- Email: [email protected]
Ion-beam-induced amorphous structures in silicon carbide
Nuclear Instruments and Methods in Physics Research B 206 (2003) 974–978 www.elsevier.com/locate/nimb
Ion-beam-induced amorphous structures in silicon carbide In-Tae Bae a, Manabu Ishimaru b,*, Yoshihiko Hirotsu b, Syo Matsumura c, Kurt E. Sickafus d a
Department of Materials Science and Engineering, Osaka University, Osaka 565-0871, Japan The Institute of Scientific and Industrial Research, Osaka University, 8-1 Mihogaoka Ibaraki, Osaka 567-0047, Japan Department of Applied Quantum Physics and Nuclear Engineering and Department of Energy Science and Engineering, Kyushu University, Fukuoka 812-8581, Japan d Materials Science and Technology Division, Los Alamos National Laboratory, NM 87545, USA
b c
Abstract Atomistic structure of ion-beam-induced amorphous silicon carbide (a-SiC) has been investigated by cross-sectional transmission electron microscopy. The electron intensities of halo patterns recorded on imaging plates were digitized quantitatively to extract reduced interference functions. We demonstrated the relationship between maximum scattering vector ðQmax Þ measured in scattering experiments and the resolution of the corresponding pair-distribution function by changing Qmax values from 160 to 230 nm1 . The results revealed that the C–C peak becomes broadened and eventually a shoulder as the Qmax value becomes shorter, indicating that Qmax values of <160 nm1 measured in previous studies are not enough to detect C–C homonuclear bonds in a-SiC. We are the first to reveal the existence of C–C and Si–Si homonuclear bonds in a-SiC using a diffraction technique. Ó 2003 Elsevier Science B.V. All rights reserved. PACS: 61.14.Lj; 61.43.Dq; 81.40.Wx Keywords: Silicon carbide; Amorphous; Transmission electron microscopy; Electron diffraction; Pair-distribution function
1. Introduction Silicon carbide (SiC) is an important semiconductor material due to its outstanding electrical, thermal, and mechanical properties. Such outstanding physical properties make its electronic devices superior to those of Si for high-power, high-frequency and high-temperature application * Corresponding author. Tel.: +81-6-68798432; fax: +81-668798434. E-mail address: [email protected] (M. Ishimaru).
[1,2]. For development of SiC device application, ion implantation is an important doping technique, especially for the doping of laterally confined local area. However, radiation damages are inevitably incorporated during a high-dose ion implantation, and an amorphous layer can be induced. During thermal annealing process, recrystallization occurs in implantation-induced amorphous layer. For precise control of recrystallizaion process, knowledge of amorphous structures is strongly required, and therefore much effort has been devoted to study the structure of amorphous SiC (a-SiC).
0168-583X/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0168-583X(03)00905-4
I.-T. Bae et al. / Nucl. Instr. and Meth. in Phys. Res. B 206 (2003) 974–978
Most of the results in previous studies using different experiments indicated that the atomistic structure of a-SiC consists of both of C–C and Si– Si homonuclear bonds as well as Si–C heteronuclear bonds [3–5], while studies using diffraction techniques have shown that the atomistic structure of a-SiC consists of Si–C heteronuclear bonds predominantly [6,7]. Recently, we have confirmed that the formation of C–C and Si–Si homonuclear bonds as well as Si–C heteronuclear bonds in aSiC networks using electron diffraction techniques [8]. The reason for the two contradictory results obtained between our diffraction study and previous diffraction studies is still unclear [6–8]. We speculated that no detection of homonuclear bonds in the previous scattering studies can be associated with much shorter maximum scattering vector ðQmax Þ measured (<160 nm1 ) [6,7] compared with that measured in our previous study (220 nm1 ) [8]. In this study, therefore, we examined the relationship between Qmax measured in scattering experiments and the resolution of the corresponding pair-distribution function (PDF) using transmission electron microscopy (TEM) followed by PDF analysis.
2. Experimental In order to fabricate a-SiC layer, Cree Research 6H–SiC [0 0 0 1] substrates were irradiated with 150 keV argon ions at room temperature to a fluence of 1 1016 /cm2 in the Ion Beam Materials Laboratory at Los Alamos National Laboratory. Cross-sectional TEM samples were prepared by a combination of tripod polishing technique and ion thinning with 4 keV Arþ ions. Electron diffraction experiment was performed using a JEOL JEM-2010 TEM operated at 200 kV in combination with imaging plates [9] as a recording material which has higher sensitivity and wider dynamic range for electron-beam intensity compared with conventional TEM film material. The intensities of the halo patterns were digitized quantitatively using an imaging plate processor, Digital Micro-Luminography FDL 5000 (Fuji Film).
975
3. Results and discussion Fig. 1 shows the number of vacancies created by 150 keV Arþ ions to a fluence of 1 1016 /cm2 and the distribution of Arþ projectiles as a function of the depth of the ion-beam-induced layer. This calculation was carried out using TRIM-90 code [10]. For the calculation, it is assumed that the threshold displacement energies of silicon and carbon correspond to 35 and 20 eV, respectively [11]. The results show a total dpa (displacement per atom) of 1.6 near surface area and 7.2 at the peak maximum of damage profile, which correspond to 4 and 18 times the critical dpa for amorphizaion, respectively [12]. Therefore, a complete amorphizaion is expected throughout the entire ion-beam-induced layer under the present irradiation condition. Fig. 2(a) shows a cross-sectional bright-field TEM image and an electron diffraction pattern (see the inset of Fig. 2(a)) of the ion-beam-induced layer. As is expected by TRIM calculation, a continuous amorphous layer is formed from the surface to a depth of 200 nm under the present irradiation condition. The electron diffraction pattern reveals that the ion-beam-induced layer is amorphized successfully. In Fig. 2(b) is shown a high-resolution TEM image. In addition to a salt and pepper contrast reminiscent of an amorphous structure, atomic medium range order (MRO)
Fig. 1. The depth distribution of the projectile Arþ ions and the number of vacancies distribution produced by 150 keV Arþ ions to a fluence of 1 1016 /cm2 calculated by TRIM-90 code.
976
I.-T. Bae et al. / Nucl. Instr. and Meth. in Phys. Res. B 206 (2003) 974–978
Fig. 2. A cross-sectional bright-field TEM image with an electron diffraction pattern (a) and a high-resolution TEM image of ion-beam-induced layer (b).
with a size of 2 nm exists in the encircled areas in Fig. 2(b). Based on the electron diffraction pattern in Fig. 2(a), a PDF analysis has been performed. Fig. 3(a) shows a reduced interference function (RIF) calculated by subtracting a smooth cubic spline curve as a background from an electron diffraction intensity profile recorded from the a-SiC layer. It is clearly seen that very weak intensity profiles up to scattering vector (Q) as high as Q ¼ 230 nm1 are recorded well above the background intensity level of the imaging plate. Fig. 3(b) shows the corre-
Fig. 3. An RIF extracted from an electron diffraction intensity profile of a-SiC layer (a) and the corresponding PDF calculated by Fourier transformation of the RIF (b). Note that ÔQmax Õ in (b) indicates the maximum scattering vector used for Fourier transformation.
sponding PDF (see the PDF marked by ÔQmax ¼ 230 nm1 Õ) calculated by Fourier transformation of the RIF. The PDF shows the probability of existence of atom as a function of distance from the center of an arbitrary origin atom. Fig. 3(b) shows a prominent peak at 0.19(0) nm which can be compared with the bond length of Si–C (0.188 nm). Besides, there exist two subpeaks located at 0.15(1) and 0.24(1) nm which correspond to the bond length
I.-T. Bae et al. / Nucl. Instr. and Meth. in Phys. Res. B 206 (2003) 974–978
of C–C and Si–Si, respectively. In particular, the subpeak at 0.15(1) nm is located in between the bond length of graphite (0.143 nm) and diamond (0.154 nm) suggesting the coexistence of both sp2 and sp3 carbon hybridization. This result is in good agreement with those of molecular dynamics simulation [4] and nuclear magnetic resonance spectra [13]. Consequently, the PDF shows both C–C and Si–Si homonuclear bonds along with Si– C heteronuclear bonds, indicating that the structure of a-SiC is not chemically ordered in that the bonding state of a-SiC is different from that of chemically ordered crystalline SiC which has Si–C heteronuclear bonds only. In addition, it should be noticed that there is no indication of peak near 0.365 nm which can be compared with Ar–Ar homonuclear bonds [14]. It suggests that the amount of projectile Arþ ions is small enough to be ignored in the PDF analysis of the present study. Meneghini et al. [6] characterized the structure of a-SiC as chemically ordered using X-ray diffraction. Bentley et al. [15] also obtained the same result using electron diffraction. These results are in apparent disagreement with the present result. This discrepancy is considered to be associated with maximum value of Q measured in scattering experiments. The maximum scattering vector ðQmax Þ measured in our study (230 nm1 ) is much larger than that measured by previous X-ray diffraction (160 nm1 [6]) and electron diffraction (150 nm1 [15]) experiments. In order to clearly show the relationship between Qmax measured in scattering experiments and the resolution of the corresponding PDF, we demonstrated PDFs using Qmax values of 160 nm1 and 180 nm1 along with 230 nm1 in Fig. 3(b). It is readily noticed that the C–C peak becomes broadened and eventually a shoulder as the Qmax value becomes shorter. Particularly, the peak shape of PDF marked by ÔQmax ¼ 160 nm1 Õ is quite similar to that of Bentley et al. [15] which shows a weak shoulder near 0.15 nm. Therefore, it can be deduced that C–C homonuclear bonds may exist in their specimen. Consequently, it is concluded that the resolution of both of the previous results was not enough to clearly show the existence of C–C and Si–Si homonuclear bonds [6,15].
977
4. Conclusions We examined atomistic structural details of aSiC using TEM. Bright-field TEM images and electron diffraction patterns indicated the formation of a complete amorphous layer in the Arþ ion irradiated single crystalline 6H–SiC [0 0 0 1] with a depth of 200 nm, while high-resolution TEM images showed local lattice images with a size of 2 nm exist due to atomic medium range order. PDFs extracted by Fourier transformation of the corresponding RIFs indicated that the a-SiC network consists of C–C and Si–Si homonuclear bonds as well as Si–C heteronuclear bonds, suggesting that the atomistic structure of a-SiC is not chemically ordered. The demonstration of PDFs using Qmax values of 160 nm1 and 180 nm1 along with 230 nm1 revealed that Qmax values of <160 nm1 measured in the previous studies are not enough to locate the existence of C–C homonuclear bonds in a-SiC. It should be noted that our results do not deny the Ôchemical orderÕ model, since a-SiC is not a single structure. In fact, we have recently observed structural changes in a-SiC upon annealing [8].
Acknowledgements This work was sponsored by the US Department of Energy (DOE), Office of Basic Sciences, Division of Materials Sciences, and the Center of Excellence (COE) program and Special Coordination Fund for Promoting Science and Technology on ÔNanohetero Metallic MaterialsÕ from the Science and Technology Agency and a Grant-inAid for Scientific Research from the Ministry of Education, Science, Sports and Culture, Japan.
References [1] W. Wesch, Nucl. Instr. and Meth. B 116 (1996) 305. [2] C. Raynaud, J. Non-Cryst. Solids 280 (2001) 1. [3] M. Gorman, S.A. Solin, Solid State Commum. 15 (1974) 761. [4] F. Finocchi, G. Galli, M. Parrinello, C.M. Bertoni, Phys. Rev. Lett. 68 (1992) 3044. [5] L.C. Fang, L. Ley, Phys. Rev. B 40 (1989) 3818.
978
I.-T. Bae et al. / Nucl. Instr. and Meth. in Phys. Res. B 206 (2003) 974–978
[6] C. Meneghini, S. Pascarelli, F. Boscherini, S. Mobilio, F. Evangelisti, J. Non-Cryst. Solids 137–138 (1991) 75. [7] A. Sproul, D.R. McKenzie, D.J.H. Cockayne, Philos. Mag. B 54 (1986) 113. [8] M. Ishimaru, I.-T. Bae, Y. Hirotsu, S. Matsumura, K.E. Sickafus, Phys. Rev. Lett. 89 (2002) 055502. [9] N. Mori, T. Oikawa, Y. Harada, J. Miyahara, J. Electron. Microsc. 39 (1990) 433. [10] J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Solids, Pergamon, New York, 1985.
[11] R. Devanathan, W.J. Weber, F. Gao, J. Appl. Phys. 90 (2001) 2303. [12] W.J. Weber, L.M. Wang, N. Yu, N.J. Hess, Mater. Sci. Eng. A 253 (1998) 62. [13] M.A. Petrich, K.K. Gleason, J.A. Reimer, Phys. Rev. B 36 (1987) 9722. [14] S.E. Donnelly, C.J. Rossouw, Nucl. Instr. and Meth. B 13 (1986) 485. [15] J. Bentley, P. Angelini, A.P. Gove, P.S. Sklad, A.T. Fisher, Inst. Phys. Conf. Ser. 98 (1990) 107.
Ion-beam-induced amorphous structures in silicon carbide In-Tae Bae a, Manabu Ishimaru b,*, Yoshihiko Hirotsu b, Syo Matsumura c, Kurt E. Sickafus d a
Department of Materials Science and Engineering, Osaka University, Osaka 565-0871, Japan The Institute of Scientific and Industrial Research, Osaka University, 8-1 Mihogaoka Ibaraki, Osaka 567-0047, Japan Department of Applied Quantum Physics and Nuclear Engineering and Department of Energy Science and Engineering, Kyushu University, Fukuoka 812-8581, Japan d Materials Science and Technology Division, Los Alamos National Laboratory, NM 87545, USA
b c
Abstract Atomistic structure of ion-beam-induced amorphous silicon carbide (a-SiC) has been investigated by cross-sectional transmission electron microscopy. The electron intensities of halo patterns recorded on imaging plates were digitized quantitatively to extract reduced interference functions. We demonstrated the relationship between maximum scattering vector ðQmax Þ measured in scattering experiments and the resolution of the corresponding pair-distribution function by changing Qmax values from 160 to 230 nm1 . The results revealed that the C–C peak becomes broadened and eventually a shoulder as the Qmax value becomes shorter, indicating that Qmax values of <160 nm1 measured in previous studies are not enough to detect C–C homonuclear bonds in a-SiC. We are the first to reveal the existence of C–C and Si–Si homonuclear bonds in a-SiC using a diffraction technique. Ó 2003 Elsevier Science B.V. All rights reserved. PACS: 61.14.Lj; 61.43.Dq; 81.40.Wx Keywords: Silicon carbide; Amorphous; Transmission electron microscopy; Electron diffraction; Pair-distribution function
1. Introduction Silicon carbide (SiC) is an important semiconductor material due to its outstanding electrical, thermal, and mechanical properties. Such outstanding physical properties make its electronic devices superior to those of Si for high-power, high-frequency and high-temperature application * Corresponding author. Tel.: +81-6-68798432; fax: +81-668798434. E-mail address: [email protected] (M. Ishimaru).
[1,2]. For development of SiC device application, ion implantation is an important doping technique, especially for the doping of laterally confined local area. However, radiation damages are inevitably incorporated during a high-dose ion implantation, and an amorphous layer can be induced. During thermal annealing process, recrystallization occurs in implantation-induced amorphous layer. For precise control of recrystallizaion process, knowledge of amorphous structures is strongly required, and therefore much effort has been devoted to study the structure of amorphous SiC (a-SiC).
0168-583X/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0168-583X(03)00905-4
I.-T. Bae et al. / Nucl. Instr. and Meth. in Phys. Res. B 206 (2003) 974–978
Most of the results in previous studies using different experiments indicated that the atomistic structure of a-SiC consists of both of C–C and Si– Si homonuclear bonds as well as Si–C heteronuclear bonds [3–5], while studies using diffraction techniques have shown that the atomistic structure of a-SiC consists of Si–C heteronuclear bonds predominantly [6,7]. Recently, we have confirmed that the formation of C–C and Si–Si homonuclear bonds as well as Si–C heteronuclear bonds in aSiC networks using electron diffraction techniques [8]. The reason for the two contradictory results obtained between our diffraction study and previous diffraction studies is still unclear [6–8]. We speculated that no detection of homonuclear bonds in the previous scattering studies can be associated with much shorter maximum scattering vector ðQmax Þ measured (<160 nm1 ) [6,7] compared with that measured in our previous study (220 nm1 ) [8]. In this study, therefore, we examined the relationship between Qmax measured in scattering experiments and the resolution of the corresponding pair-distribution function (PDF) using transmission electron microscopy (TEM) followed by PDF analysis.
2. Experimental In order to fabricate a-SiC layer, Cree Research 6H–SiC [0 0 0 1] substrates were irradiated with 150 keV argon ions at room temperature to a fluence of 1 1016 /cm2 in the Ion Beam Materials Laboratory at Los Alamos National Laboratory. Cross-sectional TEM samples were prepared by a combination of tripod polishing technique and ion thinning with 4 keV Arþ ions. Electron diffraction experiment was performed using a JEOL JEM-2010 TEM operated at 200 kV in combination with imaging plates [9] as a recording material which has higher sensitivity and wider dynamic range for electron-beam intensity compared with conventional TEM film material. The intensities of the halo patterns were digitized quantitatively using an imaging plate processor, Digital Micro-Luminography FDL 5000 (Fuji Film).
975
3. Results and discussion Fig. 1 shows the number of vacancies created by 150 keV Arþ ions to a fluence of 1 1016 /cm2 and the distribution of Arþ projectiles as a function of the depth of the ion-beam-induced layer. This calculation was carried out using TRIM-90 code [10]. For the calculation, it is assumed that the threshold displacement energies of silicon and carbon correspond to 35 and 20 eV, respectively [11]. The results show a total dpa (displacement per atom) of 1.6 near surface area and 7.2 at the peak maximum of damage profile, which correspond to 4 and 18 times the critical dpa for amorphizaion, respectively [12]. Therefore, a complete amorphizaion is expected throughout the entire ion-beam-induced layer under the present irradiation condition. Fig. 2(a) shows a cross-sectional bright-field TEM image and an electron diffraction pattern (see the inset of Fig. 2(a)) of the ion-beam-induced layer. As is expected by TRIM calculation, a continuous amorphous layer is formed from the surface to a depth of 200 nm under the present irradiation condition. The electron diffraction pattern reveals that the ion-beam-induced layer is amorphized successfully. In Fig. 2(b) is shown a high-resolution TEM image. In addition to a salt and pepper contrast reminiscent of an amorphous structure, atomic medium range order (MRO)
Fig. 1. The depth distribution of the projectile Arþ ions and the number of vacancies distribution produced by 150 keV Arþ ions to a fluence of 1 1016 /cm2 calculated by TRIM-90 code.
976
I.-T. Bae et al. / Nucl. Instr. and Meth. in Phys. Res. B 206 (2003) 974–978
Fig. 2. A cross-sectional bright-field TEM image with an electron diffraction pattern (a) and a high-resolution TEM image of ion-beam-induced layer (b).
with a size of 2 nm exists in the encircled areas in Fig. 2(b). Based on the electron diffraction pattern in Fig. 2(a), a PDF analysis has been performed. Fig. 3(a) shows a reduced interference function (RIF) calculated by subtracting a smooth cubic spline curve as a background from an electron diffraction intensity profile recorded from the a-SiC layer. It is clearly seen that very weak intensity profiles up to scattering vector (Q) as high as Q ¼ 230 nm1 are recorded well above the background intensity level of the imaging plate. Fig. 3(b) shows the corre-
Fig. 3. An RIF extracted from an electron diffraction intensity profile of a-SiC layer (a) and the corresponding PDF calculated by Fourier transformation of the RIF (b). Note that ÔQmax Õ in (b) indicates the maximum scattering vector used for Fourier transformation.
sponding PDF (see the PDF marked by ÔQmax ¼ 230 nm1 Õ) calculated by Fourier transformation of the RIF. The PDF shows the probability of existence of atom as a function of distance from the center of an arbitrary origin atom. Fig. 3(b) shows a prominent peak at 0.19(0) nm which can be compared with the bond length of Si–C (0.188 nm). Besides, there exist two subpeaks located at 0.15(1) and 0.24(1) nm which correspond to the bond length
I.-T. Bae et al. / Nucl. Instr. and Meth. in Phys. Res. B 206 (2003) 974–978
of C–C and Si–Si, respectively. In particular, the subpeak at 0.15(1) nm is located in between the bond length of graphite (0.143 nm) and diamond (0.154 nm) suggesting the coexistence of both sp2 and sp3 carbon hybridization. This result is in good agreement with those of molecular dynamics simulation [4] and nuclear magnetic resonance spectra [13]. Consequently, the PDF shows both C–C and Si–Si homonuclear bonds along with Si– C heteronuclear bonds, indicating that the structure of a-SiC is not chemically ordered in that the bonding state of a-SiC is different from that of chemically ordered crystalline SiC which has Si–C heteronuclear bonds only. In addition, it should be noticed that there is no indication of peak near 0.365 nm which can be compared with Ar–Ar homonuclear bonds [14]. It suggests that the amount of projectile Arþ ions is small enough to be ignored in the PDF analysis of the present study. Meneghini et al. [6] characterized the structure of a-SiC as chemically ordered using X-ray diffraction. Bentley et al. [15] also obtained the same result using electron diffraction. These results are in apparent disagreement with the present result. This discrepancy is considered to be associated with maximum value of Q measured in scattering experiments. The maximum scattering vector ðQmax Þ measured in our study (230 nm1 ) is much larger than that measured by previous X-ray diffraction (160 nm1 [6]) and electron diffraction (150 nm1 [15]) experiments. In order to clearly show the relationship between Qmax measured in scattering experiments and the resolution of the corresponding PDF, we demonstrated PDFs using Qmax values of 160 nm1 and 180 nm1 along with 230 nm1 in Fig. 3(b). It is readily noticed that the C–C peak becomes broadened and eventually a shoulder as the Qmax value becomes shorter. Particularly, the peak shape of PDF marked by ÔQmax ¼ 160 nm1 Õ is quite similar to that of Bentley et al. [15] which shows a weak shoulder near 0.15 nm. Therefore, it can be deduced that C–C homonuclear bonds may exist in their specimen. Consequently, it is concluded that the resolution of both of the previous results was not enough to clearly show the existence of C–C and Si–Si homonuclear bonds [6,15].
977
4. Conclusions We examined atomistic structural details of aSiC using TEM. Bright-field TEM images and electron diffraction patterns indicated the formation of a complete amorphous layer in the Arþ ion irradiated single crystalline 6H–SiC [0 0 0 1] with a depth of 200 nm, while high-resolution TEM images showed local lattice images with a size of 2 nm exist due to atomic medium range order. PDFs extracted by Fourier transformation of the corresponding RIFs indicated that the a-SiC network consists of C–C and Si–Si homonuclear bonds as well as Si–C heteronuclear bonds, suggesting that the atomistic structure of a-SiC is not chemically ordered. The demonstration of PDFs using Qmax values of 160 nm1 and 180 nm1 along with 230 nm1 revealed that Qmax values of <160 nm1 measured in the previous studies are not enough to locate the existence of C–C homonuclear bonds in a-SiC. It should be noted that our results do not deny the Ôchemical orderÕ model, since a-SiC is not a single structure. In fact, we have recently observed structural changes in a-SiC upon annealing [8].
Acknowledgements This work was sponsored by the US Department of Energy (DOE), Office of Basic Sciences, Division of Materials Sciences, and the Center of Excellence (COE) program and Special Coordination Fund for Promoting Science and Technology on ÔNanohetero Metallic MaterialsÕ from the Science and Technology Agency and a Grant-inAid for Scientific Research from the Ministry of Education, Science, Sports and Culture, Japan.
References [1] W. Wesch, Nucl. Instr. and Meth. B 116 (1996) 305. [2] C. Raynaud, J. Non-Cryst. Solids 280 (2001) 1. [3] M. Gorman, S.A. Solin, Solid State Commum. 15 (1974) 761. [4] F. Finocchi, G. Galli, M. Parrinello, C.M. Bertoni, Phys. Rev. Lett. 68 (1992) 3044. [5] L.C. Fang, L. Ley, Phys. Rev. B 40 (1989) 3818.
978
I.-T. Bae et al. / Nucl. Instr. and Meth. in Phys. Res. B 206 (2003) 974–978
[6] C. Meneghini, S. Pascarelli, F. Boscherini, S. Mobilio, F. Evangelisti, J. Non-Cryst. Solids 137–138 (1991) 75. [7] A. Sproul, D.R. McKenzie, D.J.H. Cockayne, Philos. Mag. B 54 (1986) 113. [8] M. Ishimaru, I.-T. Bae, Y. Hirotsu, S. Matsumura, K.E. Sickafus, Phys. Rev. Lett. 89 (2002) 055502. [9] N. Mori, T. Oikawa, Y. Harada, J. Miyahara, J. Electron. Microsc. 39 (1990) 433. [10] J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Solids, Pergamon, New York, 1985.
[11] R. Devanathan, W.J. Weber, F. Gao, J. Appl. Phys. 90 (2001) 2303. [12] W.J. Weber, L.M. Wang, N. Yu, N.J. Hess, Mater. Sci. Eng. A 253 (1998) 62. [13] M.A. Petrich, K.K. Gleason, J.A. Reimer, Phys. Rev. B 36 (1987) 9722. [14] S.E. Donnelly, C.J. Rossouw, Nucl. Instr. and Meth. B 13 (1986) 485. [15] J. Bentley, P. Angelini, A.P. Gove, P.S. Sklad, A.T. Fisher, Inst. Phys. Conf. Ser. 98 (1990) 107.