.ppm, according to an estimation with SRIM2006.
lar based pyramid) in the continuous stiffness measurement (CSM) mode in a Nano Indenter G200. The maximum indentation depth was about 2 lm. The data obtained from six measurements of each sample were averaged and smoothed by the Origin 8.0 program. Because of a real variation in the measured hardness due to the tip imperfection, the data at shallow depths (<100 nm) were ignored [14].
3. Results and discussion Fig. 2 presents the HRXRD spectra of the specimens implanted to Xe concentrations of 7.5, 30 and 150 at. ppm, respectively. In the spectra the main sharp Bragg peak of (0 0 0 1 2) located at 75.5° results from the unperturbed SiC crystal. At the concentration of 7.5 at. ppm (corresponding to 0.11 dpa at the damage peak), the occurrence of a plateau (with sub-peaks) at low angle side of the main sharp Bragg peak of (0 0 0 1 2) suggests that a strain gradient was built up in the direction normal to the specimen surface [5]. No fringe pattern was observed in the curve which often is used to calculate the strain profile [9]. In the case of single energy He implantation, the observed fringe pattern was ascribed to the
Table 1 Schedules to obtain nearly uniform Xe concentrations in the depth between 850 and 1800 nm to 7.5, 30, 150 at. ppm. Damage peak (dpa)
Ion energy (MeV)
Ion fluence (ions cm 2)
7.5
0.11
8 7 6 5 4 3.3 8 7 6 5 4 3.3 8 7 6 5 4 3.3
2.1 1013 1.5 1013 1.5 1013 1.5 1013 1.5 1013 1.5 1013 8.3 1013 5.8 1013 5.8 1013 5.8 1013 5.8 1013 5.8 1013 4.2 1014 2.9 1014 2.9 1014 2.9 1014 2.9 1014 2.9 1014
0.44
2.2
-(Δd/d)N -0.03
-0.02
-0.01
0.00
0.01 SiC (00012)
4
10
Intensity (arb.units)
Concentrations (at. ppm)
150
1500
Depth (nm)
2. Experiments
30
dpa
Xe concentration(at.ppm)
microstructure changes of irradiated SiC can alter the mechanical properties. Most studies show the hardness and the elastic modulus of irradiated SiC decrease with increasing fluence. When the implanted region is entirely amorphous, the hardness value decreases by about 50% [12]. In the present work, lattice damage and nanohardness of 6H– SiC were investigated by HRXRD and nanoindentation measurement after multi-energy Xe irradiation and subsequent thermal annealing at temperatures up to 1373 K. Xenon ion implantations were performed into 6H–SiC at different energies but also at selected fluences to obtain a nearly uniform Xe concentration zone. The changes in hardness were discussed with regard to the microstructure, and the difference of lattice damage was also presented between previous single energy He and multi-energy Xe (heavier inert-gas ion) implantation.
3
10
7.5 at.ppm 2
10
30 at.ppm 150 at.ppm 1
10
Virgin
0
10 72.0
72.5
73.0
73.5
74.0
74.5
75.0
75.5
76.0
76.5
Diffraction angle 2θ (degree) Fig. 2. HRXRD spectra of the unimplanted and Xe-implanted SiC to concentrations of 7.5, 30 and 150 at. ppm Xe, respectively.
J.J. Li et al. / Nuclear Instruments and Methods in Physics Research B 286 (2012) 124–128
coherent diffraction of two damaged zones of a same level of strain on either sides of Rp [6], and its absence at higher doses was due to formation of a continuous buried amorphous layer in the region of maximum damage [8]. In our experiment, in the low damage of level (0.11 dpa), the buried amorphous layer may not form. With a mass number larger than He ions, Xe ions may induce more complex collision cascades so that the defects are not evenly distributed across the ion track. As a result, it is difficult to form the same level strain layers on either sides of Rp. For the specimens implanted to 30 (0.44 dpa) and 150 (2.2 dpa) at. ppm Xe, the absence of a plateau or peak at low angle beside the main peak indicates that the implant region has been amorphized [7]. It is in agreement with previous results [15,16] which demonstrate amorphization of SiC is achieved at 0.25–0.4 dpa. The scattered intensity at the low angle side of the Bragg peak comes from the transition region between the unperturbed bulk and the amorphous zone [6], and decreases monotonically from the main peak down to the background level. Apparently, the intensity of the low angle tail in the specimen implanted to 30 at. ppm Xe is higher than that in the specimen implanted to 150 at. ppm Xe, indicating a growth of the amorphous layer occurs with increasing Xe-ion fluence that leads to a more incoherent diffraction in XRD. In the specimen Xe-implanted to a concentration of 7.5 at. ppm, the evolution of X-ray scattering intensity upon thermal annealing is displayed in Fig. 3. As shown in Fig. 3, with increasing annealing temperature the position of the plateau moves toward the Bragg peak, indicating that the strain of the damage region recovers gradually. The highest strain value decreases from 2.1% to 0.3% when the annealing temperature is increased from RT to 1373 K. The value of normal strain is obtained by differentiating Bragg’s law to give [17]:
Dd Dh cot hBragg d N
cancy complexes during the implantation or annealing process is supposed to limit the recombination of point defects. And the excess interstitials induced the crystal lattice to swell.
0.02
0.01 0.7
-0.02
0.9
1.0
1.1
1.2
Fig. 4. Arrhenius plot of the strain decrease in 6H–SiC Xe-implanted to a concentration of 7.5 at. ppm. The activation energy is 67 ± 5 meV.
a
-0.03
-(Δd/d)N
-0.02
-0.01
0.00
0.01
SiC (00012)
30 at.ppm 1073K
1373K Intensity (a.u)
3
10
773K
2
10
As-implanted
1
10
0
-0.01
0.00
0.01 SiC (00012)
-0.03
b 4
1373K
10
-0.02
-0.01
0.00
1373K
1073K
10
773K
0.01
SiC (00012)
150 at.ppm
1073K
3
1.3
10
10
3
Intensity (a.u)
intensity (arb.units)
0.8
1000/T(1/K)
4
7.5 at.ppm
4
0.014
0.012
-(Δd/d)N -0.03
0.016
10
where Dh is the difference between the diffraction angle h = (2h)/2 and the Bragg angle hBragg. Even at 1373 K, the strain remains, indicating that the defects (mainly interstitial-type) leading to the lattice expansion [8] are still subsistent. This is in agreement with previous results which demonstrate that the interstitial-type point defects were not recovered completely on annealing until 1523 K though the migration of interstitials begins above 773– 873 K [18]. The formation of clusters of point defects and Xe-va-
Ea ) kT Ea = (67 ± 5)meV
Δε = K × exp(−
0.018
Strain Decrease Δε
126
As-implanted 2
10
10
773K 2
10
As-implanted
1
10
1
10
0
10 72.5
73.0
73.5
74.0
74.5
75.0
75.5
76.0
76.5
Diffraction angle 2θ (degree) Fig. 3. HRXRD spectra of Xe-implanted 6H–SiC to a concentration of 7.5 at. ppm and then annealed at 773, 1073 and 1373 K, respectively.
0
10
73
74
75
Diffraction angle 2θ (degree)
76
Fig. 5. HRXRD spectra of Xe-implanted 6H–SiC to concentrations of (a) 30 at. ppm, (b)150 at. ppm and subsequently annealed at 773, 1073 and 1373 K, respectively.
127
J.J. Li et al. / Nuclear Instruments and Methods in Physics Research B 286 (2012) 124–128
The strain relaxation behavior upon subsequent annealing due to the recombination of point defects is related to the different energies of migration of point defects (including interstitials and vacancies). Recently it was shown that vacancy-type defects with rather high energies of migration (silicon vacancies: 3.2–3.6 eV, carbon vacancies: 3.5–5.2 eV) begin to diffuse above 1273– 1473 K [18,19] (1273–1373 K under neutron irradiation [18], 1273–1473 K under He irradiation [19]) leading to the formation of voids. So the interstitial-type defects with low energies of migration may play main roles in the strain relaxation between the annealing temperature regions 773–1373 K via their fast migration and recombination with immobile vacancies. The strain relaxation or decrease obeys an Arrhenius law with an activation energy of Ea = 67 ± 5 meV as shown in Fig. 4. However, the activation energy related to interstitial migration energy is lower than theoretical calculation (0.2–1.6 eV) [18]. Previous studies show that the strain gradient and temperature enhance the migration of interstitials [8] and may lower the migration energy. Further investigations are necessary in order to understand the mechanism. For the specimens implanted to 30 and 150 at. ppm Xe, the annealing behaviors studied by HRXRD are shown in Fig. 5a and b. As also shown in Fig. 2, in both as-implanted samples, the disappearance of a plateau or peak at a low angle beside the main peak indicates that the implant region has been amorphized. However, after the thermal annealing at 773 and 1073 K the satellite peak near the main peak reappears, and the peak position is the same in the specimens implanted to either 30 or 150 at. ppm and annealed at the same temperature (see Fig. 5). The strain value calculated from the peak decreases with increasing annealing temperature and is independent of the ion fluence. For helium
50
b 50
45
45
40
40
Hardness (GPa)
Hardness (GPa)
a
implantation below the threshold amorphization fluence, the satellite peak is ordinarily ascribed to the near surface region because the strain profile is proportional to nuclear energy loss profile [6,7,9]. But in our experiment, the amorphous layer occurs near the surface region of as-implanted samples, and especially for 150 at. ppm the surface region is all amorphized according to our Raman and nanohardness results. Previous RBS/C studies reveal that no noticeable recovery is detected in continuous amorphous layers up to 1073 K [20]. So the satellite peak that reappears after annealing at 773 and 1073 K may not be from the surface region but a buried strain layer between the surface amorphous layer and the bulk unperturbed SiC crystal. The peak position is the same in the specimens implanted to 30 and 150 at. ppm, indicating that in the buried strain layer a threshold concentration of point defects is reached. It is similar with the results from the high temperature He implantation that the position of the satellite peak from near surface region stays constant with increasing fluence [6]. At annealing at 1373 K, the main peak of (0 0 0 1 2) broadens toward high angle side in the specimens implanted to either 30 or 150 at.ppm. However the phenomenon is not observed in the XRD curve of 7.5 at.ppm (see Fig. 3). Surely, the recovery upon annealing depends not only on annealing temperature but also on damage level. The broadening of the main peak is ascribed to the shrinkage of crystal lattice. Up to 1373 K, the vacancies begin to obviously diffuse and Xe-vacancy clusters grow larger. Finally, Xe-bubbles form in the damage region. The formation of the bubbles causes the compressive stress which may be responsible for the shrinkage of crystal lattice. In addition, in annealed 150 at. ppm specimen at 1373 K, surface peeling and cracking are found by AFM and optical microscope that support the formation of Xe-bubbles.
35 30 25 20
virgin 7.5 at.ppm 30 at.ppm 150 at.ppm
15 10
35 30 25 20
virgin as-implanted: 7.5 at.ppm annealing: 773K annealing: 1073K annealing: 1373K
15 10
5
5
0
0 0
250
500
750
1000
1250
1500
1750
2000
0
250
500
750
Depth (nm)
c
50
d
45
1250
1500
1750
2000
50 45 40
35 30 25 20
virgin as-implanted: 30 at.ppm annealing: 773K annealing: 1073K annealing: 1373K
15 10 5 0
Hardness (GPa)
40
Hardness (GPa)
1000
Depth (nm)
35 30 25 20
virgin as-implanted: 150 at.ppm annealing: 773K annealing: 1073K
15 10 5 0
0
250
500
750
1000
1250
Depth (nm)
1500
1750
2000
0
250
500
750
1000
1250
1500
1750
2000
Depth (nm)
Fig. 6. Hardness versus penetration depth curves in SiC specimens in (a) unimplanted and as-implanted state, and in subsequently annealed state corresponding to Xe concentrations of (b) 7.5, (c) 30 and (d) 150 at. ppm.
128
J.J. Li et al. / Nuclear Instruments and Methods in Physics Research B 286 (2012) 124–128
Fig. 6 shows the hardness values against the penetration depth of virgin and Xe-implanted specimens to a concentration of 7.5, 30 and 150 at.ppm (a) and subsequently annealing at 773, 1073 and 1373 K (b–d) except 150 at.ppm specimen annealed at 1373 K. As shown in Fig. 6a, the hardness of virgin SiC decreases with the increasing penetration depth due to the indentation size effect [21]. The nanohardness value of the specimen implanted to 7.5 at.ppm exceeds that of virgin SiC, whereas it is opposite for both the cases of 30 and 150 at.ppm implantation due to the formation of amorphous regions. After annealing at 773, 1073 and 1373 K, no obvious change is observed in the hardness curves of 7.5 at.ppm (see Fig. 6b). It suggests that the defects that cause the hardness to increase are stable in the annealing temperature region (773–1373 K). This is consistent with our XRD results which show steady Xe-vacancy complexes or vacancy clusters may be formed during the implantation or annealing process that play a role as pinning centers to improve the hardness value. At a concentration of 30 at.ppm, the hardness value reduces firstly and then increases showing constraining coating effects as a result of buried amorphous layers [12,22]. Fig. 6c shows that the hardness penetration curves of the specimens implanted to 30 at.ppm after annealing at 773, 1073 and 1373 K, shows the same behavior as virgin SiC. For 150 at.ppm, the surface region is entirely amorphized that leads the hardness value to decrease strongly by about 45%. Such a behavior is in accordance with the results of previous studies [23,24]. Annealing behavior of 150 at.ppm specimen is also presented in the Fig. 6d. The hardness of specimen annealed at 1373 K was not measured due to its surface peeling and cracking. With increasing annealing temperature, the hardness recovers gradually. UP to 1073 K, the value of hardness is still lower than virgin specimen’s. 4. Conclusion The lattice damage and nanohardness of 6H–SiC were investigated by HRXRD and nanoindentation measurements after multienergy Xe irradiation and subsequent thermal annealing at temperatures up to 1373 K. In the low dpa regime (7.5 at.ppm), interstitial-type point defects may have a dominant effect on lattice expansion of implanted SiC. Upon subsequent annealing the strain relaxation behavior is connected with the different energies of migration of point defects (including interstitials and vacancies). The activation energy of strain relaxation (Ea = 67 ± 5 meV) related to interstitial migration energy is lower than theoretical calculations as a result of the migration of interstitial defects enhanced by the strain gradient and temperature. With increasing damage level the implanted region has been amorphized. But after thermal annealing the satellite peak near the main peak reappears which may not be from the surface region but from a buried strain layer between the surface amorphous layer and the unperturbed bulk crystal. The strain value related to the satellite peak decreases with increasing annealing temperature and is independent of the ion fluence. It suggests a saturation of point defects or different evolution of different types of defects
upon the annealing. Moreover, the formation of Xe-bubbles during the annealing process may cause the compressive stress which induces the shrinkage of the crystal lattice. Microstructure changes due to irradiation can alter the mechanical properties. The accumulation of irradiation defects results in the increase of the nanohardness of irradiated SiC at 0.11 dpa, and the defects seem to be stable in the annealing temperature region (773–1373 K). When complete amorphization is reached, the hardness value decreases strongly by about 45% in agreement with previous work. Further research is still in progress to better understand the relation between hardness and microstructure. Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant No. 10575124, 10979063) and National Basic Research Program of China (Grant No. 2010CB832904). The authors would thank members in the 320 kV High-voltage Platform in Institute of Modern Physics for their help in the ion irradiation experiment. References [1] C. Raynaud, J. Non-Cryst. Solids 280 (2001) 1. [2] R.H. Jones, L. Giancarli, A. Hasegawa, Y. Katoh, A. Kohyama, B. Riccardi, L.L. Snead, W.J. Weber, J. Nucl. Mater. 307–311 (2002) 1057. [3] L.L. Snead, T. Nozawa, Y. Katoh, T. Byun, S. Kondo, D. Petti, Nucl. Instrum. Methods B 371 (2007) 329. [4] Y.W. Zhang, I.-T. Bae, K. Sun, C.M. Wang, M. Ishimaru, Z. Zhu, W. Jiang, W.J. Weber, J. Appl. Phys. 105 (2009) 104901. [5] A. Declémy, E. Oliviero, M.F. Beaufort, J.F. Barbot, M.L. David, C. Blanchard, Y. Tessier, E. Ntsoenzok, Nucl. Instrum. Methods B 186 (2002) 318. [6] S. Leclerc, A. Declémy, M.F. Beaufort, C. Tromas, J.F. Barbot, J. Appl. Phys. 98 (2005) 113506. [7] J.F. Barbot, S. Leclerc, M.L. David, E. Oliviero, R. Montsouka, F. Pailloux, D. Eyidi, M.F. Denanot, M.F. Beaufort, A. Declémy, V. Audurier, C. Tromas, Phys. Status Solidi A 206 (2009) 1916. [8] S. Leclerc, M.F. Beaufort, A. Declémy, J.F. Barbot, J. Nucl. Mater. 397 (2010) 132. [9] S. Leclerc, M.F. Beaufort, A. Declémy, J.F. Barbot, Appl. Phys. Lett. 93 (2008) 122101. [10] W. Jiang, P. Nachimuthu, W.J. Weber, Appl. Phys. Lett. 93 (2007) 091918. [11] J. Li, L. Porter, S. Yip, J. Nucl. Mater. 255 (1998) 139. [12] C. Tromas, V. Audurier, S. Leclerc, M.F. Beaufort, A. Declémy, J.F. Barbot, Nucl. Instrum. Methods B 266 (2008) 2776. [13] J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Solids, vol. 1, Pergamon Press, New York, 1984. [14] W.C. Oliver, G.M. Pharr, J. Mater. Res. 19 (2004) 3. [15] A. Audren, A. Benyagoub, L. Thome, F. Garrido, Nucl. Instrum. Methods B 257 (2007) 227. [16] W.J. Weber, L.M. Wang, N. Yu, N.J. Hess, Mater. Sci. Eng. B 253 (1998) 62. [17] M.A. Moram, M.E. Vickers, Rep. Prog. Phys. 72 (2009) 036502. [18] T. Sawabe, M. Akiyoshi, K. Ichikawa, K. Yoshida, T. Yano, J. Nucl. Mater. 386– 388 (2009) 333. [19] J.F. Barbot, M.F. Beaufort, M. Texier, C. Tromas, J. Nucl. Mater. 413 (2011) 162. [20] T. Bus, A. van Veen, A. Shiryaev, A.V. Fedorov, H. Shut, F.D. Tichelaar, J. Sietsma, Mater. Sci. Eng. B 102 (2003) 269. [21] W. Nix, H. Gao, J. Mech. Phys. Solids 46 (1996) 411. [22] C. Tromas, V. Audurier, S. Leclerc, M.F. Beaufort, A. Declémy, J.F. Barbot, J. Nucl. Mater. 373 (2008) 142. [23] L.L. Snead, S.J. Zinkle, J.C. Hay, M.C. Osborne, Nucl. Instrum. Methods B 141 (1998) 123. [24] X. Kerbiriou, J.-M. Costantini, M. Sauzay, S. Sorieul, L. Thomé, J. Jagielski, J.-J. Grob, J. Appl. Phys. 105 (2009) 073513.