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Surface effects on the Frenkel pair defects stability in the vicinity of the Si(001) surface
Materials Science in Semiconductor Processing 32 (2015) 179–187
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Materials Science in Semiconductor Processing journal homepage: www.elsevier.com/locate/mssp
Surface effects on the Frenkel pair defects stability in the vicinity of the Si(001) surface S. Fetah a,b,n, A. Estève b,c, M. Djafari Rouhani b,d a
Université de M'sila, Faculté des sciences, Département de physique, 28000 M'sila, Algeria CNRS, LAAS, 7 avenue du colonel Roche, F-31400 Toulouse, France Université de Toulouse, LAAS, F-31400 Toulouse, France d Université de Toulouse, UPS, LAAS, F-31400 Toulouse, France b c
a r t i c l e i n f o
abstract
Available online 6 February 2015
A systematic first-principles pseudo-potential study of the stability of tetrahedral Frenkel pairs generated in the vicinity of the silicon Si(001)-(2 1) surface is reported. The defect formation energies and associated structures are discussed. We demonstrate that vacancies that are generated close to the surface are subject to annihilation processes either through recombination of the Frenkel pairs or through surface amorphization. On the other hand, interstitials that are positioned on the subsurface exhibit specific behaviors compared to those located deeper inside the bulk Si. Calculations indicate that the tetrahedral interstitial is unstable when located close to the surface and it relaxes to form a split-110 (dumbbell) configuration. In deeper layers, the tetrahedral interstitial remains rarely stable; it relaxes to hexagonal or to fourfold-coordinated configurations. The defect formation energies are given as a function of surface–vacancy and interstitial– vacancy distances. Results indicate that the formation energy is considerably reduced as the interstitial approaches the surface. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Si(001) Defects Si interstitial Frenkel pairs DFT calculations
1. Introduction Over the years, there has been extensive experimental and theoretical research effort to determine the structure of point defects in a wide range of materials, their migration paths, and their relative contributions to self-diffusion and impurity diffusion. For technological issues, since there is experimental evidence that point defects greatly influence dopant diffusion in semiconductors [1–4], understanding and further controlling their generation is of major importance. Considering the drastic downscaled level of current devices, we can assume that a variety of intrinsic or extrinsic defects will see their properties altered because of their location close to the surfaces and interfaces. In this
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Corresponding author. E-mail address: [email protected] (S. Fetah).
http://dx.doi.org/10.1016/j.mssp.2015.01.015 1369-8001/& 2015 Elsevier Ltd. All rights reserved.
frame, the way interstitial atoms are generated in relation with the processing steps (deposition, oxidation, implantation, annealing etc.) and conditions (pressure, temperature, and process duration) [5–8], is still an open and controversial issue. This is particularly true at the stacking interfaces where little is known on the detailed chemical composition and on the interface strain distribution forming the potential reservoir of interstitial species. An illustrative example is the question of the generation of Si interstitials during silicon oxidation [9,10]. First principles calculations, and mainly Density Functional Theory (DFT)-based calculations, have been the method of choice to shed light into electronic as well as thermodynamic properties of defects in semiconductors. A number of investigations have addressed point defects and their diffusion characteristics in well-ordered or amorphous bulk materials [11,12]. In fact, point defects, such as vacancies and interstitials, are known to have a
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great influence on various structural, mechanical, electrical and optical properties of crystalline and amorphous materials. In turn, these properties affect the operation of semiconductor devices. Beyond interstitial generation, the paths for migration and associated energy diagrams should also be addressed in a manner to build reliable diffusion profiles. Looking at the literature, we notice that migration paths of self-interstitial atoms during diffusion are still not uniquely determined [13–17]. Surface strain and its role in the reconstruction process have been investigated for the surfaces of some metals [18] as well as for semiconductors such as silicon and germanium [19–21,32]. Even though the importance of surface/ interface strain is well recognized [22–25], there are a relatively limited number of studies dealing with their effects on the stability of interstitials [26–29]. It was demonstrated that under strain, the formation energies of bulk defects (Frenkel pairs (FP), self-interstitial atoms) decrease. Concerning surface defects, Halicioglu et al. [27] have also noticed the decrease of their formation energies. However, they made use of Stilling–Weber empirical potential which makes it impossible to really address the defect structure evolution with sufficient precision. In this paper, by investigating FP defects, we explore the ability to produce Si interstitial atoms at the vicinity of the silicon surface. Our objective is to establish a preliminary investigation through the detailed characterization of both energetic and structural behaviors of interstitials as a function of their specific location underneath the surface. This preliminary work should lead us to the selection of the most probable defects, which could then be investigated more thoroughly, regarding both their charge states as well as their stability against various close configurations. To do so, we examine in a systematic way the creation of FP for various positions of the vacancy and the interstitial atom around the vacancy, from the subsurface layer down to the bulk. In Section 2, we briefly describe the method used in the simulations before listing in detail the investigated cases. Results are reported in Section 3 where we examine exhaustively the five vacancy positions considered. Section 4 is devoted to the discussion of these results. Finally, conclusions are drawn in Section 5. 2. Computational method and simulation model The calculations are performed with the plane-wave package VASP [30,31] in the framework of the DFT, using the generalized gradient approximation [33,34] and ultrasoft pseudo-potentials of the Vanderbilt type [35] to describe both silicon and hydrogen terminations. DFT parameters satisfy compromises between convergence criteria and the required systematic approach of the present work. We considered a plane wave cutoff of 340 eV, and kpoint sampling of the Brillouin zone was performed at the Γ point [36]. The unit cell is composed of an 11 layer Si(001) slab with eight atoms per layer (total of 88 Si atoms). Convergence tests have been performed with more extended k-point meshes (1 2 1 and 2 4 1) and cell sizes, for few configurations, in order to verify their influence on both calculated structures and energetics. As shown in Section 4, the Γ point and the standard unit cell
Fig. 1. Schematic top view of the silicon unit cell surface. The letters A–E show the positions of the vacancies, as described in the text. Thick lines represent surface dimer bonds and dashed lines the boundaries of the unit cell, to be reproduced periodically.
are sufficient to describe our geometries with the required accuracy. Sixteen hydrogen atoms are used to saturate the silicon dangling bonds underneath the slab and a vacuum space is added on top of the Si slab. The final unit cell is 20 Å thick. Periodic boundary conditions are considered in all three dimensions. Fig. 1 represents the unit cell, with the dashed lines showing its lateral limits. All atoms are free to relax during energy minimization, except H and Si atoms of the two lowest silicon layers, in contact with the hydrogen saturation layer, that are kept fixed in order to mimic the bulk material. This unit cell is first relaxed through a total energy minimization, leading to a stable defect free structure. In this structure, the eight surface atoms are p(2 1) reconstructed leading to four buckled surface dimers, divided in two dimer rows separated by a channel (see Fig. 1). Let us remind that, in our model, the most important reconstruction terms: dimerization and buckling have been taken into account. In the following, this structure has been taken as the reference in energy. Once the structure of the unit cell is defined, we create FP by removing Si atoms from their lattice sites into tetrahedral interstitial positions. The defective structure is then relaxed through a new step of total energy minimization. The formation energy (Ef) of the FP can be calculated more easily than the formation energy of isolated point defects, since the total number of atoms is conserved during all energy minimization steps. Therefore, one does not need to use either an energy reference corresponding to isolated atoms, or comparing systems containing (N 1) and N atoms. The formation energy is directly obtained by subtracting the total energy of the system with the Frenkel defect from the reference energy of the relaxed defect free surface. We can notice that the investigated defects being close to the surface, charge transfers from the surface can easily be achieved, so that our defects are not necessarily neutral. However, it is not in the scope of this paper to evaluate these charge transfers. In this paper, we have systematically considered all vacancy positions in the first two subsurface layers, and one position in the fifth subsurface layer, in order to represent a bulk vacancy. The symmetry of the p(2 1) reconstructed Si (001) surface, containing buckled dimers, implies two different vacancy positions in each subsurface layer. A total of five
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vacancy positions have therefore been investigated. The atoms are next removed from their vacancy positions and inserted into lattice tetrahedral interstitial positions, as suggested in the work of Halicioglu et al. [27]. For each single vacancy site, we considered interstitial positions ranging from the surface layer down to the fifth subsurface layer, where convergence towards published bulk values has been found. In each subsurface layer, we systematically scan all possible vacancy–interstitial relative positions, up to the fourth nearest neighbors. We considered a total of 62 different FP configurations as detailed in the next section. 3. Simulation results In this section, we focus on the formation of FP, starting from vacancy positions A–E as indicated in Fig. 1. Positions A and B correspond to vacancies right in the first subsurface layer below a silicon dimer, with Si atoms respectively in upper and lower buckling positions. Positions C and D are situated in the second subsurface layer, respectively below a silicon dimer and in the channel separating the dimers. Position E represents a vacancy in the fifth subsurface layer. A total of 62 configurations have been considered in this work. Due to the systematic screening of the interstitial sites in our work, not all of the investigated configurations lead to comprehensive results, which could be analyzed individually. The reason is that the vicinity of the surface, and the absence of symmetry around the created defects, results in the multiplication of secondary minima, all in the same energy range. One way to obtain global information on these defects is therefore to examine a large number of cases and establish energy intervals for specific characteristic structures that is one goal of the present work, to provide directions for further more detailed mechanistic studies and precise model systems. In Tables 1–5, we report the simulation results obtained for vacancy sites A–E, in terms of defect configurations and associated formation energies, as a function of the initial interstitial distances to the surface and to its corresponding vacancy. Before examining individually the interesting investigated configurations, we point out some general features of the relaxed systems. Since the vacancy is created close to the surface, lattice relaxation around the vacancy is greatly enhanced, and not limited to its nearest neighbors,
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as it is the case for vacancies in bulk materials. The relaxation is indeed accompanied by a surface amorphization, which drastically changes the whole surface atomic arrangement, down to the second subsurface layer. Overall, we have observed the following mechanisms during the relaxation process: – The (2 1) reconstruction is perturbed after total energy minimization. We observe the dissociation of existing dimers and the formation of new ones. Accordingly, an amorphization of the sublayers close to the surface occurs. – Vacancy–interstitial recombination, either directly when they are initially positioned as first neighbors, or indirectly when a second atom is kicked out by the interstitial into the vacancy. In some cases, the kick out mechanisms may involve several atoms. The indirect recombination always leads to large surface perturbations. Indeed, this mechanism is very important in understanding the formation processes of amorphousstructural silicon-dioxide films where the detailed mechanisms by which Si interstitials are generated at the surface are not known [9,13]. – Annihilation of the vacancy on the Si surface. The remaining single interstitial is stabilized in various configurations: tetrahedral, hexagonal, split 〈110〉 (dumbbell) and the fourfold-coordinated defect (FFCDþ1). These different configurations have been reported in bulk silicon using DFT calculations [16,37], where they show slightly larger energies of formation than those presented in the present work. We should remind that the configurations reported in the bulk might correspond to charged states of the interstitial atom. – The creation of FP when both the vacancy and the interstitial can be clearly identified within the unit cell. As a result, a metastable state with a positive energy may be observed after relaxation. The individual cases are now examined at the light of the above considerations. 3.1. Vacancy in site A We first consider FP generated by the displacement of the Si atom located under an atom in an up position
Table 1 Final configurations and related formation energies, as a function of the initial (before energy minimization) interstitial–surface and interstitial–vacancy (A) distances. Subsurface layer
Interstitial
Interstitial–vacancy distance (Å)
Final configuration
Defect formation energy (eV)
1st 2nd
A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11
2.88 2.33 4.56 4.73 4.67 2.64 6.11 4.42 5.87 4.42 5.87
Trimer FP Direct recombination Indirect recombination Direct recombination Dumbbell Hexagonal FP Tetrahedral FP Tetrahedral FP Tetrahedral FP Tetrahedral FP Tetrahedral FP
1.65 No defect No defect No defect 1.52 2.78 4.11 4.09 3.91 4.17 4.29
3rd
4th
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Table 2 Final configurations and related formation energies, as a function of the initial (before energy minimization) interstitial–surface and interstitial–vacancy (B) distances. Subsurface layer
Interstitial
Interstitial–vacancy distance (Å)
Final configuration
Defect formation energy (eV)
1st 2nd
B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11
2.67 2.35 4.59 4.74 4.72 2.72 6.11 4.46 5.90 4.43 5.88
Direct recombination Direct recombination Hexagonal Tetrahedral Tetrahedral Indirect recombination Amorphization Tetrahedral Tetrahedral Indirect Recombination Tetrahedral
No defect No defect 1.40 2.70 2.95 No defect No defect 3.20 3.20 No defect 3.13
3rd
4th
Table 3 Final configurations and related formation energies, as a function of the initial (before energy minimization) interstitial–surface and interstitial–vacancy (C) distances. Subsurface layer
Interstitial
Interstitial–vacancy distance (Å)
Final configuration
Defect formation energy (eV)
1st 2nd
C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18
4.30 2.71 2.72 2.40 2.40 5.96 5.94 4.54 4.54 4.72 2.73 4.70 5.93 4.50 5.94 5.93 4.50 5.94
Indirect recombination Direct recombination Direct recombination Direct recombination Direct recombination Dumbbell Tetrahedral FP Tetrahedral FP Dumbbell Tetrahedral FP Hexagonal FP Hexagonal FP Hexagonal Indirect recombination Hexagonal FP Hexagonal Indirect recombination Hexagonal FP
No defect No defect No defect No defect No defect 1.56 3.43 4.06 1.58 4.06 3.01 3.12 2.75 No defect 3.70 2.75 No defect 3.70
3rd
4th
5th
Table 4 Final configurations and related formation energies, as a function of the initial (before energy minimization) interstitial–surface and interstitial–vacancy (D) distances. Subsurface layer
Interstitial
Interstitial–vacancy distance (Å)
Final configuration
Defect formation energy (eV)
2nd
D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 D11 D12 D13 D14 D15 D16 D17
2.73 2.76 2.37 2.39 4.53 4.54 5.95 5.98 2.70 4.69 4.77 5.91 4.50 5.94 5.91 4.50 5.94
Dumbbell Amorphization Direct recombination Direct recombination Tetrahedral FP Tetrahedral FP Overhang FP Overhang FP Direct recombination Tetrahedral FP Tetrahedral FP (FFCD þ 1) FP Indirect recombination Tetrahedral FP (FFCD þ 1)FP Indirect recombination Tetrahedral FP
1.48 No defect No defect No defect 4.01 3.84 2.46 2.49 No defect 3.97 3.86 3.07 No defect 4.05 3.07 No defect 4.05
3rd
4th
5th
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Table 5 Final configurations and related formation energies, as a function of the initial (before energy minimization) interstitial–surface and interstitial–vacancy (E) distances. Subsurface layer
Interstitial
Interstitial–vacancy distance (Å)
Final configuration
Defect formation energy (eV)
1st 2nd 3rd 4th 5th
E1 E2 E3 E4 E5
5.79 5.88 4.43 2.69 2.42
Trimer FP Dumbbell Hexagonal FP Direct recombination Direct recombination
2.34 1.63 2.65 No defect No defect
Fig. 2. Side view of the super-cell indicating the location of the vacancy in position (A) and their related tetrahedral Si interstitial atoms.
regarding the buckling of the overall surface dimers (see Fig. 2). In addition to direct vacancy–interstitial recombination (cases A2 and A4 in Table 1), we observe five major structures. The first one corresponds to vacancy–interstitial pairs at initial distances above 4.4 Å (cases A7–A11). The interstitials are positioned in the third or the fourth subsurface layers, far from the surface. The interstitials remain in their initial tetrahedral sites. The vacancy is stable and does not annihilate on the surface while the surface reconstruction is maintained. FP formation energies of around 4 eV are observed. The next two structures correspond to interstitials positioned in the third subsurface layer, but relaxing from their initial tetrahedral position to a dumbbell (case A5) or to a hexagonal (case A6) configuration. The tetrahedral site becomes therefore unstable, probably because of the initial interstitial position under a silicon atom in up buckling position. The effect of surface on the relaxation of interstitials is clearly visible, despite a distance of three atomic layers between the surface and the interstitial atom. The formation energies of FP are of 1.52 eV for the dumbbell structure and 2.78 eV for the hexagonal structure. In the fourth observed structure, the interstitial is initially positioned in the second subsurface layer. The interstitial relaxation is important and leads to an amorphization process, exhibiting a complex reconstruction around the vacancy, with
Fig. 3. Side view of the super-cell indicating the location of the vacancy in position (B) and their related tetrahedral Si interstitial atoms.
overall formation energy of 0.78 eV (case A3). The interstitial is neither recombined, directly or indirectly, nor stabilized in a well defined form, such as those reported in the literature [14,15,37]. A detailed examination of atomistic movements during the energy minimization shows that a kick out mechanism, as described above, takes place. The last case corresponds to the interstitial positioned on the surface (case A1). A direct vacancy–interstitial recombination does not occur despite their small initial separation. Rather, a surface trimer is created, characterized by FP formation energy of 1.65 eV. This trimer structure involves a cluster of three atoms: the interstitial and two already dimerized atoms, close to each other with a strong interaction, reducing the FP formation energy. 3.2. Vacancy in site B Now we consider the vacancy under a surface Si atom being in a buckling down position (see Fig. 3 and Table 2). Here, observed interstitials show similar qualitative features as those observed for the vacancy in site A. The main difference comes from the vacancy behavior. Being very close to the surface atom, in a down buckling position, the vacancy is generally annihilated through the dimerization process occurring around it. This leads to lower formation energies of defects, which are now composed of the interstitial alone. As in the case of the vacancy in position A, tetrahedral interstitial atoms well separated from the vacancy before minimization,
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Fig. 4. Side view of the super-cell indicating the location of the vacancy in position (C) and their related tetrahedral Si interstitial atoms.
in the third subsurface layer (cases B4 and B5) or in the fourth subsurface layer (cases B8, B9 and B11), at distances larger than 4.4 Å, remain in their initial tetrahedral positions with a formation energy of FP of 2.70 eV, 2.95 eV, 3.20 eV, 3.20 eV and 3.13 eV, respectively, slightly lower than those reported in the literature for the bulk [14,23]. This difference may be attributed to the relaxation around the vacancy enhanced by the surface vicinity. The interstitial atom (case B3) located in the second subsurface layer, which is below a silicon surface atom in an up buckling position, relaxes spontaneously from its tetrahedral structure to a hexagonal configuration, FP formation energy is 1.40 eV. We note here that the defect is only composed of a single interstitial, the vacancy being annihilated. That is why the formation energy is about 1 eV lower than those reported above, for the vacancy in site A. Almost perfect recombination occurs for cases B1 and B2 while indirect recombination is observed for cases B6 and B10. 3.3. Vacancy in site C We consider here the cases where the vacancy is created in the second subsurface layer, below the dimer row. The objective is to address the issues related to the formation of FP deeper in the silicon layer. FP formation energies and initial vacancy–interstitial distances for this vacancy site are reported in Table 3 and the interstitial sites are shown in Fig. 4. The fact that the vacancy is now in a very strained region, under the dimer row, modifies qualitatively some of the observed features. Apart from the cases where the vacancy–interstitial are close enough to recombine directly (cases C2–C5) or by successive kick outs and surface amorphization (cases C1, C14 and C17), large surface relaxation leading to its amorphization, and to a multiplication of local minima, generally takes place. This results in lowering of the FP formation energies, either slightly through local relaxation, or more largely through transitions from tetrahedral to hexagonal or to dumbbell configurations. We observe that this local mechanism is independent of the interstitial position depth. For example, interstitials stabilized in tetrahedral configurations may be positioned in third or
Fig. 5. Side view of the super-cell indicating the location of the vacancy in position (D) and their related tetrahedral Si interstitial atoms.
fourth subsurface layers (cases C7, C8 and C10). The corresponding formation energies of FP are in the range of 3.43 to 4.06 eV, close to values found for the vacancy in site A. However, the tetrahedral interstitials in the cases (C11 and C12) situated in the fourth layer are relaxed to hexagonal positions with formation energies of 3.01 eV and 3.12 eV, respectively. The same behavior is observed for the interstitials corresponding to the cases (C15 and C18) situated in the fifth layer but now with higher energies (3.70 eV) due to their depth towards the bulk material. The interstitials in the cases (C13 and C16) also situated in the fifth layer are relaxed to hexagonal positions with lower formation energy (2.75 eV). This is likely to be due to the vacancy annihilation upon amorphization. The interstitials situated in the third subsurface layer may relax to the dumbbell configuration (cases C6 and C9) with formation energies of 1.56 eV and 1.58 eV, respectively. As for vacancy site A, the dumbbell configurations have their corresponding vacancies annihilated on the surface explaining the comparable formation energies. 3.4. Vacancy in site D As for vacancy C, the vacancy in site D is created in the second subsurface layer, but in the channel separating the dimer rows. Direct recombination is observed in the cases D3 and D4. The specificity of this vacancy site is seen from the amorphous versus recombination processes of locally created interstitials. For example, interstitials positioned at the same depth as the vacancy, in the second subsurface layer, and close to the vacancy at distances below 2.73 Å (cases D1 and D2 in Table 4 and Fig. 5), do not automatically recombine with the vacancy, as observed for the three previous vacancy sites. Rather, we observe either a dumbbell configuration for the interstitial accompanied with an annihilation of the vacancy on the surface, or a complete amorphization of the surface. These two situations occur correspondingly when the interstitial is located
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Fig. 6. Schematic view of the interstitial in overhang position above the vacancy in site D.
under a surface atom in down and up buckling positions. FP formation energies are 1.48 and 2.20 eV. For interstitials deeper in the layers, three types of behaviors are observed. In the first type, interstitials remain in their tetrahedral configurations, with FP formation energies 4.01 eV and 3.84 eV respectively in the cases (D5 and D6) located in the third layer, 3.97 eV and 3.86 eV in the cases (D10 and D11) respectively, located in the fourth layer, and with 4.05 eV in the cases (D14 and D17) located in the fifth layer. The second type concerns interstitials which relax from their tetrahedral configurations to FFCDþ1 (cases D12 and D15), where an interstitial is associated to a four-folded coordinated defect. This configuration has been reported in bulk structures [38–42]. It has been shown that this structure plays a crucial role in bringing disordered configurations [42]. FP formation energies are now reduced to 3.1 eV, about 1 eV lower than normal tetrahedral configurations. This results from the interstitial relaxation towards a (FFCDþ 1) configuration as also demonstrated in bulk calculations [4]. In a third type of behavior, represented in Fig. 6 we observe a new configuration of vacancy–interstitial pair, which we call “overhang” (cases D7 and D8). In this configuration, the interstitials, initially in the third subsurface layer, migrate towards the surface and stabilize in the first subsurface layer, just above the vacancy in the second subsurface layer. We should remind that the (2 1) reconstruction of the Si(001) surface and the presence of dimers on the surface, with atoms positioned at short distances, results in the creation of a free space above the channel. The upward migration of the interstitial is therefore facilitated to fill the free space. The term “overhang” relates to the fact that the interstitial is placed above the vacancy, in a metastable position. This vacancy–interstitial configuration is specific to the presence of the surface and we believe that no such configuration can be observed in the bulk, where a direct recombination takes place spontaneously. The vacancy–interstitial attractive interaction is large and leads to FP formation energies of 2.5 eV. 3.5. Vacancy in site E Finally, we consider the FP generated by the displacement of the Si atom positioned deep inside the bulk; in the
Fig. 7. Side view of the super-cell indicating the location of the vacancy in position (E) and their related tetrahedral Si interstitial atoms.
fifth subsurface layer (see Table 5 and Fig. 7). We can now observe situations where the vacancy is deep below the surface but the interstitial is close to the surface. These situations are opposite to some of the previous situations where the vacancy was close to the surface and the interstitial in deep layers. Three types of FP are observed where the interstitials are in hexagonal, dumbbell and trimer configurations and the vacancy is not annihilated. The respective formation energies of FP are 2.34 eV 1.63 eV and 2.65eV (cases E1–E3). The trimer configuration was already observed with the vacancy created in site A. But the FP formation energy is higher in the present situation because of the position of the vacancy, deep in the bulk, and far from the interstitial on the surface. Here, the absence of attractive vacancy–interstitial interaction leads to higher formation energy. The other cases lead to direct recombination due to the interstitial–vacancy proximity. 4. Discussion The first question is to check the impact of k-point sampling and the size of the unit cell on the accuracy of the reported results. To this end, we have tested three k-point samplings: 1 1 1 (Γ point), 1 2 1, and 2 4 1, and two substrate surface sizes: 7.2 Å 15.4 Å and 15.4 Å 15.4 Å, applied to case A10. These two unit cells contain 8 and 16 Si atoms on the (001) surface. The case A10, where the interstitial atom is neither too close nor too far from the surface, represents a good compromise between all 62 cases investigated in this paper. On pure Si(001) surface with p(2 1) reconstruction, no structural changes have been observed between all calculations. However, various k-samplings lower slightly the energies with respect to Γ point sampling: 0.13 eV and 0.16 eV per atom for 1 2 1 and 2 4 1 samplings, respectively. Looking at FP formation in the case A10, we observe slight structural deviations around the vacancy.
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We also observe a decrease of the formation energy of FP with respect to Γ point sampling: 0.35 eV and 0.16 eV for 1 2 1 and 2 4 1 samplings, respectively, representing 8% and 4% deviations. Doubling the size of the unit cell, i.e. reducing interactions between defects, lowers the FP formation energy by 4%. We can conclude that the Γ point approximation associated to a unit cell containing 88 Si atoms represents a relatively accurate model for this preliminary investigation. To summarize the previous results in order to obtain global information, we can notice that interstitials positioned deeper than the third subsurface layer hardly feel the presence of the surface. This results in interstitials in metastable tetrahedral configurations, which do not spontaneously relax to hexagonal or dumbbell configurations. As mentioned in the introduction, the activation barriers for these transitions have not been evaluated. The corresponding FP formation energies are in the range of 4 eV similar to what has been calculated for the self-interstitial. In cases where the vacancy is annihilated through amorphization of the surface, particularly when the vacancy is situated below a silicon surface atom in the down buckling position, the formation energy can decrease to 3 eV, compared to 4 eV for bulk isolated interstitials [14,16,42]. The amorphization effect can therefore be estimated to a maximum reduction of the formation energy of 1 eV. This shows that the attractive vacancy–interstitial interaction is still strong, even at distances up to 4.4 Å. As we can see later, the relaxation around the vacancy and the surface amorphization cannot explain by itself this decrease of the FP formation energy. Closer to the surface, the tetrahedral structure becomes unstable and might relax spontaneously to hexagonal or dumbbell structures. FP formation energies are in the range of 2.70–2.78 eV for hexagonal, and of 1.29–1.58 eV for dumbbell configurations. These energies are much lower than 4 eV, relative to the cases where interstitials were in tetrahedral sites. This result is contrary to the results for bulk interstitials where formation energies are almost equivalent for the three structures, namely 4.07 eV, 3.80 eV and 3.84 eV for interstitials in tetrahedral, hexagonal and dumbbell configurations, respectively [14]. This discrepancy can be explained by the large surface relaxation which completely destabilizes the tetrahedral configuration towards hexagonal and dumbbell structures, for interstitials close to the surface. The dumbbell seems to be the easiest to create, particularly at high processing temperatures, for example temperatures used during the oxidation. We observe that the surface acts as an efficient sink for the subsurface vacancies. However, in several cases, as a result of the surface buckling, subsurface vacancies remain stable. 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. We show that Si interstitials can be created with low energies (1–1.6 eV), resulting in the presence of large interstitial concentration at high processing temperatures. This tendency is enhanced if a cap, such as an oxide layer, inhibits the climb of interstitials. Another specific effect, due to the vicinity of the surface, is the annihilation of the vacancy, resulting either
from vacancy–interstitial recombination, or from more complex collective relaxation processes that cannot take place in the bulk. We have observed two different relaxation mechanisms. In the first one, we can observe vacancy–interstitial recombination via a kick out mechanism, consisting of successive atomic displacements up to the vacancy annihilation, as described in Section 3. No visible defect, vacancy or interstitial, can be seen in the final structure, but the successive atomic displacements lead to an amorphization of the surface, with an energy in the range of 0.78–1.08 eV. The second mechanism, more often observed in our calculations, is the annihilation of the vacancy by amorphization of its neighboring atoms. The vacancy is no more visible but the interstitial can be clearly identified. Although this second mechanism is energetically less favorable than the first, we think that it is kinetically more probable, since it is performed in only one step instead of multiple steps necessary for the successive atomic displacements. Whatever the mechanism, the low energies involved favor the amorphization of the surface, precursor for the subsequent growth of an amorphous oxide layer. Finally, we observe two particular atomic clustering on the surface, resulting from the migration of interstitials. The first one is the trimer configuration where the interstitial bounds to two surface atoms already forming a dimer. The second configuration, observed in the channel separating the dimer rows, is the “overhang” configuration where the migrating interstitial is placed above the vacancy, without any spontaneous recombination, although they are quite close to each other. These configurations are metastable in the sense that they correspond to a secondary energy minimum. 5. Conclusion A systematic first-principles pseudo-potential study of the stability of Frenkel pairs generated in the vicinity of the silicon Si(001)-(2 1) surface is reported. We demonstrate that vacancies that are generated close to the surface are not necessarily stable, but have a propensity to annihilate either through recombination of the Frenkel pairs or through surface amorphization originated by the vacancy itself. This statement is particularly true for vacancies situated below a surface atom in down buckling position. Below a surface atom in up buckling position, the vacancy is usually stable and in a configuration close to an interstitial in the “overhang” structure, observed inside the channel separating the dimers. However, interstitials that are positioned on the subsurface exhibit specific behaviors in comparison to those located deeper inside the bulk Si. As previously demonstrated by Halicioglu et al. [27], we qualitatively observe that the interstitials are easier to generate in the subsurface than in the bulk. Beyond this, we quantitatively give both the formation energies of these defects and associated structures. We also show that the dumbbell configuration is the most stable for subsurface interstitials. In contrast, the tetrahedral interstitials located deeper into the bulk remain stable, or may relax to hexagonal, as well as to fourfold-coordinated configurations (FFCDþ1), in specific cases. Both these structures have been observed in the bulk and described in the
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literature: the tetrahedral structure for the charged selfinterstitial and the hexagonal structure for the neutral selfinterstitial [42]. Finally, two structures: trimer and overhang are reported as surface specific configurations, not observed in the bulk. In general, we can conclude that the vicinity of the surface facilitates the relaxation of defects and has a similar effect as the temperature for defect creation in the bulk. The migration of Frenkel pairs, towards the surface or into the bulk, presently under investigation, should complete this work and help to understand several experimental trends. In particular, it has been experimentally observed that germanium atoms, in SiGe alloys, have a tendency to migrate towards the surface. However, if the surface is capped with a silicon oxide layer, the same Ge atoms go deep in the bulk and condense as germanium precipitates. We believe that this preliminary study can serve as a basis for further investigation and determination of migration pathways in the vicinity of surface/interfaces. It can also be seen as a reference for considering addition of further elements (such as germanium), doping species and oxidizing species.
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Contents lists available at ScienceDirect
Materials Science in Semiconductor Processing journal homepage: www.elsevier.com/locate/mssp
Surface effects on the Frenkel pair defects stability in the vicinity of the Si(001) surface S. Fetah a,b,n, A. Estève b,c, M. Djafari Rouhani b,d a
Université de M'sila, Faculté des sciences, Département de physique, 28000 M'sila, Algeria CNRS, LAAS, 7 avenue du colonel Roche, F-31400 Toulouse, France Université de Toulouse, LAAS, F-31400 Toulouse, France d Université de Toulouse, UPS, LAAS, F-31400 Toulouse, France b c
a r t i c l e i n f o
abstract
Available online 6 February 2015
A systematic first-principles pseudo-potential study of the stability of tetrahedral Frenkel pairs generated in the vicinity of the silicon Si(001)-(2 1) surface is reported. The defect formation energies and associated structures are discussed. We demonstrate that vacancies that are generated close to the surface are subject to annihilation processes either through recombination of the Frenkel pairs or through surface amorphization. On the other hand, interstitials that are positioned on the subsurface exhibit specific behaviors compared to those located deeper inside the bulk Si. Calculations indicate that the tetrahedral interstitial is unstable when located close to the surface and it relaxes to form a split-110 (dumbbell) configuration. In deeper layers, the tetrahedral interstitial remains rarely stable; it relaxes to hexagonal or to fourfold-coordinated configurations. The defect formation energies are given as a function of surface–vacancy and interstitial– vacancy distances. Results indicate that the formation energy is considerably reduced as the interstitial approaches the surface. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Si(001) Defects Si interstitial Frenkel pairs DFT calculations
1. Introduction Over the years, there has been extensive experimental and theoretical research effort to determine the structure of point defects in a wide range of materials, their migration paths, and their relative contributions to self-diffusion and impurity diffusion. For technological issues, since there is experimental evidence that point defects greatly influence dopant diffusion in semiconductors [1–4], understanding and further controlling their generation is of major importance. Considering the drastic downscaled level of current devices, we can assume that a variety of intrinsic or extrinsic defects will see their properties altered because of their location close to the surfaces and interfaces. In this
n
Corresponding author. E-mail address: [email protected] (S. Fetah).
http://dx.doi.org/10.1016/j.mssp.2015.01.015 1369-8001/& 2015 Elsevier Ltd. All rights reserved.
frame, the way interstitial atoms are generated in relation with the processing steps (deposition, oxidation, implantation, annealing etc.) and conditions (pressure, temperature, and process duration) [5–8], is still an open and controversial issue. This is particularly true at the stacking interfaces where little is known on the detailed chemical composition and on the interface strain distribution forming the potential reservoir of interstitial species. An illustrative example is the question of the generation of Si interstitials during silicon oxidation [9,10]. First principles calculations, and mainly Density Functional Theory (DFT)-based calculations, have been the method of choice to shed light into electronic as well as thermodynamic properties of defects in semiconductors. A number of investigations have addressed point defects and their diffusion characteristics in well-ordered or amorphous bulk materials [11,12]. In fact, point defects, such as vacancies and interstitials, are known to have a
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great influence on various structural, mechanical, electrical and optical properties of crystalline and amorphous materials. In turn, these properties affect the operation of semiconductor devices. Beyond interstitial generation, the paths for migration and associated energy diagrams should also be addressed in a manner to build reliable diffusion profiles. Looking at the literature, we notice that migration paths of self-interstitial atoms during diffusion are still not uniquely determined [13–17]. Surface strain and its role in the reconstruction process have been investigated for the surfaces of some metals [18] as well as for semiconductors such as silicon and germanium [19–21,32]. Even though the importance of surface/ interface strain is well recognized [22–25], there are a relatively limited number of studies dealing with their effects on the stability of interstitials [26–29]. It was demonstrated that under strain, the formation energies of bulk defects (Frenkel pairs (FP), self-interstitial atoms) decrease. Concerning surface defects, Halicioglu et al. [27] have also noticed the decrease of their formation energies. However, they made use of Stilling–Weber empirical potential which makes it impossible to really address the defect structure evolution with sufficient precision. In this paper, by investigating FP defects, we explore the ability to produce Si interstitial atoms at the vicinity of the silicon surface. Our objective is to establish a preliminary investigation through the detailed characterization of both energetic and structural behaviors of interstitials as a function of their specific location underneath the surface. This preliminary work should lead us to the selection of the most probable defects, which could then be investigated more thoroughly, regarding both their charge states as well as their stability against various close configurations. To do so, we examine in a systematic way the creation of FP for various positions of the vacancy and the interstitial atom around the vacancy, from the subsurface layer down to the bulk. In Section 2, we briefly describe the method used in the simulations before listing in detail the investigated cases. Results are reported in Section 3 where we examine exhaustively the five vacancy positions considered. Section 4 is devoted to the discussion of these results. Finally, conclusions are drawn in Section 5. 2. Computational method and simulation model The calculations are performed with the plane-wave package VASP [30,31] in the framework of the DFT, using the generalized gradient approximation [33,34] and ultrasoft pseudo-potentials of the Vanderbilt type [35] to describe both silicon and hydrogen terminations. DFT parameters satisfy compromises between convergence criteria and the required systematic approach of the present work. We considered a plane wave cutoff of 340 eV, and kpoint sampling of the Brillouin zone was performed at the Γ point [36]. The unit cell is composed of an 11 layer Si(001) slab with eight atoms per layer (total of 88 Si atoms). Convergence tests have been performed with more extended k-point meshes (1 2 1 and 2 4 1) and cell sizes, for few configurations, in order to verify their influence on both calculated structures and energetics. As shown in Section 4, the Γ point and the standard unit cell
Fig. 1. Schematic top view of the silicon unit cell surface. The letters A–E show the positions of the vacancies, as described in the text. Thick lines represent surface dimer bonds and dashed lines the boundaries of the unit cell, to be reproduced periodically.
are sufficient to describe our geometries with the required accuracy. Sixteen hydrogen atoms are used to saturate the silicon dangling bonds underneath the slab and a vacuum space is added on top of the Si slab. The final unit cell is 20 Å thick. Periodic boundary conditions are considered in all three dimensions. Fig. 1 represents the unit cell, with the dashed lines showing its lateral limits. All atoms are free to relax during energy minimization, except H and Si atoms of the two lowest silicon layers, in contact with the hydrogen saturation layer, that are kept fixed in order to mimic the bulk material. This unit cell is first relaxed through a total energy minimization, leading to a stable defect free structure. In this structure, the eight surface atoms are p(2 1) reconstructed leading to four buckled surface dimers, divided in two dimer rows separated by a channel (see Fig. 1). Let us remind that, in our model, the most important reconstruction terms: dimerization and buckling have been taken into account. In the following, this structure has been taken as the reference in energy. Once the structure of the unit cell is defined, we create FP by removing Si atoms from their lattice sites into tetrahedral interstitial positions. The defective structure is then relaxed through a new step of total energy minimization. The formation energy (Ef) of the FP can be calculated more easily than the formation energy of isolated point defects, since the total number of atoms is conserved during all energy minimization steps. Therefore, one does not need to use either an energy reference corresponding to isolated atoms, or comparing systems containing (N 1) and N atoms. The formation energy is directly obtained by subtracting the total energy of the system with the Frenkel defect from the reference energy of the relaxed defect free surface. We can notice that the investigated defects being close to the surface, charge transfers from the surface can easily be achieved, so that our defects are not necessarily neutral. However, it is not in the scope of this paper to evaluate these charge transfers. In this paper, we have systematically considered all vacancy positions in the first two subsurface layers, and one position in the fifth subsurface layer, in order to represent a bulk vacancy. The symmetry of the p(2 1) reconstructed Si (001) surface, containing buckled dimers, implies two different vacancy positions in each subsurface layer. A total of five
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vacancy positions have therefore been investigated. The atoms are next removed from their vacancy positions and inserted into lattice tetrahedral interstitial positions, as suggested in the work of Halicioglu et al. [27]. For each single vacancy site, we considered interstitial positions ranging from the surface layer down to the fifth subsurface layer, where convergence towards published bulk values has been found. In each subsurface layer, we systematically scan all possible vacancy–interstitial relative positions, up to the fourth nearest neighbors. We considered a total of 62 different FP configurations as detailed in the next section. 3. Simulation results In this section, we focus on the formation of FP, starting from vacancy positions A–E as indicated in Fig. 1. Positions A and B correspond to vacancies right in the first subsurface layer below a silicon dimer, with Si atoms respectively in upper and lower buckling positions. Positions C and D are situated in the second subsurface layer, respectively below a silicon dimer and in the channel separating the dimers. Position E represents a vacancy in the fifth subsurface layer. A total of 62 configurations have been considered in this work. Due to the systematic screening of the interstitial sites in our work, not all of the investigated configurations lead to comprehensive results, which could be analyzed individually. The reason is that the vicinity of the surface, and the absence of symmetry around the created defects, results in the multiplication of secondary minima, all in the same energy range. One way to obtain global information on these defects is therefore to examine a large number of cases and establish energy intervals for specific characteristic structures that is one goal of the present work, to provide directions for further more detailed mechanistic studies and precise model systems. In Tables 1–5, we report the simulation results obtained for vacancy sites A–E, in terms of defect configurations and associated formation energies, as a function of the initial interstitial distances to the surface and to its corresponding vacancy. Before examining individually the interesting investigated configurations, we point out some general features of the relaxed systems. Since the vacancy is created close to the surface, lattice relaxation around the vacancy is greatly enhanced, and not limited to its nearest neighbors,
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as it is the case for vacancies in bulk materials. The relaxation is indeed accompanied by a surface amorphization, which drastically changes the whole surface atomic arrangement, down to the second subsurface layer. Overall, we have observed the following mechanisms during the relaxation process: – The (2 1) reconstruction is perturbed after total energy minimization. We observe the dissociation of existing dimers and the formation of new ones. Accordingly, an amorphization of the sublayers close to the surface occurs. – Vacancy–interstitial recombination, either directly when they are initially positioned as first neighbors, or indirectly when a second atom is kicked out by the interstitial into the vacancy. In some cases, the kick out mechanisms may involve several atoms. The indirect recombination always leads to large surface perturbations. Indeed, this mechanism is very important in understanding the formation processes of amorphousstructural silicon-dioxide films where the detailed mechanisms by which Si interstitials are generated at the surface are not known [9,13]. – Annihilation of the vacancy on the Si surface. The remaining single interstitial is stabilized in various configurations: tetrahedral, hexagonal, split 〈110〉 (dumbbell) and the fourfold-coordinated defect (FFCDþ1). These different configurations have been reported in bulk silicon using DFT calculations [16,37], where they show slightly larger energies of formation than those presented in the present work. We should remind that the configurations reported in the bulk might correspond to charged states of the interstitial atom. – The creation of FP when both the vacancy and the interstitial can be clearly identified within the unit cell. As a result, a metastable state with a positive energy may be observed after relaxation. The individual cases are now examined at the light of the above considerations. 3.1. Vacancy in site A We first consider FP generated by the displacement of the Si atom located under an atom in an up position
Table 1 Final configurations and related formation energies, as a function of the initial (before energy minimization) interstitial–surface and interstitial–vacancy (A) distances. Subsurface layer
Interstitial
Interstitial–vacancy distance (Å)
Final configuration
Defect formation energy (eV)
1st 2nd
A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11
2.88 2.33 4.56 4.73 4.67 2.64 6.11 4.42 5.87 4.42 5.87
Trimer FP Direct recombination Indirect recombination Direct recombination Dumbbell Hexagonal FP Tetrahedral FP Tetrahedral FP Tetrahedral FP Tetrahedral FP Tetrahedral FP
1.65 No defect No defect No defect 1.52 2.78 4.11 4.09 3.91 4.17 4.29
3rd
4th
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Table 2 Final configurations and related formation energies, as a function of the initial (before energy minimization) interstitial–surface and interstitial–vacancy (B) distances. Subsurface layer
Interstitial
Interstitial–vacancy distance (Å)
Final configuration
Defect formation energy (eV)
1st 2nd
B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11
2.67 2.35 4.59 4.74 4.72 2.72 6.11 4.46 5.90 4.43 5.88
Direct recombination Direct recombination Hexagonal Tetrahedral Tetrahedral Indirect recombination Amorphization Tetrahedral Tetrahedral Indirect Recombination Tetrahedral
No defect No defect 1.40 2.70 2.95 No defect No defect 3.20 3.20 No defect 3.13
3rd
4th
Table 3 Final configurations and related formation energies, as a function of the initial (before energy minimization) interstitial–surface and interstitial–vacancy (C) distances. Subsurface layer
Interstitial
Interstitial–vacancy distance (Å)
Final configuration
Defect formation energy (eV)
1st 2nd
C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18
4.30 2.71 2.72 2.40 2.40 5.96 5.94 4.54 4.54 4.72 2.73 4.70 5.93 4.50 5.94 5.93 4.50 5.94
Indirect recombination Direct recombination Direct recombination Direct recombination Direct recombination Dumbbell Tetrahedral FP Tetrahedral FP Dumbbell Tetrahedral FP Hexagonal FP Hexagonal FP Hexagonal Indirect recombination Hexagonal FP Hexagonal Indirect recombination Hexagonal FP
No defect No defect No defect No defect No defect 1.56 3.43 4.06 1.58 4.06 3.01 3.12 2.75 No defect 3.70 2.75 No defect 3.70
3rd
4th
5th
Table 4 Final configurations and related formation energies, as a function of the initial (before energy minimization) interstitial–surface and interstitial–vacancy (D) distances. Subsurface layer
Interstitial
Interstitial–vacancy distance (Å)
Final configuration
Defect formation energy (eV)
2nd
D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 D11 D12 D13 D14 D15 D16 D17
2.73 2.76 2.37 2.39 4.53 4.54 5.95 5.98 2.70 4.69 4.77 5.91 4.50 5.94 5.91 4.50 5.94
Dumbbell Amorphization Direct recombination Direct recombination Tetrahedral FP Tetrahedral FP Overhang FP Overhang FP Direct recombination Tetrahedral FP Tetrahedral FP (FFCD þ 1) FP Indirect recombination Tetrahedral FP (FFCD þ 1)FP Indirect recombination Tetrahedral FP
1.48 No defect No defect No defect 4.01 3.84 2.46 2.49 No defect 3.97 3.86 3.07 No defect 4.05 3.07 No defect 4.05
3rd
4th
5th
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Table 5 Final configurations and related formation energies, as a function of the initial (before energy minimization) interstitial–surface and interstitial–vacancy (E) distances. Subsurface layer
Interstitial
Interstitial–vacancy distance (Å)
Final configuration
Defect formation energy (eV)
1st 2nd 3rd 4th 5th
E1 E2 E3 E4 E5
5.79 5.88 4.43 2.69 2.42
Trimer FP Dumbbell Hexagonal FP Direct recombination Direct recombination
2.34 1.63 2.65 No defect No defect
Fig. 2. Side view of the super-cell indicating the location of the vacancy in position (A) and their related tetrahedral Si interstitial atoms.
regarding the buckling of the overall surface dimers (see Fig. 2). In addition to direct vacancy–interstitial recombination (cases A2 and A4 in Table 1), we observe five major structures. The first one corresponds to vacancy–interstitial pairs at initial distances above 4.4 Å (cases A7–A11). The interstitials are positioned in the third or the fourth subsurface layers, far from the surface. The interstitials remain in their initial tetrahedral sites. The vacancy is stable and does not annihilate on the surface while the surface reconstruction is maintained. FP formation energies of around 4 eV are observed. The next two structures correspond to interstitials positioned in the third subsurface layer, but relaxing from their initial tetrahedral position to a dumbbell (case A5) or to a hexagonal (case A6) configuration. The tetrahedral site becomes therefore unstable, probably because of the initial interstitial position under a silicon atom in up buckling position. The effect of surface on the relaxation of interstitials is clearly visible, despite a distance of three atomic layers between the surface and the interstitial atom. The formation energies of FP are of 1.52 eV for the dumbbell structure and 2.78 eV for the hexagonal structure. In the fourth observed structure, the interstitial is initially positioned in the second subsurface layer. The interstitial relaxation is important and leads to an amorphization process, exhibiting a complex reconstruction around the vacancy, with
Fig. 3. Side view of the super-cell indicating the location of the vacancy in position (B) and their related tetrahedral Si interstitial atoms.
overall formation energy of 0.78 eV (case A3). The interstitial is neither recombined, directly or indirectly, nor stabilized in a well defined form, such as those reported in the literature [14,15,37]. A detailed examination of atomistic movements during the energy minimization shows that a kick out mechanism, as described above, takes place. The last case corresponds to the interstitial positioned on the surface (case A1). A direct vacancy–interstitial recombination does not occur despite their small initial separation. Rather, a surface trimer is created, characterized by FP formation energy of 1.65 eV. This trimer structure involves a cluster of three atoms: the interstitial and two already dimerized atoms, close to each other with a strong interaction, reducing the FP formation energy. 3.2. Vacancy in site B Now we consider the vacancy under a surface Si atom being in a buckling down position (see Fig. 3 and Table 2). Here, observed interstitials show similar qualitative features as those observed for the vacancy in site A. The main difference comes from the vacancy behavior. Being very close to the surface atom, in a down buckling position, the vacancy is generally annihilated through the dimerization process occurring around it. This leads to lower formation energies of defects, which are now composed of the interstitial alone. As in the case of the vacancy in position A, tetrahedral interstitial atoms well separated from the vacancy before minimization,
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Fig. 4. Side view of the super-cell indicating the location of the vacancy in position (C) and their related tetrahedral Si interstitial atoms.
in the third subsurface layer (cases B4 and B5) or in the fourth subsurface layer (cases B8, B9 and B11), at distances larger than 4.4 Å, remain in their initial tetrahedral positions with a formation energy of FP of 2.70 eV, 2.95 eV, 3.20 eV, 3.20 eV and 3.13 eV, respectively, slightly lower than those reported in the literature for the bulk [14,23]. This difference may be attributed to the relaxation around the vacancy enhanced by the surface vicinity. The interstitial atom (case B3) located in the second subsurface layer, which is below a silicon surface atom in an up buckling position, relaxes spontaneously from its tetrahedral structure to a hexagonal configuration, FP formation energy is 1.40 eV. We note here that the defect is only composed of a single interstitial, the vacancy being annihilated. That is why the formation energy is about 1 eV lower than those reported above, for the vacancy in site A. Almost perfect recombination occurs for cases B1 and B2 while indirect recombination is observed for cases B6 and B10. 3.3. Vacancy in site C We consider here the cases where the vacancy is created in the second subsurface layer, below the dimer row. The objective is to address the issues related to the formation of FP deeper in the silicon layer. FP formation energies and initial vacancy–interstitial distances for this vacancy site are reported in Table 3 and the interstitial sites are shown in Fig. 4. The fact that the vacancy is now in a very strained region, under the dimer row, modifies qualitatively some of the observed features. Apart from the cases where the vacancy–interstitial are close enough to recombine directly (cases C2–C5) or by successive kick outs and surface amorphization (cases C1, C14 and C17), large surface relaxation leading to its amorphization, and to a multiplication of local minima, generally takes place. This results in lowering of the FP formation energies, either slightly through local relaxation, or more largely through transitions from tetrahedral to hexagonal or to dumbbell configurations. We observe that this local mechanism is independent of the interstitial position depth. For example, interstitials stabilized in tetrahedral configurations may be positioned in third or
Fig. 5. Side view of the super-cell indicating the location of the vacancy in position (D) and their related tetrahedral Si interstitial atoms.
fourth subsurface layers (cases C7, C8 and C10). The corresponding formation energies of FP are in the range of 3.43 to 4.06 eV, close to values found for the vacancy in site A. However, the tetrahedral interstitials in the cases (C11 and C12) situated in the fourth layer are relaxed to hexagonal positions with formation energies of 3.01 eV and 3.12 eV, respectively. The same behavior is observed for the interstitials corresponding to the cases (C15 and C18) situated in the fifth layer but now with higher energies (3.70 eV) due to their depth towards the bulk material. The interstitials in the cases (C13 and C16) also situated in the fifth layer are relaxed to hexagonal positions with lower formation energy (2.75 eV). This is likely to be due to the vacancy annihilation upon amorphization. The interstitials situated in the third subsurface layer may relax to the dumbbell configuration (cases C6 and C9) with formation energies of 1.56 eV and 1.58 eV, respectively. As for vacancy site A, the dumbbell configurations have their corresponding vacancies annihilated on the surface explaining the comparable formation energies. 3.4. Vacancy in site D As for vacancy C, the vacancy in site D is created in the second subsurface layer, but in the channel separating the dimer rows. Direct recombination is observed in the cases D3 and D4. The specificity of this vacancy site is seen from the amorphous versus recombination processes of locally created interstitials. For example, interstitials positioned at the same depth as the vacancy, in the second subsurface layer, and close to the vacancy at distances below 2.73 Å (cases D1 and D2 in Table 4 and Fig. 5), do not automatically recombine with the vacancy, as observed for the three previous vacancy sites. Rather, we observe either a dumbbell configuration for the interstitial accompanied with an annihilation of the vacancy on the surface, or a complete amorphization of the surface. These two situations occur correspondingly when the interstitial is located
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Fig. 6. Schematic view of the interstitial in overhang position above the vacancy in site D.
under a surface atom in down and up buckling positions. FP formation energies are 1.48 and 2.20 eV. For interstitials deeper in the layers, three types of behaviors are observed. In the first type, interstitials remain in their tetrahedral configurations, with FP formation energies 4.01 eV and 3.84 eV respectively in the cases (D5 and D6) located in the third layer, 3.97 eV and 3.86 eV in the cases (D10 and D11) respectively, located in the fourth layer, and with 4.05 eV in the cases (D14 and D17) located in the fifth layer. The second type concerns interstitials which relax from their tetrahedral configurations to FFCDþ1 (cases D12 and D15), where an interstitial is associated to a four-folded coordinated defect. This configuration has been reported in bulk structures [38–42]. It has been shown that this structure plays a crucial role in bringing disordered configurations [42]. FP formation energies are now reduced to 3.1 eV, about 1 eV lower than normal tetrahedral configurations. This results from the interstitial relaxation towards a (FFCDþ 1) configuration as also demonstrated in bulk calculations [4]. In a third type of behavior, represented in Fig. 6 we observe a new configuration of vacancy–interstitial pair, which we call “overhang” (cases D7 and D8). In this configuration, the interstitials, initially in the third subsurface layer, migrate towards the surface and stabilize in the first subsurface layer, just above the vacancy in the second subsurface layer. We should remind that the (2 1) reconstruction of the Si(001) surface and the presence of dimers on the surface, with atoms positioned at short distances, results in the creation of a free space above the channel. The upward migration of the interstitial is therefore facilitated to fill the free space. The term “overhang” relates to the fact that the interstitial is placed above the vacancy, in a metastable position. This vacancy–interstitial configuration is specific to the presence of the surface and we believe that no such configuration can be observed in the bulk, where a direct recombination takes place spontaneously. The vacancy–interstitial attractive interaction is large and leads to FP formation energies of 2.5 eV. 3.5. Vacancy in site E Finally, we consider the FP generated by the displacement of the Si atom positioned deep inside the bulk; in the
Fig. 7. Side view of the super-cell indicating the location of the vacancy in position (E) and their related tetrahedral Si interstitial atoms.
fifth subsurface layer (see Table 5 and Fig. 7). We can now observe situations where the vacancy is deep below the surface but the interstitial is close to the surface. These situations are opposite to some of the previous situations where the vacancy was close to the surface and the interstitial in deep layers. Three types of FP are observed where the interstitials are in hexagonal, dumbbell and trimer configurations and the vacancy is not annihilated. The respective formation energies of FP are 2.34 eV 1.63 eV and 2.65eV (cases E1–E3). The trimer configuration was already observed with the vacancy created in site A. But the FP formation energy is higher in the present situation because of the position of the vacancy, deep in the bulk, and far from the interstitial on the surface. Here, the absence of attractive vacancy–interstitial interaction leads to higher formation energy. The other cases lead to direct recombination due to the interstitial–vacancy proximity. 4. Discussion The first question is to check the impact of k-point sampling and the size of the unit cell on the accuracy of the reported results. To this end, we have tested three k-point samplings: 1 1 1 (Γ point), 1 2 1, and 2 4 1, and two substrate surface sizes: 7.2 Å 15.4 Å and 15.4 Å 15.4 Å, applied to case A10. These two unit cells contain 8 and 16 Si atoms on the (001) surface. The case A10, where the interstitial atom is neither too close nor too far from the surface, represents a good compromise between all 62 cases investigated in this paper. On pure Si(001) surface with p(2 1) reconstruction, no structural changes have been observed between all calculations. However, various k-samplings lower slightly the energies with respect to Γ point sampling: 0.13 eV and 0.16 eV per atom for 1 2 1 and 2 4 1 samplings, respectively. Looking at FP formation in the case A10, we observe slight structural deviations around the vacancy.
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We also observe a decrease of the formation energy of FP with respect to Γ point sampling: 0.35 eV and 0.16 eV for 1 2 1 and 2 4 1 samplings, respectively, representing 8% and 4% deviations. Doubling the size of the unit cell, i.e. reducing interactions between defects, lowers the FP formation energy by 4%. We can conclude that the Γ point approximation associated to a unit cell containing 88 Si atoms represents a relatively accurate model for this preliminary investigation. To summarize the previous results in order to obtain global information, we can notice that interstitials positioned deeper than the third subsurface layer hardly feel the presence of the surface. This results in interstitials in metastable tetrahedral configurations, which do not spontaneously relax to hexagonal or dumbbell configurations. As mentioned in the introduction, the activation barriers for these transitions have not been evaluated. The corresponding FP formation energies are in the range of 4 eV similar to what has been calculated for the self-interstitial. In cases where the vacancy is annihilated through amorphization of the surface, particularly when the vacancy is situated below a silicon surface atom in the down buckling position, the formation energy can decrease to 3 eV, compared to 4 eV for bulk isolated interstitials [14,16,42]. The amorphization effect can therefore be estimated to a maximum reduction of the formation energy of 1 eV. This shows that the attractive vacancy–interstitial interaction is still strong, even at distances up to 4.4 Å. As we can see later, the relaxation around the vacancy and the surface amorphization cannot explain by itself this decrease of the FP formation energy. Closer to the surface, the tetrahedral structure becomes unstable and might relax spontaneously to hexagonal or dumbbell structures. FP formation energies are in the range of 2.70–2.78 eV for hexagonal, and of 1.29–1.58 eV for dumbbell configurations. These energies are much lower than 4 eV, relative to the cases where interstitials were in tetrahedral sites. This result is contrary to the results for bulk interstitials where formation energies are almost equivalent for the three structures, namely 4.07 eV, 3.80 eV and 3.84 eV for interstitials in tetrahedral, hexagonal and dumbbell configurations, respectively [14]. This discrepancy can be explained by the large surface relaxation which completely destabilizes the tetrahedral configuration towards hexagonal and dumbbell structures, for interstitials close to the surface. The dumbbell seems to be the easiest to create, particularly at high processing temperatures, for example temperatures used during the oxidation. We observe that the surface acts as an efficient sink for the subsurface vacancies. However, in several cases, as a result of the surface buckling, subsurface vacancies remain stable. 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. We show that Si interstitials can be created with low energies (1–1.6 eV), resulting in the presence of large interstitial concentration at high processing temperatures. This tendency is enhanced if a cap, such as an oxide layer, inhibits the climb of interstitials. Another specific effect, due to the vicinity of the surface, is the annihilation of the vacancy, resulting either
from vacancy–interstitial recombination, or from more complex collective relaxation processes that cannot take place in the bulk. We have observed two different relaxation mechanisms. In the first one, we can observe vacancy–interstitial recombination via a kick out mechanism, consisting of successive atomic displacements up to the vacancy annihilation, as described in Section 3. No visible defect, vacancy or interstitial, can be seen in the final structure, but the successive atomic displacements lead to an amorphization of the surface, with an energy in the range of 0.78–1.08 eV. The second mechanism, more often observed in our calculations, is the annihilation of the vacancy by amorphization of its neighboring atoms. The vacancy is no more visible but the interstitial can be clearly identified. Although this second mechanism is energetically less favorable than the first, we think that it is kinetically more probable, since it is performed in only one step instead of multiple steps necessary for the successive atomic displacements. Whatever the mechanism, the low energies involved favor the amorphization of the surface, precursor for the subsequent growth of an amorphous oxide layer. Finally, we observe two particular atomic clustering on the surface, resulting from the migration of interstitials. The first one is the trimer configuration where the interstitial bounds to two surface atoms already forming a dimer. The second configuration, observed in the channel separating the dimer rows, is the “overhang” configuration where the migrating interstitial is placed above the vacancy, without any spontaneous recombination, although they are quite close to each other. These configurations are metastable in the sense that they correspond to a secondary energy minimum. 5. Conclusion A systematic first-principles pseudo-potential study of the stability of Frenkel pairs generated in the vicinity of the silicon Si(001)-(2 1) surface is reported. We demonstrate that vacancies that are generated close to the surface are not necessarily stable, but have a propensity to annihilate either through recombination of the Frenkel pairs or through surface amorphization originated by the vacancy itself. This statement is particularly true for vacancies situated below a surface atom in down buckling position. Below a surface atom in up buckling position, the vacancy is usually stable and in a configuration close to an interstitial in the “overhang” structure, observed inside the channel separating the dimers. However, interstitials that are positioned on the subsurface exhibit specific behaviors in comparison to those located deeper inside the bulk Si. As previously demonstrated by Halicioglu et al. [27], we qualitatively observe that the interstitials are easier to generate in the subsurface than in the bulk. Beyond this, we quantitatively give both the formation energies of these defects and associated structures. We also show that the dumbbell configuration is the most stable for subsurface interstitials. In contrast, the tetrahedral interstitials located deeper into the bulk remain stable, or may relax to hexagonal, as well as to fourfold-coordinated configurations (FFCDþ1), in specific cases. Both these structures have been observed in the bulk and described in the
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literature: the tetrahedral structure for the charged selfinterstitial and the hexagonal structure for the neutral selfinterstitial [42]. Finally, two structures: trimer and overhang are reported as surface specific configurations, not observed in the bulk. In general, we can conclude that the vicinity of the surface facilitates the relaxation of defects and has a similar effect as the temperature for defect creation in the bulk. The migration of Frenkel pairs, towards the surface or into the bulk, presently under investigation, should complete this work and help to understand several experimental trends. In particular, it has been experimentally observed that germanium atoms, in SiGe alloys, have a tendency to migrate towards the surface. However, if the surface is capped with a silicon oxide layer, the same Ge atoms go deep in the bulk and condense as germanium precipitates. We believe that this preliminary study can serve as a basis for further investigation and determination of migration pathways in the vicinity of surface/interfaces. It can also be seen as a reference for considering addition of further elements (such as germanium), doping species and oxidizing species.
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