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Stability of Frenkel pairs in Si(1 0 0) surface in the presence of germanium and oxygen atoms
Microelectronic Engineering 88 (2011) 503–505
Contents lists available at ScienceDirect
Microelectronic Engineering journal homepage: www.elsevier.com/locate/mee
Stability of Frenkel pairs in Si(1 0 0) surface in the presence of germanium and oxygen atoms S. Fetah a,b,c,d,⇑, A. Chikouche f, A. Dkhissi c,d, G. Landa c,d, P. Pochet e a
Université de Sétif UFAS, Faculté des sciences, Département de physique, Sétif, Algeria Laboratoire d’analyse et traitement des signaux, Université de M’sila, Algeria c CNRS, LAAS, 7 avenue du colonel Roche, F-31077 Toulouse, France d Université de Toulouse, UPS, INSA, INP, ISAE, LAAS, F-31077 Toulouse, France e Laboratoire de Simulation Atomistique (L_Sim), SP2M, INAC, CEA-UJF, 38054 Grenoble Cedex 9, France f Unité de Développement d’Equipements Solaires (UDES), 42415 Tipaza, Algeria b
a r t i c l e
i n f o
Article history: Available online 9 December 2010 Keywords: Si(1 0 0) Point defect Si interstitial Frenkel pairs DFT calculations Formation energy
a b s t r a c t A first-principles pseudo-potential study of Frenkel pair generation close to the Si(1 0 0) surface in the presence of germanium and oxygen atoms is reported. The energies and structures of the defect structures (i.e. vacancy and relaxed tetrahedral Si interstitial) are calculated using supercell with up to 88 atoms. We present results obtained using the generalized gradient approximation (GGA) for the exchange–correlation energy. We examine the effect of the presence of germanium and oxygen atoms on the stability of Frenkel pairs generated near the Si(1 0 0) surface by comparing a number of individual cases, starting from vacancy interstitial pairs situated at various positions. The general tendency of the created interstitials is to climb towards the surface, but they generally remain in subsurface layers, ready to migrate into the layer. This tendency is enhanced by the presence of the Ge and/or O atoms. We show that the formation energy is lower and Si interstitials can be created with energies as low as 1.5 eV. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction The incorporation of Ge into modern Si-based electronics has generated a renewed interest in the detailed understanding of diffusion processes during Si devices processing. For example, the presence of Ge affects dopant diffusion, metallization, and oxidation kinetics [1–6]. In the other side, there is experimental evidence that point defects greatly enhance or retard dopant diffusion in semiconductors [7–9], understanding and further controlling their generation is of major interest for subsequent downscaling and integration of devices. Indeed, as defects are the source of charge states into the gap, controlling both electrical and optical properties will depend on the exact characterization of these defects [10–14]. While it has been difficult to obtain these parameters directly from experiments, it has become possible to study the energetic of defect formation as well as their interaction with impurities using theoretical first principles approaches. Many theoretical studies have been performed. The most advanced of these have used Density Functional calculations to calculate the defect formation energies and energy barriers to diffusion [15–17]. Interstitials, vacancies, substitutionals, doping into ⇑ Corresponding author at: Université de Toulouse, UPS, INSA, INP, ISAE, LAAS, F-31077 Toulouse, France. E-mail addresses: [email protected], [email protected] (S. Fetah). 0167-9317/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2010.11.044
various materials of interest for microelectronics applications, silicon, silicon germanium, silicon dioxide, high-k materials, etc. have been systematically screened. A huge number of investigations have contributed to the examination of local defects and their diffusion characteristics in well-ordered defect less bulk model-systems [18–21]. The interstitial generation during Si and SiGe oxidation has often been reported in the literature. This mechanism has also been suggested to explain the Ge enrichment during SiGe oxidation. Considering the drastic down-scaled level of current devices, we can assume that a variety of the preceding intrinsic or extrinsic defects will see their properties altered because of their location nearby surfaces and interfaces [22–27]. In this study, we will try to understand the interstitial generation close to the surfaces/interfaces of silicon-based semiconductors. We examine in a systematic way the creation of Frenkel pairs which is constituted of a neutral vacancy and its associated interstitial, in the vicinity of Si(1 0 0), Ge containing Si(1 0 0) surfaces and theirs oxides. The structure and stability of these defects are analyzed and the role of germanium and oxygen presence is highlighted by comparing the energies of a number of point defects. To do so, we examine in a systematic way the creation of Frenkel pairs (FP), i.e. a neutral vacancy plus an interstitial atom placed in various tetrahedral positions around the vacancy from the subsurface layer down to the bulk.
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2. Simulation method First principles calculations are performed with the plane-wave package VASP [28] in the framework of the Density Functional Theory (DFT) using the generalized gradient approximation and ultrasoft pseudo-potentials of the Vanderbilt type [29] to describe the silicon, germanium, oxygen and hydrogen core electrons. We considered a plane wave cutoff of 475 eV. Spin polarization has been taken into account. The conjugate gradient method is used for all atomic relaxation. The Brillouin zone is performed at the C point. The unit cell is composed of an 11-layer slab with eight atoms per layer. Sixteen hydrogen atoms are used to saturate the silicon dangling bonds underneath the surface. All atoms are free to relax during minimization except H atoms and Si atoms of the two lowest silicon layers in contact to the hydrogen saturation layer that are kept fixed in order to mimic the bulk material. In pure silicon surfaces, the surface reconstructed 2 1 has been taken as the reference in energy. The SiGe model has been created by replacing a surface Si atom with a Ge atom and minimizing the energy. The surface remains buckled and the most stable dimer structure for the Si–Ge dimer is found to be down-up as recently published [30,31]. Both Si and SiGe surfaces are partially oxidized by incorporating two oxygen atoms onto the surface (SiO2, SiGeO2). The oxygen positioning follows the reaction pathways found in a previous work [32,33] as indicated in Fig. 1. Due the limitations of space and in order to focus on the main goal of this paper, namely to study the effect of Ge and O on the stability of the Frenkel pairs, we decided to focus on the formation of Frenkel pairs starting from silicon atoms in position A of the subsurface, as indicated in Fig. 2. These atoms are successively removed from their lattice position and systematically inserted into tetrahedral interstitial positions of the layers. We considered various interstitial positions from the subsurface layer down to the bulk (up to the fourth layer if the surface layer is counted as 0). This corresponds to Frenkel pairs where interstitial/vacancy are 4th neighbors as their maximum distances. It is to be noted
Fig. 1. Schematic top view of the unit cell surface. Presenting the vacancy, Ge and O atom positions.
Fig. 2. Zoom of the side view of the supercell indicating the location of tetrahedral Si interstitial atoms when the vacancy is created in position A.
that the vacancy here is created under an atom in an up position regarding the buckling of the overall surface dimers. This situation allows us to discuss and compare the formation energy of various Frenkel pairs (where the vacancy is not annihilated and the interstitial is relaxed to various configurations such us; stable, hexagonal and dumbbell as recently published [31]. The formation energy of the so created Frenkel pair is directly obtained by subtracting the total energy of the system with the Frenkel defect and that before the creation of the defect for each of the four studied surfaces. 3. Results In all of the four surfaces (Si, SiGe, SiO2, SiGeO2) the ‘‘artificially’’ created Frenkel pairs starting from tetrahedral interstitial positions give rise to several end structures. Basically, we do observe: (a) Recombination, the created defect is not stable: Direct Recombination is observed when the Si interstitial is located as the 1st neighbors, where the interstitial return directly to the vacancy (case 1); and Indirect Recombination where the interstitial kicks out another silicon atom to the vacancy (cases corresponding to formation energy of about 1 eV). (b) Surface amorphization: the (2 1) reconstruction is perturbed by the dissociation of existing dimers and the formation of new ones. (c) Frenkel pair defect: identified when the vacancy is not annihilated and the Si interstitial is relaxed to various configurations such us stable, hexagonal and dumbbell (split h1 0 0i) positions. In the following, 1st, 2nd, and 3rd will refer to the first, second and third layer below the surface. Fig. 3 displays the formation energies of these defects for each surface; pure silicon surface, germanium containing silicon surface and theirs oxidized surfaces. We start by observing the Frenkel pair behaviors generated in the 1st subsurface layer. This corresponds to the cases 1 and 2. The tetrahedral interstitials return to the created vacancy and whatever the considered surface. Here the presence of Ge and O has virtually no effect because the amorphization process is preponderant. Considering now the second situation corresponding to those created in the second surface layer, where the so created Frenkel pairs are not recombined (cases 3, 4, 5, 6). In pure Si the interstitial is relaxed to dumbbell position (E = 1.5 eV) related to the case 4, to the hexagonal position (E = 2.8 eV) in the case 5 and it is stable (E = 1 eV) in the case 6. Clearly, we observe in Fig. 3 a changes in the formation energy values introduced by the presence of Ge and/or O atoms where the Frenkel pairs lower theirs energies and an energy plateau is observed. The tetrahedral interstitials
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interstitial located deeper into the bulk (3rd subsurface layer) it is rarely relaxed to dumbbell position, it remains stable or it relaxes to hexagonal positions with higher formation energy. These preliminary results must be completed by considering Si interstitials generated deeper in the layer and by considering Ge interstitial generation in the capped surface with a silicon oxide layer (i.e. by incorporating more than two oxygen atoms) in order to investigate Ge condensation. Acknowledgements
Fig. 3. Formation energies of various defects with initial vacancy in position A. Results are presented in dark for pure Si surface, in green for Ge containing Si surface, in blue for SiO2 surface and in red for SiGeO2 surface. Defects are numbered with their initial position according to Fig. 2. (For interpretation of color mentioned in this figure the reader is referred to the web version of the article.)
are relaxed to dumbbell positions with an energy E = 1.6 eV in SiGe surface, with higher energy E = 1.9 eV in SiO2 surface and with E = 1.8 eV in SiGeO2 surface. Entre les deux. We note here that the cases where the formation energy is E = 1.0 eV correspond to the Indirect Recombination of the Frenkel pairs and once the interstitial do not return to the vacancy it relaxes to dumbbell position which is the most stable configuration. Evidently, the third one corresponds to the interstitial generated in the third layer (cases 7, 8, 9, 10), they are stables in pure Si with an energy of about E = 4.0 eV (a small difference in the formation energy values is make by the surface amorphization). We note that the presence of Ge and/or O atoms lowers the formation energy also. The interstitial corresponding to the case 9 is still stable with an energy of E = 3.5 eV in SiGe surface, with a higher energy of E = 3.6 eV and with E = 3.7 eV in SiO2 and SiGeO2 surfaces, respectively. And the one of the case 10 is relaxed to hexagonal position with an energy of E = 3.1 eV in SiGe, with a higher energy of E = 3.3 eV and of E = 3.4 eV in SiO2 and SiGeO2 surfaces, respectively. However those of the cases 7 and 8 exhibit particular behaviors; In SiGe surface, the interstitial of the case 8 is relaxed to hexagonal position (E = 2.8 eV). Contrarily, in SiO2 and SiGeO2 surfaces it kicks out another atom to the vacancy (Indirect Recombination). The interstitial of the case 7 recombined in SiGe, is relaxed to dumbbell position (E = 2.2 eV) in SiO2 and it is diffused up to the SiGeO2 surface to form a surface trimer with much higher energy (E = 2.6 eV). 4. Conclusion We present a comparison study of Si interstitial generation near the surface, during technological processes used in microelectronics device fabrication. A large number of individual cases, starting from vacancy interstitial pairs situated at various positions, have been considered. In general, we can conclude that the vicinity of the surface facilitates the relaxation of defects. The tetrahedral Si interstitial near the surface (1st and 2nd layers) is rarely stable. It returns to the created vacancy or it relaxes to dumbbell and hexagonal positions where we note that the dumbbell position is the most stable end structures. Furthermore, in all examined cases, similar behavior is observed, the presence of Ge and/or O atoms is shown to enhance the generation of Si interstitials. We observe that the Frenkel pair lowers its formation energy it can be created in the second subsurface layer with energies around 1.5 eV where the Si interstitials relaxes to dumbbell position. In contrast, the tetrahedral
The authors wish to thank the CALMIP supercomputer Centre for calculation facilities. This work was founded by the French National Research Agency (ANR) through OsiGe_Sim project No. ANR-05-NANO-004. References [1] J.M. Bonar, A.F.W. Willoughby, A.H. Dan, B.M. McGregor, W. Lerch, D. Loeffelmacher, G.A. Cooke, M.G. Dowssett, J. Mater. Sci. Mater. Electron. 12 (2001) 219. [2] N.R. Zagenberg, J. Fage-Pederson, J.L. Hansen, A.N. Larsen, J. Appl. Phys. 94 (2003) 3883. [3] M.A. Rabie, Y.M. Haddara, J. Carette, J. Appl. Phys. 98 (2005) 074904. [4] C.C. Wang, Y.M. Sheu, S. Liu, R. Duffy, A. Heringa, N.E.B. Cowern, P.B. Griffin, Mater. Sci. Eng. B 124–125 (2005) 39. [5] Z. Di, M. Zhang, W. Liu, M. Zhu, C. Lin, P.K. Chu, Mater. Sci. Eng. B 124–125 (2005) 153. [6] S. Rizk, Y.M. Haddara, A. Sibaja-Hernandez, J. Vac. Sci. Technol. B 24 (2006) 1365. [7] Lin Shao, Jiarui Liu, Quark Y. Chen, Wei-Kan Chu, Mater. Sci. Eng. R 42 (2003) 65–114. [8] A. Bentzen, A. Holt, Mater. Sci. Eng. B 159–160 (2009) 228–234. [9] De Salvador, E. Napolitani, S. Mirabella, E. Bruno, G. Impellizzeri, G. Bisognin, E.F. Pecora, F. Priolo, A. Carnera, Mater. Sci. Eng. B 154–155 (2008) 240–246. [10] Amartya Chowdhury, Sumita Mukhopadhyay, Swati Ray, Thin Solid Films 516 (2008) 6858–6862. [11] Xian-Qi Dai, Wei-Wei Ju, Guang-Tao Wang, M.H. Xie, Surf. Sci. 572 (2004) 77– 83. [12] O.K. Al-Mushadani, R.J. Needs, Phys. Rev. B 68 (2003) 235205. [13] R. Jones, A. Carvalho, J.P. Goss, P.R. Briddon, Mater. Sci. Eng. B 159–160 (2009) 112–116. [14] Jing Zhu, L.H. Yang, C. Mailhiot, Tomas Diaz de la Rubia, G.H. Gilmer, Nucl. Instrum. Methods Phys. Res. B 102 (1995) 29–32. [15] R.J. Needs, Phys. Rev. Condens. Matter 11 (1999) 10437–10450. [16] Damien Caliste, Pascal Pochet, Thierry Deutsch, Frédéric Lançon, Phys. Rev. B 75 (2007) 125203. [17] W.-K. Leung, R.J. Needs, G. Rajagopal, S. Itoh, S. Ihara, Phys. Rev. Lett. 83 (1999) 2351–2354. [18] D. Muñoz Ramo, J.L. Gavartin, A.L. Shluger, Phys. Rev. B 75 (2007) 205336. [19] Angelo Bongiorno, Alfred Pasquarello, Phys. Rev. Lett. 93 (2004) 086102. [20] P.I. Gaiduk, A. Nylandsted Larsen, W. Wesch, Nucl. Instrum. Methods Phys. Res. B 267 (8/9) (2009) 1239–1242. [21] K. Tanahashi, N. Inoue, N. Akutsu, Microelectron. Eng. 56 (2001) 133–137. [22] Tomoya Ono, Yoshiyuki Egami, Katsuhiro Kutsuki, Heiji Watanabe, Kikuji Hirose, J. Phys. Condens. Matter 19 (2007) 365202 (7pp). [23] S.N. Rashkeev, K. van Benthem, S.T. Pantelides, S.J. Pennycook, Microelectron. Eng. 80 (2005) 416–419. [24] J.L. Gavartin, A.L. Shluger, Microelectron. Eng. 84 (2007) 2412–2415. [25] D. Kropman, E. Mellikov, T. Korner, U. Ugaste, T. Laas, I. Heinmaa, A. Medvid, Mater. Sci. Eng. B 134 (2006) 222–226. [26] Yu.V. Gorelkinskii, Kh.A. Abdullin, B.N. Mukashev, T.S. Turmagambetov, Physica B 404 (2009) 4579–4582. [27] M. Suezawa, Y. Yamamoto, M. Suemitsu, I. Yonenaga, Physica B 404 (23–24) (2009) 5156–5158. [28] G. Kresse, J. Furthmüller, Phys. Rev. B 54 (1996) 11169; G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758 (Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set). [29] D. Vanderbit, Phys. Rev. B 41 (1990) 7892 (Soft self-consistent pseudo potentials in generalized eigenvalue formalism). [30] J.-H. Cho, M.-H. Kang, Phys. Rev. B 61 (2000) 1688. [31] S. Fetah, A. Chikouche, A. Dkhissi, A. Estève, M. Djafari Rouhani, G. Landa, P. Pochet, Thin Solid Films 518 (2010) 2418–2421. [32] A. Hémeryck, A. Mayne, N. Richard, A. Estève, N. Richard, Y.J. Chabal, M. Djafari Rouhani, G. Dujardin, G. Comptet, J. Chem. Phys. 126 (2007) 114707. [33] A. Dkhissi, A.K. Upadhyay, A. Hémeryck, A. Estève, Djafari Rouhani, G. Landa, P. Pochet, M. Djafari Rouhani, Appl. Phys. Lett. 94 (2009) 041912.
Contents lists available at ScienceDirect
Microelectronic Engineering journal homepage: www.elsevier.com/locate/mee
Stability of Frenkel pairs in Si(1 0 0) surface in the presence of germanium and oxygen atoms S. Fetah a,b,c,d,⇑, A. Chikouche f, A. Dkhissi c,d, G. Landa c,d, P. Pochet e a
Université de Sétif UFAS, Faculté des sciences, Département de physique, Sétif, Algeria Laboratoire d’analyse et traitement des signaux, Université de M’sila, Algeria c CNRS, LAAS, 7 avenue du colonel Roche, F-31077 Toulouse, France d Université de Toulouse, UPS, INSA, INP, ISAE, LAAS, F-31077 Toulouse, France e Laboratoire de Simulation Atomistique (L_Sim), SP2M, INAC, CEA-UJF, 38054 Grenoble Cedex 9, France f Unité de Développement d’Equipements Solaires (UDES), 42415 Tipaza, Algeria b
a r t i c l e
i n f o
Article history: Available online 9 December 2010 Keywords: Si(1 0 0) Point defect Si interstitial Frenkel pairs DFT calculations Formation energy
a b s t r a c t A first-principles pseudo-potential study of Frenkel pair generation close to the Si(1 0 0) surface in the presence of germanium and oxygen atoms is reported. The energies and structures of the defect structures (i.e. vacancy and relaxed tetrahedral Si interstitial) are calculated using supercell with up to 88 atoms. We present results obtained using the generalized gradient approximation (GGA) for the exchange–correlation energy. We examine the effect of the presence of germanium and oxygen atoms on the stability of Frenkel pairs generated near the Si(1 0 0) surface by comparing a number of individual cases, starting from vacancy interstitial pairs situated at various positions. The general tendency of the created interstitials is to climb towards the surface, but they generally remain in subsurface layers, ready to migrate into the layer. This tendency is enhanced by the presence of the Ge and/or O atoms. We show that the formation energy is lower and Si interstitials can be created with energies as low as 1.5 eV. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction The incorporation of Ge into modern Si-based electronics has generated a renewed interest in the detailed understanding of diffusion processes during Si devices processing. For example, the presence of Ge affects dopant diffusion, metallization, and oxidation kinetics [1–6]. In the other side, there is experimental evidence that point defects greatly enhance or retard dopant diffusion in semiconductors [7–9], understanding and further controlling their generation is of major interest for subsequent downscaling and integration of devices. Indeed, as defects are the source of charge states into the gap, controlling both electrical and optical properties will depend on the exact characterization of these defects [10–14]. While it has been difficult to obtain these parameters directly from experiments, it has become possible to study the energetic of defect formation as well as their interaction with impurities using theoretical first principles approaches. Many theoretical studies have been performed. The most advanced of these have used Density Functional calculations to calculate the defect formation energies and energy barriers to diffusion [15–17]. Interstitials, vacancies, substitutionals, doping into ⇑ Corresponding author at: Université de Toulouse, UPS, INSA, INP, ISAE, LAAS, F-31077 Toulouse, France. E-mail addresses: [email protected], [email protected] (S. Fetah). 0167-9317/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2010.11.044
various materials of interest for microelectronics applications, silicon, silicon germanium, silicon dioxide, high-k materials, etc. have been systematically screened. A huge number of investigations have contributed to the examination of local defects and their diffusion characteristics in well-ordered defect less bulk model-systems [18–21]. The interstitial generation during Si and SiGe oxidation has often been reported in the literature. This mechanism has also been suggested to explain the Ge enrichment during SiGe oxidation. Considering the drastic down-scaled level of current devices, we can assume that a variety of the preceding intrinsic or extrinsic defects will see their properties altered because of their location nearby surfaces and interfaces [22–27]. In this study, we will try to understand the interstitial generation close to the surfaces/interfaces of silicon-based semiconductors. We examine in a systematic way the creation of Frenkel pairs which is constituted of a neutral vacancy and its associated interstitial, in the vicinity of Si(1 0 0), Ge containing Si(1 0 0) surfaces and theirs oxides. The structure and stability of these defects are analyzed and the role of germanium and oxygen presence is highlighted by comparing the energies of a number of point defects. To do so, we examine in a systematic way the creation of Frenkel pairs (FP), i.e. a neutral vacancy plus an interstitial atom placed in various tetrahedral positions around the vacancy from the subsurface layer down to the bulk.
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S. Fetah et al. / Microelectronic Engineering 88 (2011) 503–505
2. Simulation method First principles calculations are performed with the plane-wave package VASP [28] in the framework of the Density Functional Theory (DFT) using the generalized gradient approximation and ultrasoft pseudo-potentials of the Vanderbilt type [29] to describe the silicon, germanium, oxygen and hydrogen core electrons. We considered a plane wave cutoff of 475 eV. Spin polarization has been taken into account. The conjugate gradient method is used for all atomic relaxation. The Brillouin zone is performed at the C point. The unit cell is composed of an 11-layer slab with eight atoms per layer. Sixteen hydrogen atoms are used to saturate the silicon dangling bonds underneath the surface. All atoms are free to relax during minimization except H atoms and Si atoms of the two lowest silicon layers in contact to the hydrogen saturation layer that are kept fixed in order to mimic the bulk material. In pure silicon surfaces, the surface reconstructed 2 1 has been taken as the reference in energy. The SiGe model has been created by replacing a surface Si atom with a Ge atom and minimizing the energy. The surface remains buckled and the most stable dimer structure for the Si–Ge dimer is found to be down-up as recently published [30,31]. Both Si and SiGe surfaces are partially oxidized by incorporating two oxygen atoms onto the surface (SiO2, SiGeO2). The oxygen positioning follows the reaction pathways found in a previous work [32,33] as indicated in Fig. 1. Due the limitations of space and in order to focus on the main goal of this paper, namely to study the effect of Ge and O on the stability of the Frenkel pairs, we decided to focus on the formation of Frenkel pairs starting from silicon atoms in position A of the subsurface, as indicated in Fig. 2. These atoms are successively removed from their lattice position and systematically inserted into tetrahedral interstitial positions of the layers. We considered various interstitial positions from the subsurface layer down to the bulk (up to the fourth layer if the surface layer is counted as 0). This corresponds to Frenkel pairs where interstitial/vacancy are 4th neighbors as their maximum distances. It is to be noted
Fig. 1. Schematic top view of the unit cell surface. Presenting the vacancy, Ge and O atom positions.
Fig. 2. Zoom of the side view of the supercell indicating the location of tetrahedral Si interstitial atoms when the vacancy is created in position A.
that the vacancy here is created under an atom in an up position regarding the buckling of the overall surface dimers. This situation allows us to discuss and compare the formation energy of various Frenkel pairs (where the vacancy is not annihilated and the interstitial is relaxed to various configurations such us; stable, hexagonal and dumbbell as recently published [31]. The formation energy of the so created Frenkel pair is directly obtained by subtracting the total energy of the system with the Frenkel defect and that before the creation of the defect for each of the four studied surfaces. 3. Results In all of the four surfaces (Si, SiGe, SiO2, SiGeO2) the ‘‘artificially’’ created Frenkel pairs starting from tetrahedral interstitial positions give rise to several end structures. Basically, we do observe: (a) Recombination, the created defect is not stable: Direct Recombination is observed when the Si interstitial is located as the 1st neighbors, where the interstitial return directly to the vacancy (case 1); and Indirect Recombination where the interstitial kicks out another silicon atom to the vacancy (cases corresponding to formation energy of about 1 eV). (b) Surface amorphization: the (2 1) reconstruction is perturbed by the dissociation of existing dimers and the formation of new ones. (c) Frenkel pair defect: identified when the vacancy is not annihilated and the Si interstitial is relaxed to various configurations such us stable, hexagonal and dumbbell (split h1 0 0i) positions. In the following, 1st, 2nd, and 3rd will refer to the first, second and third layer below the surface. Fig. 3 displays the formation energies of these defects for each surface; pure silicon surface, germanium containing silicon surface and theirs oxidized surfaces. We start by observing the Frenkel pair behaviors generated in the 1st subsurface layer. This corresponds to the cases 1 and 2. The tetrahedral interstitials return to the created vacancy and whatever the considered surface. Here the presence of Ge and O has virtually no effect because the amorphization process is preponderant. Considering now the second situation corresponding to those created in the second surface layer, where the so created Frenkel pairs are not recombined (cases 3, 4, 5, 6). In pure Si the interstitial is relaxed to dumbbell position (E = 1.5 eV) related to the case 4, to the hexagonal position (E = 2.8 eV) in the case 5 and it is stable (E = 1 eV) in the case 6. Clearly, we observe in Fig. 3 a changes in the formation energy values introduced by the presence of Ge and/or O atoms where the Frenkel pairs lower theirs energies and an energy plateau is observed. The tetrahedral interstitials
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interstitial located deeper into the bulk (3rd subsurface layer) it is rarely relaxed to dumbbell position, it remains stable or it relaxes to hexagonal positions with higher formation energy. These preliminary results must be completed by considering Si interstitials generated deeper in the layer and by considering Ge interstitial generation in the capped surface with a silicon oxide layer (i.e. by incorporating more than two oxygen atoms) in order to investigate Ge condensation. Acknowledgements
Fig. 3. Formation energies of various defects with initial vacancy in position A. Results are presented in dark for pure Si surface, in green for Ge containing Si surface, in blue for SiO2 surface and in red for SiGeO2 surface. Defects are numbered with their initial position according to Fig. 2. (For interpretation of color mentioned in this figure the reader is referred to the web version of the article.)
are relaxed to dumbbell positions with an energy E = 1.6 eV in SiGe surface, with higher energy E = 1.9 eV in SiO2 surface and with E = 1.8 eV in SiGeO2 surface. Entre les deux. We note here that the cases where the formation energy is E = 1.0 eV correspond to the Indirect Recombination of the Frenkel pairs and once the interstitial do not return to the vacancy it relaxes to dumbbell position which is the most stable configuration. Evidently, the third one corresponds to the interstitial generated in the third layer (cases 7, 8, 9, 10), they are stables in pure Si with an energy of about E = 4.0 eV (a small difference in the formation energy values is make by the surface amorphization). We note that the presence of Ge and/or O atoms lowers the formation energy also. The interstitial corresponding to the case 9 is still stable with an energy of E = 3.5 eV in SiGe surface, with a higher energy of E = 3.6 eV and with E = 3.7 eV in SiO2 and SiGeO2 surfaces, respectively. And the one of the case 10 is relaxed to hexagonal position with an energy of E = 3.1 eV in SiGe, with a higher energy of E = 3.3 eV and of E = 3.4 eV in SiO2 and SiGeO2 surfaces, respectively. However those of the cases 7 and 8 exhibit particular behaviors; In SiGe surface, the interstitial of the case 8 is relaxed to hexagonal position (E = 2.8 eV). Contrarily, in SiO2 and SiGeO2 surfaces it kicks out another atom to the vacancy (Indirect Recombination). The interstitial of the case 7 recombined in SiGe, is relaxed to dumbbell position (E = 2.2 eV) in SiO2 and it is diffused up to the SiGeO2 surface to form a surface trimer with much higher energy (E = 2.6 eV). 4. Conclusion We present a comparison study of Si interstitial generation near the surface, during technological processes used in microelectronics device fabrication. A large number of individual cases, starting from vacancy interstitial pairs situated at various positions, have been considered. In general, we can conclude that the vicinity of the surface facilitates the relaxation of defects. The tetrahedral Si interstitial near the surface (1st and 2nd layers) is rarely stable. It returns to the created vacancy or it relaxes to dumbbell and hexagonal positions where we note that the dumbbell position is the most stable end structures. Furthermore, in all examined cases, similar behavior is observed, the presence of Ge and/or O atoms is shown to enhance the generation of Si interstitials. We observe that the Frenkel pair lowers its formation energy it can be created in the second subsurface layer with energies around 1.5 eV where the Si interstitials relaxes to dumbbell position. In contrast, the tetrahedral
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