- Email: [email protected]
Positron annihilation study of dopant effects on proton-irradiation defect in silicon
Physica B 273}274 (1999) 480}484
Positron annihilation study of dopant e!ects on proton-irradiation defect in silicon F. Hori!,*, T. Chijiiwa!, R. Oshima!, T. Hisamatsu" !Research Institute for Advanced Science and Technology, Osaka Prefecture University 1-2, Gakuen-cho, Sakai, Osaka 599-8570, Japan "National Space Development Agency of Japan, Tsukuba, Ibaragi 305-8505, Japan
Abstract Positron annihilation lifetime and doppler broadening measurements have been performed to examine the e!ects of B, Al and Ga dopants of Czochralski-grown Si (CZ-Si) on defects induced by 10 MeV proton irradiations at room temperature with a total dose from 3]1012 p/cm2 to 5]1014 p/cm2. Isochronal annealing experiments were also carried out after the irradiations. In spite of the high-energy proton irradiation, a short lifetime component q of about 100 ps 1 was observed in all of the specimens, which is considered to be responsible for dopant}oxygen}vacancy complexes. The long lifetime component becomes remarkable in specimens with irradiation more than 1014 p/cm2. In isochronal annealing experiments, annealing stages at 527 and 552 K were observed for the irradiated B doped CZ-Si with resistivities of 10 and 2 )cm, respectively. This corresponds to the formation of larger vacancy clusters. We found that the formation of the vacancy}oxygen complex depends on the species of dopant atoms of silicon, especially at irradiation below 1014 p/cm2. ( 1999 Elsevier Science B.V. All rights reserved. Keywords: Positron annihilation; Silicon; Proton irradiation; Dopant atoms
1. Introduction The nature of radiation-induced vacancy-type defects in silicon has been well established by positron annihilation techniques [1}5]. High-energy particle irradiation with high #uence on the order of above 1014 p/cm2 [1,2] and 1017 e/cm2 [3,4] has mainly been used in previous experiments. Since positron annihilation experiments can detect defects with a concentration greater than the order of ppm, it is natural that few data for experiments with #uences under 1014 p/cm2 have been analyzed. On the other hand, recent studies have shown that serious problems concerning interactions between small amounts of dopants, oxygen, and point defects arise during crystal growth process such as the formation of octahedral voids. The concentrations of these defects should be
* Corresponding author: Phone: #81-722-54-9812; fax: #81-722-54-9935. E-mail address: [email protected] (F. Hori)
considerably low. The atomic concentrations of interstitial oxygen in the bulk silicon were of 9.5]1017&1.6]1018 cm~3 for CZ-Si and were of the order of 1015 cm~3 for #oat zone grown Si (FZ-Si). Dopant atom concentrations were about 4 orders of magnitude lower than those of oxygen in CZ-Si. These interactions have not been clari"ed yet. In this paper, positron annihilation experiments after low dose proton irradiation into silicon were performed to examine the interactions among oxygen, dopants and vacancy type defects. 2. Experiment CZ-Si wafers with B, Ga and Al dopants were prepared as shown in Table 1. Samples (8 mm]8 mm, 0.23 mm thick) for positron annihilation measurements were cut from the wafers. The 10 MeV-proton irradiations with total doses from 3]1012 to 5]1014 p/cm2 were performed at room temperature with an AVF cyclotron at Takasaki Radiation Chemistry Research Establishment
0921-4526/99/$ - see front matter ( 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 0 5 3 0 - X
F. Hori et al. / Physica B 273}274 (1999) 480}484
481
Table 1 Summary of CZ-Si samples and the total dose of proton irradiations with energy of 10 MwV Dopant
Resistivety () cm)
Fluence (1013 p/cm2)
B B Al Ga None
10 2 10 10 862
0.3, 0.3, 0.3, 0.3, 0.3,
1, 1, 1, 1, 1,
6, 10, 6, 10, 6, 10, 6, 10, 10
20, 20, 20, 20,
50 50 50 50
of the Japan Atomic Energy Research Institute (JAERI). The total doses of proton employed in this study were lower than the previous ones used in most positron annihilation studies on proton-irradiated Si with doses above 1014 p/cm2. The penetration depths of 10 MeVprotons were calculated to be at a maximum of 700 lm. Therefore, protons were thought to penetrate and only create cascade-type defects homogeneously in all specimens. Positron annihilation c-ray energy spectrum doppler broadening measurements and positron lifetime measurements were simultaneously performed at room temperature. The isochronal annealing was carried out in a vacuum with a heating rate of 0.8 min/K. The positron source was 22NaCl of 570 kBq that was sealed by 3 lm thickness Kapton foils and sandwiched between two identical Si samples. The full-width at half-maximum (FWHM) of a resolution curve for all positron lifetime spectra with total counts of 1.1]106 was about 220 ps. To evaluate the contribution from source components, we measured the positron lifetime spectrum of FZ-Si before irradiation. All of the positron lifetime spectra were analyzed with `RESOLUTIONa and `POSITRONFITa programs by Ris+ [6]. In the analyses, the lifetime spectra could be "tted by applying a two state trapping model with su$cient precision. Observations of doppler broadening distributions using an energy dispersive Ge detector were performed. The resolutional c energy (FWHM) at 122 keV c-line of 57Co was about 581 eV. The spectrum with a total count of 3.5]107 was measured for each measurement.
3. Results and discussion 3.1. As-irradiated specimen Fig. 1 shows the #uence dependence of positron annihilation lifetimes on 10 MeV proton irradiated nondoped CZ-Si. The long lifetime component of positron q and its relative intensity I are almost unchanged with 2 2 increases in the dose of proton up to 5]1014 p/cm2. This is because low #uence irradiation induces an extremely
Fig. 1. Positron annihilation lifetime versus #uence of 10 MeV proton irradiation for non-doped CZ-Si. Filled and open circles denote the long- and short-lifetime components, respectively.
Fig. 2. Positron annihilation lifetimes q and q versus #uence 1 2 of 10 MeV proton irradiation for B, Al and Ga doped CZ-Si. Filled and open marks denote the long- and short-lifetime components, respectively.
low concentration of defects, and it is hard to decompose vacancy type defects from the positron lifetime spectra. Fig. 2 shows the result of positron lifetime measurements for B, Al and Ga doped CZ-Si after proton irradiations. In Figs. 1 and 2, a short lifetime component q1 of nearly 100 ps appeared in each case. This short lifetime component did not appear in FZ-Si before irradiation. In another positron experiment for Si with proton irradiation more than 1014 p/cm2, only long lifetime components related to vacancy clusters were detected and no indication of short lifetime components could be found [1,2].
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F. Hori et al. / Physica B 273}274 (1999) 480}484
Fig. 3. Change in S parameters versus #uence of 10 MeV proton irradiation for B (open circle), Al ("lled circle) and Ga (closed square) doped CZ-Si.
Fig. 4. Change in S parameters as a function of total dose of 10 MeV proton for B-doped CZ-Si with the resistivety of 10 and 2 ) cm.
According to the two-state trapping model, the deduced lifetime of the Si matrix from the lifetime component of defect q and its intensity I are calculated by the equa$ $ tion
The S value of the 2 ) cm sample slightly decreases with increasing #uence. This is also because the electron densities around the defects formed by irradiation depend on the amount of dopant. The value of doppler broadening S parameter for neutral charged VO (A center) has been reported larger than that for the bulk silicon, while that for VO is smaller than that for the bulk [9]. The poten2 tial energy of a positron associated with coulomb correlation and its annihilation rate are mainly related to the surrounding electron density. In a condensed oxygen cluster, the atomic density and the electron density will be higher than in the bulk Si, and hence the positron lifetime will become shorter and the S parameter will be smaller than in the bulk Si. Therefore, it is believed that complexes consisting of oxygen, dopant atoms and radiation-induced defects are formed during proton irradiation, and such complexes exhibit di!erent lifetimes and S parameters depending on the species of dopant atoms in positron annihilation experiments.
q#!- "(1!I )/(1/q !I /q ), "6-, $ & $ $
(1)
where q is the positron lifetime of bulk Si to be referred, & and q "216 ps, which is obtained for un-irradiated FZ& Si, is used in the present case. In this equation, we assume that the short lifetime component q is the defect com1 ponent, and q#!- agrees with the analyzed bulk compon"6-, ent q . Short lifetime components of positron annihila2 tion experiments for Si have been reported by Dannefear et al. [7,8]. They suggest that this type of defect is associated with oxygen clusters. Our result is in good agreement with their results. Moreover, q components in B, 1 Al and Ga doped Si are slightly higher than those in non-doped Si. Therefore, oxygen}impurity complexes most likely formed in the CZ-Si during proton irradiation with a total dose less than 5]1014 p/cm2, could be detected in the experiments. Fig. 3 shows the change in doppler broadening S parameters versus the #uence of proton irradiation. All of these S values are normalized by the value of each specimen before irradiation. The S parameter changes with the proton #uence do not have the same tendencies among B, Al and Ga doped Si. The S values slightly decreases with increase of the dose of proton irradiation only in B doped Si. This is because the electron densities around complexes depend on the species of the dopant atoms, and their charge states of the complexes are re#ected in the S value. Fig. 4 shows the changes in S parameters for specimens of B doped CZ-Si with the resistivities of 2 and 10 ) cm as a function of irradiation #uence.
3.2. Annealing experiment after irradiation Figs. 5 and 6 shows the positron lifetimes and their relative intensities for B-doped CZ-Si with electrical resistivities of 2 and 10 ) cm after 1]1013 p/cm2 proton irradiation as a function of annealing temperature. After prolonged annealing, long lifetime components corresponding to vacancy clusters appeared in both cases. A marked annealing stage varied from 527 to 552 K with increased B content. It is well known that di-vacancy migration takes place in Si around these temperature ranges. Accordingly, it is believed that this stage corresponds to the formation of larger vacancy clusters due to the clustering of free vacancies produced by the dissociation of the preexisting oxygen}vacancy-B complexes. The
F. Hori et al. / Physica B 273}274 (1999) 480}484
483
Fig. 5. Positron annihilation lifetimes q , q and its relative 1 2 intensity I after 10 MeV proton irradiation with the #uence of 2 1]1013 p/cm2 as a function of annealing temperature for Bdoped CZ-Si with the resistivety of 2 ) cm.
Fig. 6. Positron annihilation lifetimes q , q and its relative 1 2 intensity I after 10 MeV proton irradiation with the #uence of 2 1]1013 p/cm2 as a function of annealing temperature for Bdoped CZ-Si with the resistivety of 10 ) cm.
di!erence in the temperature stage by 25 K is considered to result from the amount of dopant. Therefore, it can be concluded that more dopant B atoms result in greater suppression of the dissociation and the formation of vacancy clusters. This result is in good agreement with the positron annihilation results of dopant e!ect of Si with no irradiation [10]. The present results show that radiation-induced excessive vacancies play an important role in the agglomeration of supersaturated oxygen atoms via vacancy mechanism, and also play a role in the formation of their complexes with oxygen and dopant atoms during the process of agglomeration.
centration of dopant atoms. The number of dopant atoms in the complexes increases with dopant atom concentrations. These complexes were detected only in CZ-Si irradiated with proton at low doses less than 1015 p/cm2, and vacancy-type defects were detected in the specimens with irradiation more than 1015 p/cm2 by positron techniques.
4. Conclusions The e!ect of dopant atoms on the defect complex formation in Si after low-dose proton irradiation has been investigated. In CZ-Si containing a small amount of point defects induced by low-dose proton irradiations up to 1014 p/cm2, both oxygen and dopant}related complexes were formed. These complexes account for the positron annihilation lifetimes of about 100 ps, exhibiting that the defects have higher electron densities than those in Si with no defects and impurities. Annealing stages that correspond to the dissociation of vacancies from the oxygen}vacancy}impurity complexes and the formation of larger clusters depend on the con-
Acknowledgements The authors would like to express their cordial thanks to the sta! of JAERI Takasaki facility for the proton irradiation.
References [1] A. Uedono, Y.K. Cho, S. Tanigawa, A. Ikari, Jpn. J. Appl. Phys. 33 (1994) 1. [2] S. Dannefaer, P. Mascher, D. Kerr, J. Appl. Phys. 73 (1993) 3740. [3] P. Mascher, S. Dannefaer, D. Kerr, Phys. Rev. B 40 (1989) 11764. [4] V. Avalos, S. Dannefaer, Phys. Rev. B 54 (1996) 1724. [5] G. Dlubek, C. Ascheron, R. Krause, H. Erhard, D. Klimm, Phys. Stat. Solid A 106 (1988) 81.
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F. Hori et al. / Physica B 273}274 (1999) 480}484
[6] P. Kirkegaard, M. Eldrup, O.E. Mogensen, N.J. Pedersen, Comput. Phys. Commun. 23 (1981) 307. [7] S. Dannefaer, Phys. Stat. Solid A 102 (1987) 481. [8] S. Dannefaer, D. Kerr, J. Appl. Phys. 60 (1986) 1313.
[9] A. Uedono, Y. Ujihira, A. Ikari, O. Yoda, Material Science Forum. 105}110 (1992) 1301. [10] W. Pu!, P. Mascher, D. Kerr, S. Dannefaer, Materials Science Forum. 38}41 (1989) 225.
Positron annihilation study of dopant e!ects on proton-irradiation defect in silicon F. Hori!,*, T. Chijiiwa!, R. Oshima!, T. Hisamatsu" !Research Institute for Advanced Science and Technology, Osaka Prefecture University 1-2, Gakuen-cho, Sakai, Osaka 599-8570, Japan "National Space Development Agency of Japan, Tsukuba, Ibaragi 305-8505, Japan
Abstract Positron annihilation lifetime and doppler broadening measurements have been performed to examine the e!ects of B, Al and Ga dopants of Czochralski-grown Si (CZ-Si) on defects induced by 10 MeV proton irradiations at room temperature with a total dose from 3]1012 p/cm2 to 5]1014 p/cm2. Isochronal annealing experiments were also carried out after the irradiations. In spite of the high-energy proton irradiation, a short lifetime component q of about 100 ps 1 was observed in all of the specimens, which is considered to be responsible for dopant}oxygen}vacancy complexes. The long lifetime component becomes remarkable in specimens with irradiation more than 1014 p/cm2. In isochronal annealing experiments, annealing stages at 527 and 552 K were observed for the irradiated B doped CZ-Si with resistivities of 10 and 2 )cm, respectively. This corresponds to the formation of larger vacancy clusters. We found that the formation of the vacancy}oxygen complex depends on the species of dopant atoms of silicon, especially at irradiation below 1014 p/cm2. ( 1999 Elsevier Science B.V. All rights reserved. Keywords: Positron annihilation; Silicon; Proton irradiation; Dopant atoms
1. Introduction The nature of radiation-induced vacancy-type defects in silicon has been well established by positron annihilation techniques [1}5]. High-energy particle irradiation with high #uence on the order of above 1014 p/cm2 [1,2] and 1017 e/cm2 [3,4] has mainly been used in previous experiments. Since positron annihilation experiments can detect defects with a concentration greater than the order of ppm, it is natural that few data for experiments with #uences under 1014 p/cm2 have been analyzed. On the other hand, recent studies have shown that serious problems concerning interactions between small amounts of dopants, oxygen, and point defects arise during crystal growth process such as the formation of octahedral voids. The concentrations of these defects should be
* Corresponding author: Phone: #81-722-54-9812; fax: #81-722-54-9935. E-mail address: [email protected] (F. Hori)
considerably low. The atomic concentrations of interstitial oxygen in the bulk silicon were of 9.5]1017&1.6]1018 cm~3 for CZ-Si and were of the order of 1015 cm~3 for #oat zone grown Si (FZ-Si). Dopant atom concentrations were about 4 orders of magnitude lower than those of oxygen in CZ-Si. These interactions have not been clari"ed yet. In this paper, positron annihilation experiments after low dose proton irradiation into silicon were performed to examine the interactions among oxygen, dopants and vacancy type defects. 2. Experiment CZ-Si wafers with B, Ga and Al dopants were prepared as shown in Table 1. Samples (8 mm]8 mm, 0.23 mm thick) for positron annihilation measurements were cut from the wafers. The 10 MeV-proton irradiations with total doses from 3]1012 to 5]1014 p/cm2 were performed at room temperature with an AVF cyclotron at Takasaki Radiation Chemistry Research Establishment
0921-4526/99/$ - see front matter ( 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 0 5 3 0 - X
F. Hori et al. / Physica B 273}274 (1999) 480}484
481
Table 1 Summary of CZ-Si samples and the total dose of proton irradiations with energy of 10 MwV Dopant
Resistivety () cm)
Fluence (1013 p/cm2)
B B Al Ga None
10 2 10 10 862
0.3, 0.3, 0.3, 0.3, 0.3,
1, 1, 1, 1, 1,
6, 10, 6, 10, 6, 10, 6, 10, 10
20, 20, 20, 20,
50 50 50 50
of the Japan Atomic Energy Research Institute (JAERI). The total doses of proton employed in this study were lower than the previous ones used in most positron annihilation studies on proton-irradiated Si with doses above 1014 p/cm2. The penetration depths of 10 MeVprotons were calculated to be at a maximum of 700 lm. Therefore, protons were thought to penetrate and only create cascade-type defects homogeneously in all specimens. Positron annihilation c-ray energy spectrum doppler broadening measurements and positron lifetime measurements were simultaneously performed at room temperature. The isochronal annealing was carried out in a vacuum with a heating rate of 0.8 min/K. The positron source was 22NaCl of 570 kBq that was sealed by 3 lm thickness Kapton foils and sandwiched between two identical Si samples. The full-width at half-maximum (FWHM) of a resolution curve for all positron lifetime spectra with total counts of 1.1]106 was about 220 ps. To evaluate the contribution from source components, we measured the positron lifetime spectrum of FZ-Si before irradiation. All of the positron lifetime spectra were analyzed with `RESOLUTIONa and `POSITRONFITa programs by Ris+ [6]. In the analyses, the lifetime spectra could be "tted by applying a two state trapping model with su$cient precision. Observations of doppler broadening distributions using an energy dispersive Ge detector were performed. The resolutional c energy (FWHM) at 122 keV c-line of 57Co was about 581 eV. The spectrum with a total count of 3.5]107 was measured for each measurement.
3. Results and discussion 3.1. As-irradiated specimen Fig. 1 shows the #uence dependence of positron annihilation lifetimes on 10 MeV proton irradiated nondoped CZ-Si. The long lifetime component of positron q and its relative intensity I are almost unchanged with 2 2 increases in the dose of proton up to 5]1014 p/cm2. This is because low #uence irradiation induces an extremely
Fig. 1. Positron annihilation lifetime versus #uence of 10 MeV proton irradiation for non-doped CZ-Si. Filled and open circles denote the long- and short-lifetime components, respectively.
Fig. 2. Positron annihilation lifetimes q and q versus #uence 1 2 of 10 MeV proton irradiation for B, Al and Ga doped CZ-Si. Filled and open marks denote the long- and short-lifetime components, respectively.
low concentration of defects, and it is hard to decompose vacancy type defects from the positron lifetime spectra. Fig. 2 shows the result of positron lifetime measurements for B, Al and Ga doped CZ-Si after proton irradiations. In Figs. 1 and 2, a short lifetime component q1 of nearly 100 ps appeared in each case. This short lifetime component did not appear in FZ-Si before irradiation. In another positron experiment for Si with proton irradiation more than 1014 p/cm2, only long lifetime components related to vacancy clusters were detected and no indication of short lifetime components could be found [1,2].
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F. Hori et al. / Physica B 273}274 (1999) 480}484
Fig. 3. Change in S parameters versus #uence of 10 MeV proton irradiation for B (open circle), Al ("lled circle) and Ga (closed square) doped CZ-Si.
Fig. 4. Change in S parameters as a function of total dose of 10 MeV proton for B-doped CZ-Si with the resistivety of 10 and 2 ) cm.
According to the two-state trapping model, the deduced lifetime of the Si matrix from the lifetime component of defect q and its intensity I are calculated by the equa$ $ tion
The S value of the 2 ) cm sample slightly decreases with increasing #uence. This is also because the electron densities around the defects formed by irradiation depend on the amount of dopant. The value of doppler broadening S parameter for neutral charged VO (A center) has been reported larger than that for the bulk silicon, while that for VO is smaller than that for the bulk [9]. The poten2 tial energy of a positron associated with coulomb correlation and its annihilation rate are mainly related to the surrounding electron density. In a condensed oxygen cluster, the atomic density and the electron density will be higher than in the bulk Si, and hence the positron lifetime will become shorter and the S parameter will be smaller than in the bulk Si. Therefore, it is believed that complexes consisting of oxygen, dopant atoms and radiation-induced defects are formed during proton irradiation, and such complexes exhibit di!erent lifetimes and S parameters depending on the species of dopant atoms in positron annihilation experiments.
q#!- "(1!I )/(1/q !I /q ), "6-, $ & $ $
(1)
where q is the positron lifetime of bulk Si to be referred, & and q "216 ps, which is obtained for un-irradiated FZ& Si, is used in the present case. In this equation, we assume that the short lifetime component q is the defect com1 ponent, and q#!- agrees with the analyzed bulk compon"6-, ent q . Short lifetime components of positron annihila2 tion experiments for Si have been reported by Dannefear et al. [7,8]. They suggest that this type of defect is associated with oxygen clusters. Our result is in good agreement with their results. Moreover, q components in B, 1 Al and Ga doped Si are slightly higher than those in non-doped Si. Therefore, oxygen}impurity complexes most likely formed in the CZ-Si during proton irradiation with a total dose less than 5]1014 p/cm2, could be detected in the experiments. Fig. 3 shows the change in doppler broadening S parameters versus the #uence of proton irradiation. All of these S values are normalized by the value of each specimen before irradiation. The S parameter changes with the proton #uence do not have the same tendencies among B, Al and Ga doped Si. The S values slightly decreases with increase of the dose of proton irradiation only in B doped Si. This is because the electron densities around complexes depend on the species of the dopant atoms, and their charge states of the complexes are re#ected in the S value. Fig. 4 shows the changes in S parameters for specimens of B doped CZ-Si with the resistivities of 2 and 10 ) cm as a function of irradiation #uence.
3.2. Annealing experiment after irradiation Figs. 5 and 6 shows the positron lifetimes and their relative intensities for B-doped CZ-Si with electrical resistivities of 2 and 10 ) cm after 1]1013 p/cm2 proton irradiation as a function of annealing temperature. After prolonged annealing, long lifetime components corresponding to vacancy clusters appeared in both cases. A marked annealing stage varied from 527 to 552 K with increased B content. It is well known that di-vacancy migration takes place in Si around these temperature ranges. Accordingly, it is believed that this stage corresponds to the formation of larger vacancy clusters due to the clustering of free vacancies produced by the dissociation of the preexisting oxygen}vacancy-B complexes. The
F. Hori et al. / Physica B 273}274 (1999) 480}484
483
Fig. 5. Positron annihilation lifetimes q , q and its relative 1 2 intensity I after 10 MeV proton irradiation with the #uence of 2 1]1013 p/cm2 as a function of annealing temperature for Bdoped CZ-Si with the resistivety of 2 ) cm.
Fig. 6. Positron annihilation lifetimes q , q and its relative 1 2 intensity I after 10 MeV proton irradiation with the #uence of 2 1]1013 p/cm2 as a function of annealing temperature for Bdoped CZ-Si with the resistivety of 10 ) cm.
di!erence in the temperature stage by 25 K is considered to result from the amount of dopant. Therefore, it can be concluded that more dopant B atoms result in greater suppression of the dissociation and the formation of vacancy clusters. This result is in good agreement with the positron annihilation results of dopant e!ect of Si with no irradiation [10]. The present results show that radiation-induced excessive vacancies play an important role in the agglomeration of supersaturated oxygen atoms via vacancy mechanism, and also play a role in the formation of their complexes with oxygen and dopant atoms during the process of agglomeration.
centration of dopant atoms. The number of dopant atoms in the complexes increases with dopant atom concentrations. These complexes were detected only in CZ-Si irradiated with proton at low doses less than 1015 p/cm2, and vacancy-type defects were detected in the specimens with irradiation more than 1015 p/cm2 by positron techniques.
4. Conclusions The e!ect of dopant atoms on the defect complex formation in Si after low-dose proton irradiation has been investigated. In CZ-Si containing a small amount of point defects induced by low-dose proton irradiations up to 1014 p/cm2, both oxygen and dopant}related complexes were formed. These complexes account for the positron annihilation lifetimes of about 100 ps, exhibiting that the defects have higher electron densities than those in Si with no defects and impurities. Annealing stages that correspond to the dissociation of vacancies from the oxygen}vacancy}impurity complexes and the formation of larger clusters depend on the con-
Acknowledgements The authors would like to express their cordial thanks to the sta! of JAERI Takasaki facility for the proton irradiation.
References [1] A. Uedono, Y.K. Cho, S. Tanigawa, A. Ikari, Jpn. J. Appl. Phys. 33 (1994) 1. [2] S. Dannefaer, P. Mascher, D. Kerr, J. Appl. Phys. 73 (1993) 3740. [3] P. Mascher, S. Dannefaer, D. Kerr, Phys. Rev. B 40 (1989) 11764. [4] V. Avalos, S. Dannefaer, Phys. Rev. B 54 (1996) 1724. [5] G. Dlubek, C. Ascheron, R. Krause, H. Erhard, D. Klimm, Phys. Stat. Solid A 106 (1988) 81.
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F. Hori et al. / Physica B 273}274 (1999) 480}484
[6] P. Kirkegaard, M. Eldrup, O.E. Mogensen, N.J. Pedersen, Comput. Phys. Commun. 23 (1981) 307. [7] S. Dannefaer, Phys. Stat. Solid A 102 (1987) 481. [8] S. Dannefaer, D. Kerr, J. Appl. Phys. 60 (1986) 1313.
[9] A. Uedono, Y. Ujihira, A. Ikari, O. Yoda, Material Science Forum. 105}110 (1992) 1301. [10] W. Pu!, P. Mascher, D. Kerr, S. Dannefaer, Materials Science Forum. 38}41 (1989) 225.