- Email: [email protected]
Crystallographic analysis of extended defects in diamond-type crystals
Nuclear Instruments and Methods in Physics Research B 232 (2005) 322–326 www.elsevier.com/locate/nimb
Crystallographic analysis of extended defects in diamond-type crystals S.T. Nakagawa
a,*
, K. Ikuse a, T. Ono b, H.J. Whitlow
c,d
, G. Betz
e
a Graduate School of Science, Okayama University of Science, Okayama 700-0005, Japan Graduate School of Information, Okayama University of Science, Okayama 700-0005, Japan c Department of Physics, University of Jyva¨skyla¨, FIN-40014, Finland d School of Technology and Society, Malmo¨ University, SE-205 06 Malmo¨, Sweden Institut fu¨r Allgemeine Physik, Technische Universita¨t Wien, Wiedner Hauptstraße 8-10, A-1040 Wien, Austria b
e
Available online 23 May 2005
Abstract To investigate irradiation-induced Si amorphization during its initial stages, we have performed a classical molecular-dynamics (MD) calculation for the case of self-irradiation by 5 keV ions at a low temperature of 100 K. We examined the geometry of self-interstitial atom (SIA) clusters using the pixel mapping (PM) method, on the output data of MD calculations. Perfect crystalline silicon (c-Si) is amorphized by self-irradiation, and we observe that many SIA are produced. During sequential self-irradiation, the most frequently observed species were isolated SIA, i.e. I1 (monomer). The fractions of SIA clusters decreased as I2 (dimer), I3 (trimer), and I4 (tetramer) clusters, respectively. For I2 clusters, the h1 1 0i oriented I2Õs were the dominant I2 species, which agree with previous predictions based on static calculations. Nevertheless, other I2Õs with different orientations were also significant. Some of them have been proposed as intermediate I2Õs in forming dislocations. The present results imply that irradiation-induced SIAÕs play an important role in the triggering of amorphization, and MD combined with PM can reveal the intermediate processes underlying extended-defect formation. 2005 Elsevier B.V. All rights reserved. PACS: 61.50.Ah; 31.15.Qg; 68.35.Rh; 61.72.y Keywords: Amorphization; c-Si; Self-irradiation; Long-range-order interaction; Self-interstitial atom cluster; Molecular-dynamics
1. Introduction *
Corresponding author. Tel./fax: +81 86 256 9458. E-mail address: [email protected] (S.T. Nakagawa).
Ion beam irradiation at kiloelectronvolt energies instigates radiation damage in crystalline materials by creation of point defects that are
0168-583X/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2005.03.066
S.T. Nakagawa et al. / Nucl. Instr. and Meth. in Phys. Res. B 232 (2005) 322–326
self-interstitial atoms (SIA) and vacancies. Some of these are annihilated by recombination. The isolated primary defects may combine to create extended-defects, such as linear and planar defects and eventually cause amorphization of a crystalline target. The outcome is strongly affected by the temperature of the host target. In the case of crystalline silicon (c-Si), Seidman et al. [1] first emphasized the role of SIA and SIA clusters in amorphization (SIA cluster model). Other models are the vacancy–interstitial complex of Tang et al. [2], the combination of a vacancy– interstitial complex and SIAÕs by Marque´s et al. [3], formation of di-vacancy and di-interstitial pairs by Motooka [4], and more. Here we examine the SIA cluster model, with respect to the spatial orientation and location of the SIA clusters in c-Si. Watkins et al. [5] first proposed an interstitial cluster a ‘‘split-I2 (dimer)’’ of a carbon I2 in c-Si, which expands into the h1 0 0i and h1 1 0i directions. Later Tan [6] adopted the model of the ‘‘split-I2’’ comprised of SIAÕs in c-Si, to investigate the process of dislocation formation that occurs on habit planes, from which epitaxial growth starts. During dislocation formation, I2 with other orientations also emerged intermediately, e.g. h1 1 1i and h1 1 2i. Predictions of h1 0 0i oriented I2 have also been presented [7]. Energy minimization calculations based on ab initio methods supported the h1 1 0i model [8,9], with the presence of excess SIAÕs. Furthermore, an equilateral triangle I3 on a (1 1 1) plane [9–11], and a square I4 on a (1 0 0) plane [7,11] were modeled. The closest distance, rc, between atoms within such an SIA cluster is not always well defined. For example, for a h1 1 0i split-I2 on the (1 1 0) planes, rc has been given as +5% [9], +9% [12] +10% [8] of the equilib˚ ). In the case of square rium distance (r0 = 2.35 A I4 on a (1 0 0) plane, rc is shorter than r0 by 1.8% [7]. It has always been problematic, if energy minimization static calculations can reproduce the non-equilibrium phenomena occurring under ion bombardment. To unravel the triggering of amorphization and to identify what kind of SIA clusters will be preferably produced under ion bombardment we performed a molecular-dynamics (MD) [13] simulation.
323
2. Method: pixel mapping (PM) to analyze extended-defects in a crystal The self-irradiation of c-Si was simulated by means of a classical MD calculation [13]. The MD (cubic) box containing 1728 Si atoms was taken to be well-embedded in bulk c-Si. Thus we assume that energetic Si ions (a few 10 keV) hit the crystal and loose energy until they reach our MD box along their range where their energy has decreased to 5 keV [13]. We assume the Si ion projectiles with energy of 5 keV impinge normally on the (1 0 0) surface of the MD box. Most of them penetrate the MD box, producing many defects on their way through. The Tersoff-3 interatomic potential [14] was assumed to describe the interaction among Si atoms. While this is strictly a near-equilibrium potential the 2-body term was splined to a ZBL core potential so the composite potential is expected to intuitively behave in a realistic manner even for close atoms. The temperature inside the box was set at 100 K. Prior to the first ion impact the atoms in the box were thermalized at 100 K for 3 ps. After each ion impact, we wait until the target becomes thermally stabilized (about 10–20 ps) before PM analysis [13] and subsequent ion impingement. PM is a crystallographic method that can characterize the atomistic defects in a crystal, from the spatial distribution of atoms in a crystalline target, such as those obtained from MD calculations. PM can reveal crystalline to amorphous (CA) transition, by quantifying the degree of long-range-order of a crystal [15], and also identify SIAÕs as atoms not sited in a stable pixel, whose center coincides with a regular lattice point [16]. The long-range order is characterized by the fraction of those pixels corresponding to a perfect crystal that contain an atom. Moreover, the PM method can identify extended-defects by using vector analysis, because the PM labels the address of each atom with a set of three-integers [15]. The detailed explanation and further applications will be covered elsewhere. The first step to analyze extended-defects is to seek the ‘‘neighboring-SIA’’ in different atomic planes. If an SIA cluster has a flat structure, like an equilateral triangle I3 in (1 1 1) [9] or a square I4 in (1 0 0)
324
S.T. Nakagawa et al. / Nucl. Instr. and Meth. in Phys. Res. B 232 (2005) 322–326
[7], PM can detect those planes uniquely. Note that the number of physically meaningful atomic planes is not infinite, but habit planes with low Miller-indices {g, j, k} may be important for SIA forming extended-defects in a plane. The principle habit planes for Si are {3 1 1}, {2 1 1}, and {1 1 1}. Therefore we take the upper limit of ‘‘3’’ for the component indices g, j, k. This condition covers most of important atomic planes. In practice this is done by slicing the MD box into parallel slabs of significant atomic planes, and testing to see if neighboring SIAÕs lie in the planes. The second step is to find the intersecting vector between the two atomic planes. This intersecting vector then uniquely defines the orientation of the SIA cluster. This approach of determining the atomic planes and the intersecting vectors is powerful approach because it mathematically defines the surface of a polyhedral SIA cluster.
Fig. 1. PM profiling for Si self-implantation at 5 keV up to the 50th impact. The solid lines, thin dotted line and thick broken lines indicate the long-range order parameters that show the fraction of atoms at stable, unstable and metastable pixels, respectively, see [15].
3. Results 3.1. The definition of an SIA cluster A key issue is the definition of if a SIA is part of a cluster, or not. This is done by determining if the closest distance between SIAÕs does not exceed a threshold value, rc. In previous calculations, the probable value of rc, ranged from 5% [9] to +10% [8] of r0. We calculated using MD the radial distribution function g(r) of SIAÕs, with 5% of randomly distributed excess SIAÕs. The initial locations of the excess SIAÕs depend on the seed number of the random number generator, thus we averaged over many calculations, using different seed numbers. From the g(r), we took the criterion, rc < 1.05r0 to determine if a pair of SIA belongs to the same SIA cluster. 3.2. SIA clusters produced by ion impact, without excess SIA’s In Section 3.1 we did not consider the effect of ion irradiation. In order to study the amorphization process, we performed a MD calculation for self-irradiation with 5 keV Si ions in c-Si. No excess SIA were introduced. Fig. 1 shows a typical
PM profiling of CA transition, for sequential ion impacts. The two solid lines indicate the fraction of atoms accommodated at regular lattice points, while all the other lines indicate that of SIAÕs. At the onset of irradiation, most of the Si atoms remain on regular lattice sites, as shown by the initial value of 0.5 for the two solid lines [15]. With increasing ion fluence the solid lines indicative of long range order signal decrease whilst the other signals increased. (Fig. 1) PM profiling finally showed an amorphous state, where all Si atoms are distributed uniformly in a Si target. For all calculations, with different seed numbers, Si amorphization was always completed before the 50th impact, as illustrated in Fig. 1. We took the initial stage of amorphization to correspond on average to the 25th impact. (An ion fluence of 2 · 1014 ions/cm2.) It can be seen from Fig. 1 there is a sharp rise in the number of SIAÕs produced at the CA transition. The dominant fraction of SIAÕs was I1 (single SIA). The number of I2 (dimer) and I3 (trimer) clusters decreased, respectively. It is emphasized that we count the number of the neighboring SIAÕs and not that of net increase of SIA as is the case for static calculations.
S.T. Nakagawa et al. / Nucl. Instr. and Meth. in Phys. Res. B 232 (2005) 322–326 Table 1 Dimers produced with low indices in the MD box under two different conditions: (a) No ion impacts but initial 5% surplus Si atoms (b) With ion impacts and initially no surplus Si atoms Dimer orientation
SIA induced no ion impacts 5% (+86 Si)
SIA induced 5 keV impacts 0% (+0 Si)
h1 0 0i h1 1 0i h1 1 1i h1 1 2i Average number of SIA dimers formed in the MD box with 1728 Si atoms)
5.6% 38.7% 41.8% 14.0% 5.8
35.2% 40.0% 19.8% 5.0% 8.5
3.3. Determination of the geometry of SIA clusters after ion impacts using PM Although I3 and I4 clusters appeared in our calculations, they could not be assigned to specific planes or directions. The longest line defect observed was I3. In Table 1 we summarize the favored orientations of I2 focusing on low indices. Four different orientations were found. The h1 1 0i oriented I2 has been thought to be the most probable dimer [8,9,12], followed by h1 0 0i [5,7]. The h1 1 1i and h1 1 2i oriented dimers have been proposed as intermediate SIA clusters during the dislocation formation [6]. The last column shows the result after irradiation with an ion fluence of 2 · 1014 ions/cm2. The h1 1 0i oriented I2Õs dominate, followed h1 0 0i oriented I2Õs. The h1 1 1i and h1 1 2i oriented I2 were also observed in small numbers. The h1 1 2i oriented I2 have been omitted as insignificant from previous papers.
4. Conclusions By developing a crystallographic PM method, we have examined the extended-defects caused by ion bombardment in crystalline silicon (c-Si). Our purpose was to examine the triggering of amorphization caused by ion bombardment, according to the SIA (self-interstitial atoms)
325
cluster model, with the help of a classical molecular-dynamics calculation. We studied the geometry of SIA clusters at 100 K. For ion induced amorphization there is a significant rise in the number of SIAÕs at a fluence corresponding to the CA transition. Although most SIAÕs were isolated, we detected I2Õs along h1 1 0i, h1 0 0i, h1 1 1i orientations, with respectively decreasing fractions. The dynamic simulation showed that not only the often-predicted h1 1 0i oriented I2 is important, but also I2Õs with different orientations, which have been suggested as intermediates of I2 clusters [6] in dislocation formation, are also significant during the onset of amorphization.
Acknowledgements The authors are indebted to the financial support from the Frontier Project of the Ministry of Education, Culture, Sports, Science and Technology of Japan. H.J.W. is grateful for support from the Japan Society for Promotion of Science, ref. RC 20349103.
References [1] D.N. Seidman, R.S. Averback, P.R. Okamoto, A.C. Baily, Phys. Rev. Lett. 58 (1987) 900. [2] M. Tang, L. Colombo, J. Zhu, T.D. de la Rubia, Phys. Rev. B 55 (1997) 14279. [3] L. Marque´s, L. Pelaz, J. Herna´ndez, J. Barbolla, G.H. Gilmer, Phys. Rev. B 64 (2001) 045214. [4] T. Motooka, Phys. Rev. B 49 (1994) 16367. [5] G.D. Watkins, R.P. Messmer, C. Weigel, D. Peak, J.W. Corbett, Phys. Rev. Lett. 27 (1971) 1573. [6] T.Y. Tan, Philos. Mag. A 44 (1981) 101. [7] S. Takeda, J. Yamazaki, Phys. Rev. Lett. 83 (1999) 320; See also, N. Arai, S. Takeda, M. Kohyama, Phys. Rev. Lett. 78 (1997) 4265. [8] D.J. Chadi, Phys. Rev. B 46 (1992) 9400. [9] M. Gharaibeh, S.K. Estreicher, P.A. Fedders, Physica B 273–274 (1999) 532. [10] S.K. Erstreicher, M. Gharaibeh, P.A. Fedders, P. Ordeion, Phys. Rev. Lett. 86 (2001) 1247. [11] R. Jones, T.A.G. Eberlein, N. Pinho, B.J. Coomer, J.P. ¨ berg, Nucl. Instr. and Meth. B Goss, P.R. Briddon, S. O 186 (2002) 10.
326
S.T. Nakagawa et al. / Nucl. Instr. and Meth. in Phys. Res. B 232 (2005) 322–326
[12] H.R. Schober, Phys. Rev. B 39 (1989) 13013. [13] S.T. Nakagawa, G. Betz, Nucl. Instr. and Meth. B 180 (2001) 91. [14] J. Tersoff, Phys. Rev. B 38 (1988) 9902.
[15] S.T. Nakagawa, Phys. Rev. B 66 (2002) 094103/1–094103/ 7; See also, S.T. Nakagawa, Physica B 308–310 (2001) 272. [16] S.T. Nakagawa, Nucl. Instr. and Meth. B 206 (2003) 13.
Crystallographic analysis of extended defects in diamond-type crystals S.T. Nakagawa
a,*
, K. Ikuse a, T. Ono b, H.J. Whitlow
c,d
, G. Betz
e
a Graduate School of Science, Okayama University of Science, Okayama 700-0005, Japan Graduate School of Information, Okayama University of Science, Okayama 700-0005, Japan c Department of Physics, University of Jyva¨skyla¨, FIN-40014, Finland d School of Technology and Society, Malmo¨ University, SE-205 06 Malmo¨, Sweden Institut fu¨r Allgemeine Physik, Technische Universita¨t Wien, Wiedner Hauptstraße 8-10, A-1040 Wien, Austria b
e
Available online 23 May 2005
Abstract To investigate irradiation-induced Si amorphization during its initial stages, we have performed a classical molecular-dynamics (MD) calculation for the case of self-irradiation by 5 keV ions at a low temperature of 100 K. We examined the geometry of self-interstitial atom (SIA) clusters using the pixel mapping (PM) method, on the output data of MD calculations. Perfect crystalline silicon (c-Si) is amorphized by self-irradiation, and we observe that many SIA are produced. During sequential self-irradiation, the most frequently observed species were isolated SIA, i.e. I1 (monomer). The fractions of SIA clusters decreased as I2 (dimer), I3 (trimer), and I4 (tetramer) clusters, respectively. For I2 clusters, the h1 1 0i oriented I2Õs were the dominant I2 species, which agree with previous predictions based on static calculations. Nevertheless, other I2Õs with different orientations were also significant. Some of them have been proposed as intermediate I2Õs in forming dislocations. The present results imply that irradiation-induced SIAÕs play an important role in the triggering of amorphization, and MD combined with PM can reveal the intermediate processes underlying extended-defect formation. 2005 Elsevier B.V. All rights reserved. PACS: 61.50.Ah; 31.15.Qg; 68.35.Rh; 61.72.y Keywords: Amorphization; c-Si; Self-irradiation; Long-range-order interaction; Self-interstitial atom cluster; Molecular-dynamics
1. Introduction *
Corresponding author. Tel./fax: +81 86 256 9458. E-mail address: [email protected] (S.T. Nakagawa).
Ion beam irradiation at kiloelectronvolt energies instigates radiation damage in crystalline materials by creation of point defects that are
0168-583X/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2005.03.066
S.T. Nakagawa et al. / Nucl. Instr. and Meth. in Phys. Res. B 232 (2005) 322–326
self-interstitial atoms (SIA) and vacancies. Some of these are annihilated by recombination. The isolated primary defects may combine to create extended-defects, such as linear and planar defects and eventually cause amorphization of a crystalline target. The outcome is strongly affected by the temperature of the host target. In the case of crystalline silicon (c-Si), Seidman et al. [1] first emphasized the role of SIA and SIA clusters in amorphization (SIA cluster model). Other models are the vacancy–interstitial complex of Tang et al. [2], the combination of a vacancy– interstitial complex and SIAÕs by Marque´s et al. [3], formation of di-vacancy and di-interstitial pairs by Motooka [4], and more. Here we examine the SIA cluster model, with respect to the spatial orientation and location of the SIA clusters in c-Si. Watkins et al. [5] first proposed an interstitial cluster a ‘‘split-I2 (dimer)’’ of a carbon I2 in c-Si, which expands into the h1 0 0i and h1 1 0i directions. Later Tan [6] adopted the model of the ‘‘split-I2’’ comprised of SIAÕs in c-Si, to investigate the process of dislocation formation that occurs on habit planes, from which epitaxial growth starts. During dislocation formation, I2 with other orientations also emerged intermediately, e.g. h1 1 1i and h1 1 2i. Predictions of h1 0 0i oriented I2 have also been presented [7]. Energy minimization calculations based on ab initio methods supported the h1 1 0i model [8,9], with the presence of excess SIAÕs. Furthermore, an equilateral triangle I3 on a (1 1 1) plane [9–11], and a square I4 on a (1 0 0) plane [7,11] were modeled. The closest distance, rc, between atoms within such an SIA cluster is not always well defined. For example, for a h1 1 0i split-I2 on the (1 1 0) planes, rc has been given as +5% [9], +9% [12] +10% [8] of the equilib˚ ). In the case of square rium distance (r0 = 2.35 A I4 on a (1 0 0) plane, rc is shorter than r0 by 1.8% [7]. It has always been problematic, if energy minimization static calculations can reproduce the non-equilibrium phenomena occurring under ion bombardment. To unravel the triggering of amorphization and to identify what kind of SIA clusters will be preferably produced under ion bombardment we performed a molecular-dynamics (MD) [13] simulation.
323
2. Method: pixel mapping (PM) to analyze extended-defects in a crystal The self-irradiation of c-Si was simulated by means of a classical MD calculation [13]. The MD (cubic) box containing 1728 Si atoms was taken to be well-embedded in bulk c-Si. Thus we assume that energetic Si ions (a few 10 keV) hit the crystal and loose energy until they reach our MD box along their range where their energy has decreased to 5 keV [13]. We assume the Si ion projectiles with energy of 5 keV impinge normally on the (1 0 0) surface of the MD box. Most of them penetrate the MD box, producing many defects on their way through. The Tersoff-3 interatomic potential [14] was assumed to describe the interaction among Si atoms. While this is strictly a near-equilibrium potential the 2-body term was splined to a ZBL core potential so the composite potential is expected to intuitively behave in a realistic manner even for close atoms. The temperature inside the box was set at 100 K. Prior to the first ion impact the atoms in the box were thermalized at 100 K for 3 ps. After each ion impact, we wait until the target becomes thermally stabilized (about 10–20 ps) before PM analysis [13] and subsequent ion impingement. PM is a crystallographic method that can characterize the atomistic defects in a crystal, from the spatial distribution of atoms in a crystalline target, such as those obtained from MD calculations. PM can reveal crystalline to amorphous (CA) transition, by quantifying the degree of long-range-order of a crystal [15], and also identify SIAÕs as atoms not sited in a stable pixel, whose center coincides with a regular lattice point [16]. The long-range order is characterized by the fraction of those pixels corresponding to a perfect crystal that contain an atom. Moreover, the PM method can identify extended-defects by using vector analysis, because the PM labels the address of each atom with a set of three-integers [15]. The detailed explanation and further applications will be covered elsewhere. The first step to analyze extended-defects is to seek the ‘‘neighboring-SIA’’ in different atomic planes. If an SIA cluster has a flat structure, like an equilateral triangle I3 in (1 1 1) [9] or a square I4 in (1 0 0)
324
S.T. Nakagawa et al. / Nucl. Instr. and Meth. in Phys. Res. B 232 (2005) 322–326
[7], PM can detect those planes uniquely. Note that the number of physically meaningful atomic planes is not infinite, but habit planes with low Miller-indices {g, j, k} may be important for SIA forming extended-defects in a plane. The principle habit planes for Si are {3 1 1}, {2 1 1}, and {1 1 1}. Therefore we take the upper limit of ‘‘3’’ for the component indices g, j, k. This condition covers most of important atomic planes. In practice this is done by slicing the MD box into parallel slabs of significant atomic planes, and testing to see if neighboring SIAÕs lie in the planes. The second step is to find the intersecting vector between the two atomic planes. This intersecting vector then uniquely defines the orientation of the SIA cluster. This approach of determining the atomic planes and the intersecting vectors is powerful approach because it mathematically defines the surface of a polyhedral SIA cluster.
Fig. 1. PM profiling for Si self-implantation at 5 keV up to the 50th impact. The solid lines, thin dotted line and thick broken lines indicate the long-range order parameters that show the fraction of atoms at stable, unstable and metastable pixels, respectively, see [15].
3. Results 3.1. The definition of an SIA cluster A key issue is the definition of if a SIA is part of a cluster, or not. This is done by determining if the closest distance between SIAÕs does not exceed a threshold value, rc. In previous calculations, the probable value of rc, ranged from 5% [9] to +10% [8] of r0. We calculated using MD the radial distribution function g(r) of SIAÕs, with 5% of randomly distributed excess SIAÕs. The initial locations of the excess SIAÕs depend on the seed number of the random number generator, thus we averaged over many calculations, using different seed numbers. From the g(r), we took the criterion, rc < 1.05r0 to determine if a pair of SIA belongs to the same SIA cluster. 3.2. SIA clusters produced by ion impact, without excess SIA’s In Section 3.1 we did not consider the effect of ion irradiation. In order to study the amorphization process, we performed a MD calculation for self-irradiation with 5 keV Si ions in c-Si. No excess SIA were introduced. Fig. 1 shows a typical
PM profiling of CA transition, for sequential ion impacts. The two solid lines indicate the fraction of atoms accommodated at regular lattice points, while all the other lines indicate that of SIAÕs. At the onset of irradiation, most of the Si atoms remain on regular lattice sites, as shown by the initial value of 0.5 for the two solid lines [15]. With increasing ion fluence the solid lines indicative of long range order signal decrease whilst the other signals increased. (Fig. 1) PM profiling finally showed an amorphous state, where all Si atoms are distributed uniformly in a Si target. For all calculations, with different seed numbers, Si amorphization was always completed before the 50th impact, as illustrated in Fig. 1. We took the initial stage of amorphization to correspond on average to the 25th impact. (An ion fluence of 2 · 1014 ions/cm2.) It can be seen from Fig. 1 there is a sharp rise in the number of SIAÕs produced at the CA transition. The dominant fraction of SIAÕs was I1 (single SIA). The number of I2 (dimer) and I3 (trimer) clusters decreased, respectively. It is emphasized that we count the number of the neighboring SIAÕs and not that of net increase of SIA as is the case for static calculations.
S.T. Nakagawa et al. / Nucl. Instr. and Meth. in Phys. Res. B 232 (2005) 322–326 Table 1 Dimers produced with low indices in the MD box under two different conditions: (a) No ion impacts but initial 5% surplus Si atoms (b) With ion impacts and initially no surplus Si atoms Dimer orientation
SIA induced no ion impacts 5% (+86 Si)
SIA induced 5 keV impacts 0% (+0 Si)
h1 0 0i h1 1 0i h1 1 1i h1 1 2i Average number of SIA dimers formed in the MD box with 1728 Si atoms)
5.6% 38.7% 41.8% 14.0% 5.8
35.2% 40.0% 19.8% 5.0% 8.5
3.3. Determination of the geometry of SIA clusters after ion impacts using PM Although I3 and I4 clusters appeared in our calculations, they could not be assigned to specific planes or directions. The longest line defect observed was I3. In Table 1 we summarize the favored orientations of I2 focusing on low indices. Four different orientations were found. The h1 1 0i oriented I2 has been thought to be the most probable dimer [8,9,12], followed by h1 0 0i [5,7]. The h1 1 1i and h1 1 2i oriented dimers have been proposed as intermediate SIA clusters during the dislocation formation [6]. The last column shows the result after irradiation with an ion fluence of 2 · 1014 ions/cm2. The h1 1 0i oriented I2Õs dominate, followed h1 0 0i oriented I2Õs. The h1 1 1i and h1 1 2i oriented I2 were also observed in small numbers. The h1 1 2i oriented I2 have been omitted as insignificant from previous papers.
4. Conclusions By developing a crystallographic PM method, we have examined the extended-defects caused by ion bombardment in crystalline silicon (c-Si). Our purpose was to examine the triggering of amorphization caused by ion bombardment, according to the SIA (self-interstitial atoms)
325
cluster model, with the help of a classical molecular-dynamics calculation. We studied the geometry of SIA clusters at 100 K. For ion induced amorphization there is a significant rise in the number of SIAÕs at a fluence corresponding to the CA transition. Although most SIAÕs were isolated, we detected I2Õs along h1 1 0i, h1 0 0i, h1 1 1i orientations, with respectively decreasing fractions. The dynamic simulation showed that not only the often-predicted h1 1 0i oriented I2 is important, but also I2Õs with different orientations, which have been suggested as intermediates of I2 clusters [6] in dislocation formation, are also significant during the onset of amorphization.
Acknowledgements The authors are indebted to the financial support from the Frontier Project of the Ministry of Education, Culture, Sports, Science and Technology of Japan. H.J.W. is grateful for support from the Japan Society for Promotion of Science, ref. RC 20349103.
References [1] D.N. Seidman, R.S. Averback, P.R. Okamoto, A.C. Baily, Phys. Rev. Lett. 58 (1987) 900. [2] M. Tang, L. Colombo, J. Zhu, T.D. de la Rubia, Phys. Rev. B 55 (1997) 14279. [3] L. Marque´s, L. Pelaz, J. Herna´ndez, J. Barbolla, G.H. Gilmer, Phys. Rev. B 64 (2001) 045214. [4] T. Motooka, Phys. Rev. B 49 (1994) 16367. [5] G.D. Watkins, R.P. Messmer, C. Weigel, D. Peak, J.W. Corbett, Phys. Rev. Lett. 27 (1971) 1573. [6] T.Y. Tan, Philos. Mag. A 44 (1981) 101. [7] S. Takeda, J. Yamazaki, Phys. Rev. Lett. 83 (1999) 320; See also, N. Arai, S. Takeda, M. Kohyama, Phys. Rev. Lett. 78 (1997) 4265. [8] D.J. Chadi, Phys. Rev. B 46 (1992) 9400. [9] M. Gharaibeh, S.K. Estreicher, P.A. Fedders, Physica B 273–274 (1999) 532. [10] S.K. Erstreicher, M. Gharaibeh, P.A. Fedders, P. Ordeion, Phys. Rev. Lett. 86 (2001) 1247. [11] R. Jones, T.A.G. Eberlein, N. Pinho, B.J. Coomer, J.P. ¨ berg, Nucl. Instr. and Meth. B Goss, P.R. Briddon, S. O 186 (2002) 10.
326
S.T. Nakagawa et al. / Nucl. Instr. and Meth. in Phys. Res. B 232 (2005) 322–326
[12] H.R. Schober, Phys. Rev. B 39 (1989) 13013. [13] S.T. Nakagawa, G. Betz, Nucl. Instr. and Meth. B 180 (2001) 91. [14] J. Tersoff, Phys. Rev. B 38 (1988) 9902.
[15] S.T. Nakagawa, Phys. Rev. B 66 (2002) 094103/1–094103/ 7; See also, S.T. Nakagawa, Physica B 308–310 (2001) 272. [16] S.T. Nakagawa, Nucl. Instr. and Meth. B 206 (2003) 13.