Diffusion of oxygen atom in the topmost layer of the Si(100) surface: Structures and oxidation kinetics

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1 Surface Science 601 (2007) Diffusion of oxygen atom in the topmost layer of the Si(100) surface: Structures and oxidation kinetics A. Hemeryck a, *, N. Richard b, A. Estève a, M. Djafari Rouhani a a Laboratoire d Analyse et d Architecture des Systèmes, CNRS, 7, av. Colonel Roche, Toulouse, France b CEA-DIF, BP12, Bruyères Le Châtel, France Received 12 January 2007; accepted for publication 22 March 2007 Available online 2 April 2007 Abstract The incorporations and migrations of the atomic oxygen in the topmost layer Si(1 0 0)-p(2 2) silicon surface, are investigated theoretically using density functional theory. We show that the diffusion is dependent on the starting and the final surrounding environment and does not simply consist in hops from one silicon silicon bond to another. The activation energies range from 0.11 ev to 2.59 ev. Ó 2007 Elsevier B.V. All rights reserved. Keywords: Density functional calculations; Surface diffusion; Oxidation; Semiconducting surfaces 1. Introduction Because of the obvious constant scaling down of the silicon-based devices in microelectronic [1] and because the Deal Grove Model breaks down for the ultrathin oxides [2,3], the understanding of reaction mechanisms occurring at the earlier stages of the silicon oxidation at the atomic scale becomes important. Considering elementary reaction processes on the Si(1 0 0) surface, the oxidation also relies on the dissociation of the molecular oxygen, the adsorption, the penetration and the diffusion of the atomic oxygen in the topmost layer, creating and breaking bonds between the oxygen and silicon atoms near the surface and at the interface. These diverse mechanisms have to be characterized not only in terms of atomic structures and the corresponding stability of resulting oxygen and silicon atoms, but also in terms of oxidation kinetics, by defining their activation energies in the oxidation reactions. * Corresponding author. Tel.: ; fax: address: ahemeryc@laas.fr (A. Hemeryck). The oxidation kinetics have been tackled in many studies, for example, about the oxidant species diffusion in silica using peroxy-like structures [4 7], or at the interface [8], with Monte Carlo techniques or molecular dynamics underlying threefold coordinated structures [9,10], all using a silicon dioxide already formed on the silicon substrate. With theoretical calculations, Kato et al. [11] carried out investigations about the diffusion of atomic oxygen from dimer bond to the backbond through an on-top configuration, Lee et al. [12] studied the chain migrations of O 2! O 9. However, studies completely dedicated to the kinetics of initial reactions of surface layer or subsurface layer have never been performed to our knowledge. These kinetics are important to determine the oxide growth at the first stages of the silicon oxidation when the interface begins to form. In this paper, our challenge draw up the mechanisms linked to the capacity of an oxygen atom to incorporate, and then to diffuse in the topmost surface layer. Actually, the diffusions of oxygen atom from Si Si bonds to Si Si bonds [12] are not sufficient, but it is primary to study each diffusion considering the starting structure. According to Ramamoorthy and Pantelides [13], the complexity of the oxygen diffusion problem comes from /$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi: /j.susc

2 2340 A. Hemeryck et al. / Surface Science 601 (2007) the breaking and reformation of bonds. Firstly, the different ways for the oxygen atom to incorporate in the surface layer of the silicon substrate once the oxygen molecule dissociated, is studied. Then, the diffusion of these atoms in the topmost layers is presented. The critical parameter in a kinetic study is the activation energy, which is given for each diffusion as well as the restructuring and the formation of bonds for the pathway structures. All the activation energies calculated are associated to an occurrence time in order to give a highlight on the most probable diffusions. This time is determined at 900 C, a conventional thermal growth temperature, considering a typical attempt frequency of m =10 14 s 1 [14]. 2. Calculation details The calculations are performed using the density functional theory (DFT) with the plane wave-pseudopotentials program package VASP [15]. The density is described with the generalized gradient approximation (GGA) [16]. The energy cutoff is fixed at 475 ev. The ions are described by ultrasoft pseudopotentials [17]. All the atomic relaxations are performed using the conjugate gradient method. We take into account spin-polarization to properly describe the possible spin conversion during diffusion. The Brillouin zone is sampled at the C point. This only point is sufficient to describe accurately the geometries of semiconductors. The reaction pathways and activation energies are calculated with the nudged elastic band method (NEB) [18]. The Si(100)-p(2 2) used in this paper, is modelled as a periodic cell of a slab Si 48 H 16 consisting in six layers of eight silicon atoms, with the two lowest layers kept fixed in their crystalline positions to simulate the bulk, whereas the other layers are allowed to fully relax. A channel and a buckled dimer row on the surface are present on the surface due to the p(2 2) reconstruction [19]. A vacuum inter-slab zone of 10 Å is placed along the z-axis to create a surface effect, and the dangling bonds of the silicon atoms underneath the slab are passivated with 16 hydrogen atoms. 3. Results and discussion 3.1. Oxygen atom incorporations Fig. 1. Energetic diagram of the one oxygen atom structures, the white circles correspond to silicon atoms and the black ones to the oxygen atoms. Figure A corresponds to a down backbond position, B to a 2nd layer Si Si bond position, C to a dimer bond position, D to a Si O Si bridge in the channel, E to an on-top position, F to a siloxane bridge. Previous calculations [20,21] have revealed that once the oxygen molecule is dissociated, the oxygen atoms are stabilized first on the silicon surface in on-top configurations due to the presence of the dangling bond on each surface silicon atom. The energetic diagram in Fig. 1 confirms that the oxygen atom prefers to incorporate in the topmost layer in a Si Si bond centre since the backbond (BB) and the dimer bond are energetically more favourable [22,23] leading to a two-steps oxidation process: adsorption and then incorporation of oxygen atom. Starting from the on-top configuration, we estimate three possible incorporations of the oxygen atom. The corresponding pathways are described in Fig Oxygen atom incorporation in the dimer bond: pathway #1 When the oxygen atom is in on-top position, the dimer bond is broken and the SiO bond is 1.54 Å long. During the incorporation of the oxygen atom, the length of the SiO bond increases whereas the length of the dimer bond decreases until the dimer bond is reformed. The oxygen atom in the on-top position can be easily incorporated in the dimer bond with a small activation barrier of magnitude of 0.11 ev (hti = s), as shown in Fig. 2, #1. The final structure obtained is more stable by 1 ev than the on-top configuration. In this structure, the Si O Si angle is close to 85 and the Si O bonds are both of 1.70 Å long. The reformed dimer bond has a distance of 2.32 Å and the buckling in the dimer is locally reduced Oxygen atom incorporation in the backbond: pathway #2 In on-top configuration, the Si@O bond measures 1.54 Å and the Si Si backbond is of 2.38 Å long. During the diffusion process, the Si@O length stretches until 1.62 Å and then, the oxygen atom incorporates in the Si Si backbond still formed. So, the incorporation in the backbond, has a higher activation energy of 0.38 ev (hti = s) compared to the incorporation in the dimer bond (Fig. 2, #2) for an equal energy gain of around 1 ev. This result is consistent with the previous values obtained by Kato [11]. Finally, the BB breaks and the final structure has a Si O Si angle of 125, Si O bonds of 1.62 Å and 1.69 Å, and a Si Si distance of around 3 Å. We can notice that the oxygen atom is more linked to the surface silicon atom Oxygen atom diffusion in the siloxane bridge: pathway #3 We define as siloxane bridge, referred surface-bridging oxygen and noted sbo in Ref. [23], a bridge created by an oxygen atom incorporated between two dangling bonds of silicon atoms of two adjacent dimers: a Si O Si bridge is then formed between two dimers perpendicularly to the dimer row (schematised in Fig. 1-F).

3 A. Hemeryck et al. / Surface Science 601 (2007) Fig. 2. Minimum-energy pathways #1, #2, #3 for the incorporation in dimer bond #1, in the backbond #2, and in the siloxane bridge #3, respectively, the oxygen atoms are in black and the silicon atoms are in grey. The sbo has a Si O Si angle of around 105 and then distorts the two dimers: the dimer silicon atoms move out of their crystalline positions, and the final Si O bonds are of around 1.75 Å. We have to specify that the siloxane bridge structure is less stable than the on-top configuration by 0.29 ev, as shown in Fig. 2, #3. The incorporation of the oxygen atom in the sbo configuration is characterized by a large activation barrier of 0.88 ev (hti = s) and has a low probability to occur in the case of the migration of a single atom. However, this diffusion has to be taken into account, because it is the only way for an oxygen atom to diffuse along the dimer row, without the full incorporation of the oxygen atom. Moreover, Yamasaki et al. [23] show that the sbo position is energetically favourable configuration when the number of oxygen atoms is superior at 3, and promotes the full coverage of the first layer. We will show in a further paper, that the activation barrier we found is reduced with the presence of other oxygen atoms. These calculations underline that the thermodynamically favourable first incorporation occurs in the Si Si centre bonds in the dimer bond as well as in the backbond because their activation energies are both small compared to the 2 ev obtained during the dissociative chemisorption [20,21]. These two first incorporations are consistent with the silanone structure [24,25] which appears to be an primordial state during the silicon oxidation. Once incorporated, the oxygen atom is able to diffuse from Si Si bond to another adjacent Si Si bond BB to BB diffusion: pathway #4 The corresponding pathway is shown in Fig. 3. In our case, this diffusion occurs through an intermediate state like a two-steps reaction process. The intermediate state used is the sbo configuration as described above. The starting configuration is the backbond. This pathway is constructed with the help of two diffusions pathways calculations, the first from the BB centre to the sbo position, and the second from the sbo configuration to the BB centre of the second dimer. The BB centres and the sbo positions are fully relaxed. Fig. 3. Minimum-energy pathway #4 for the BB to BB diffusion through the siloxane bridge, obtained with two minimum-energy pathway calculations. The two BB points (global minima points A and E) and the siloxane bridge position (local minimum point C) are fully relaxed, whereas the other points of the curve are stressed. The oxygen atoms are in black and the silicon atoms are in grey. The energy barrier for this extraction is large (1.86 ev (hti = s)). At this low level of coverage, the high activation barrier obtained to extract the oxygen atom from the BB gives a low probability to the reaction to occur. The stressed peak point of the diffusion (point B and D in Fig. 3) is close to the sbo configuration shown in Fig. 2, #3 but the Si O Si angle is larger (125.6 measured in the peak point structure compared to in the sbo structure). The siloxane bridge is more stable of 0.57 ev compared to the peak point, this value is the activation energy to get the BB from the siloxane bridge (hti = s). The reaction intermediate, i.e. the siloxane bridge, is clearly a metastable state, as it exists two more stable states of around 1.5 ev in the surroundings of the oxygen atom. Typically, this diffusion shows that the oxygen atom migration needs to break and to recreate Si O and Si Si bonds. This two-steps reaction process provides strong evidence that the diffusion process is an adiabatic reaction because of the symmetry in the reaction minimum-energy pathway Channel crossing From the BB position, the oxygen atom can diffuse through the channel. We investigate two ways for the oxygen atom to go across the channel schematised in

4 2342 A. Hemeryck et al. / Surface Science 601 (2007) Fig. 4. Channel side view and schematisation of the pathways for the channel crossings: #5 via a Si O Si bridge and #6, the white circles correspond to silicon atoms and the black and dash circles to the oxygen atoms. Fig. 4: through a Si O Si bridge (pathway #5) or through hops from Si Si bond to Si Si bond (pathway #6) The channel crossing through an intermediate: pathway #5 This pathway, formed with the help of the association of two diffusion pathways calculations, consists in a stabilized oxygen atom bonded to two channel silicon atoms (a and b in Fig. 4). In this intermediate configuration which is a local minimum of the pathway (point C in Fig. 5, #5), the two silicon atoms (a and b) are four-bonded. This structure is fully relaxed. In fact, one of the BB in the bulk under the dimer row is broken, because these two silicon atoms are shifted from their crystalline positions of 0.7 Å along the z-axis. The Si O Si angle for this channel intermediate is of and the Si O bonds are around 1.7 Å. Yamasaki et al. referred this oxygen atom position as a bbo, meaning bulk-bridging oxygen [23]. This particular position is obtained when a P b0 centre is created during the oxidation of deeper layers. As explained in the previous part for the BB to BB diffusion, the BB starting configuration (point A in Fig. 5, #5) is the most stable state and it is very difficult to move out the oxygen atom from the BB. The extraction shown in Fig. 5, #5, needs thus to overcome an large energy barrier of 1.87 ev (hti = s) to reach the bbo position. The bbo position is a metastable state less stable than the BB structure by 0.56 ev. The large activation energy and the less favourable bbo position obtained reveal that this diffusion at low coverage can not be reach. We can notice that during this diffusion, the oxygen atom gets to an on-top position in the channel called peak point of the diffusion minimum-energy pathway with a Si O length of 1.53 Å similar to the on-top position on the surface. The second step in this diffusion is the pathway from the intermediate (point C in Fig. 5, #5) to the BB (point E in Fig. 5, #5) at the opposite side of the channel. This process requires an activation barrier of 1.36 ev (hti = s) through the stressed peak point D. This two steps pathway is symmetric underlying that the diffusion process is adiabatic, as the second step is the back-reaction of the first step The channel crossing through hops #6 The second pathway to cross the channel occurs via several hops from Si Si bond to Si Si bond by extracting an oxygen atom from the BB to insert it in the second layer Si Si bond (as described #6 in Figs. 4 and 5). The oxygen atom is initially in the BB position and diffuses towards the second layer BB. We can notice here that the second layer BB configuration is less favourable than the first layer BB with an energetic difference of 0.18 ev. In the second layer the Si O Si angle is larger than in the BB, with 143 and 116, respectively, and the Si O bonds are typically around Å. During the migration, the Si O bond near the surface is stretched and then breaks, leading once again to a on-top configuration in the channel: this point corresponds to the peak point of the diffusion pathway. To reach the second layer, the oxygen atom had to overcome a huge activation barrier of 2.59 ev (hti = s), which is consistent with Watanabe et al. (2.4 ev) [26]. This high-energy barrier suggests that this kind of diffusion is not probable at low coverage. But, Watanabe also found an experimental value of 0.3 ev during the layer-bylayer oxidation. This large energetic difference can be explained by the fact that experimentally, the first layer is fully oxidized, whereas in our calculations the surface has only one diffusing oxygen atom, or by the stress effects at the interface lowering the activation barrier for the second layer. Moreover, it has been shown that the diffusion is made easier with the presence of other oxygen atoms, as shown in the case of chain diffusions [12]. The diffusions to cross the channel or to get lower layer are difficult at low coverage. When the number of oxygen Fig. 5. Minimum-energy pathways #5 and #6 for the channel crossing through a Si O Si bridge #5 and using hops from Si Si to Si Si bonds #6. The pathway #5 obtained is due to the addition of two calculations. The two BB points (global minima points A and E) and the channel intermediate state (local minimum point C) are fully relaxed, whereas the other points of the curve are stressed. The oxygen atoms are in black and the silicon atoms are in grey.

5 A. Hemeryck et al. / Surface Science 601 (2007) atoms incorporated in the surface increases, the most probable diffusion is the pathway #5, as suggested by Yamasaki et al. [23]. Our calculations confirm that the oxidation proceeds first in a lateral manner and then by layer-by-layer way, and that a high coverage close to the full coverage of the first layer is necessary to oxidize the deeper layer. 4. Conclusions In this paper, we have presented a list of the possible incorporations from the on-top configuration and migrations from Si Si bond to Si Si bond of the atomic oxygen in the topmost layer Si(1 0 0)-p(2 2) silicon surface. Thus, diffusion barriers are also extremely sensitive to the local topology and range, in the topmost layer, from 0.11 ev for the oxygen incorporation in the substrate to 1.87 ev for the diffusion in the first layer in the channel (2.59 ev for the incorporation in the second layer). But in all cases, oxygen atom seems to diffuse preferentially in the dimer and in the backbond Si Si bonds, whereas the other diffusions such as the incorporation in the siloxane bridge are promoted when the coverage is increased. The migration pathway is also influenced not simply by the adiabatic minimum-energy pathway, but also by the dynamics of the diffusion hop and the local atomic configuration. References [1] G.E. Moore, Electronics 38 (1965). [2] B.E. Deal, A.S. Grove, J. Appl. Phys. 36 (1965) [3] E.P. Gusev, H.C. Lu, T. Gustafsson, E. Garfunkel, Phys. Rev. B 52 (1995) [4] T. Bakos, S.N. Rashkeev, S.T. Pantelides, Phys. Rev. Lett. 88 (2002) [5] M.A. Szymanski, A.L. Schluger, A.M. Stoneham, Phys. Rev. B 63 (2001) [6] J.R. Chelikowsky, D.J. Chadi, N. Binggeli, Phys. Rev. B 62 (2000) R2251. [7] A.M. Stoneham, M.A. Szymanski, A.L. Schluger, Phys. Rev. B 63 (2001) [8] T. Akiyama, H. Kageshima, Appl. Surf. Sci. 216 (2003) 270. [9] A. Pasquarello, M.S. Hybertsen, R. Car, Nature 396 (1998) 58. [10] K.-O. Ng, D. Vanderbilt, Phys. Rev. B 59 (1999) [11] K. Kato, T. Uda, K. Terakura, Phys. Rev. Lett. 80 (1998) 2000; K. Kato, T. Uda, Phys. Rev. B 62 (2000) [12] Y.J. Lee, J. von Boehm, M. Pesola, R.M. Nieminen, Phys. Rev. B 65 (2002) [13] M. Ramamoorthy, S.T. Pantelides, Phys. Rev. Lett. 76 (1996) 267. [14] H.Z. Massoud, J.D. Plummer, E.A. Irene, J. Electrochem. Soc. 132 (1985) [15] G. Kresse, J. Furthmüller, Phys. Rev. B 54 (1996) 11169; G. Kresse, J. Joubert, Phys. Rev. B 59 (1999) [16] J.P. Perdew, Y. Wang, Phys. Rev. B 45 (1992) [17] D. Vanderbilt, Phys. Rev. B 41 (1990) [18] G. Mills, H. Jònsson, G.K. Schenter, Surf. Sci. 324 (1995) 305; H. Jònsson, G. Mills, K.W. Jacobsen, in: B.J. Berne, G. Ciccotti, D.F. Coker (Eds.), Classical and Quantum Dynamics in Condensed Phase Simulations, World Scientific, Singapore, 1998, p [19] A. Ramstad, G. Brocks, P.J. Kelly, Phys. Rev. B 51 (1995) [20] N. Richard, A. Estève, M. Djafari Rouhani, Comp. Mater. Sci. 33 (2005) 26. [21] A. Hemeryck, N. Richard, A. Estève, M. Djafari Rouhani, J. Non- Cryst. Solids 353 (2007) 594. [22] Y. Miyamoto, A. Oshiyama, Phys. Rev. B 41 (1990) [23] T. Yamasaki, K. Kato, T. Uda, Phys. Rev. Lett. 91 (2003) [24] A. Hemeryck, A. Mayne, N. Richard, A. Estève, Y.J. Chabal, M. Djafari Rouhani, G. Dujardin, G. Comtet, J. Chem. Phys. 126 (2007) [25] Y.J. Chabal, K. Raghavachari, X. Zhang, E. Garfunkel, Phys. Rev. B 66 (2002) [26] H. Watanabe, K. Kato, T. Uda, K. Fujita, M. Ichikawa, T. Kawamura, K. Terakura, Phys. Rev. Lett. 80 (1998) 345.