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Simulations of initial stages of boron deposition on (1 1 0) tungsten surface
Surface Science 566–568 (2004) 676–682 www.elsevier.com/locate/susc
Simulations of initial stages of boron deposition on (1 1 0) tungsten surface Simon Dorfman a, Ronan R. Braga b, Kleber C. Mundim b, David Fuks
c,*
a
c
Department of Physics, Technion-Israel Institute of Technology, 32000 Haifa, Israel b Inst. Quimica, Uni. Brasilia, C.P. 4478, 70919-970 Brasilia, Brazil Department of Materials Engineering, Ben-Gurion University of the Negev, P.O. Box 653, 84105 Beer Sheva, Israel Available online 11 June 2004
Abstract Non-empirical potentials are employed in atomistic simulations of the deposition process of boron on tungsten (1 1 0) surface in the framework of the generalized simulation annealing formalism. A comparative analysis of the fine atomic structure in the vicinity of the surface clears up the behavior of the system in the simulated deposition process. Existence of a number of energy barriers in the adhesion path of the boron atom demonstrates the dependence of adhesion conditions on the energy of the atom approaching the surface. This result also shows that the conditions of the metalloid adhesion are influenced by the directional bonding nature and the structural reconstruction of the substrate surface. Ó 2004 Elsevier B.V. All rights reserved. Keywords: Adsorption kinetics; Tungsten; Boron; Monte Carlo simulations; Adhesion
1. Introduction The past decade has brought an impressive progress in cubic boron nitride (c-BN) thin film technology. This is true for the development of deposition techniques and processes, theoretical understanding of the underlying mechanisms and the characterization of basic and application-related film properties alike (for recent reviews see [1–6]). c-BN possesses many interesting properties,
* Corresponding author. Tel.: +972-8-6461460; fax: +972-86472946. E-mail addresses: [email protected] (S. Dorfman), [email protected] (D. Fuks).
such as high hardness close to that of diamond, large band gap, small friction coefficient, excellent optical transmission, high thermal conductivity and chemical inertness. Large compressive intrinsic stress and poor adhesion are normally found in these films due to non-stoichiometric boron nitride deposition [7], which results in the delaminating of film from the surface. Problems such as high stress and the poor adhesion of the deposited film with the substrate are commonly observed. The problems obviously prevent c-BN’s variety of technical applications and thus must be solved. Cubic boron nitride film formation usually involves the deposition of boron or boron nitride film from solid or gaseous precursors, and the bombardment of this growing film with either a mixture of nitrogen and inert gas ions or pure inert gas ions [1,3–6].
0039-6028/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2004.05.128
S. Dorfman et al. / Surface Science 566–568 (2004) 676–682
In our work, the study of the interactions of boron atoms with tungsten (1 1 0) surface has been conducted. The study is expected to give useful information on the first step of the direct deposition so as to provide insight on achieving a better adhesion of c-BN films. Investigation of the metalloid deposits on metal surfaces has attracted a lot of attention in recent years [8,9]. Nevertheless, despite of the application importance, and, hence, the very extensive research undertaken in this field over the last decade, there is still a limited knowledge about the underlying physics and chemistry of such systems [10]. In relation to this, it is necessary to perform further investigation on the adsorption of metalloid atoms, clusters and thin films on the surfaces of metals. The microscopic features of metal–metalloid interfaces including the reconstruction of the surface where the metalloid atom is adsorbed are only rarely known from direct measurements [11]. Some aspects of adsorption of O, H, C on low-index W surfaces were studied recently [12] showing the importance of both chemical and structural effects in the binding of adsorbed atoms to the surface. In this communication we illustrate directly the importance of directional bonding in simulations of the deposition process on the tungsten (1 1 0) surface.
2. Methodology Interatomic potentials [9,13] that we use in our simulations do not contain any adjustable parameters to obtain better agreement with experiments and are absolutely ab initio. In the development of these potentials the problem of determination of the tungsten–boron interatomic potential was solved. W–W, W–B, and B–B interacting potentials were derived on the basis of non-empirical calculations of total energies within the recursive procedure. For details we refer to our recent papers [9,13–17]. In atomistic simulations we used the MC methodology in the generalized simulated annealing approach (GSA) (see, for example, Ref. [14] and references therein). GSA is based on the correlation between the minimization of a cost func-
677
tion (conformational energy) and the geometry randomly obtained through slow cooling. In this technique, an artificial temperature is introduced, and the system is gradually cooled in a complete analogy with the annealing technique used in metallurgy when a molten metal reaches its crystalline state (the global minimum of the thermodynamic energy). In our case the temperature plays the role of an external noise. The artificial temperature (or a set of temperatures) acts as a convenient stochastic source for eventual detraining from local minima. The procedure of searching the minima (global and local) or mapping the energy hypersurface consists of comparing the energies of two consecutive random geometries xtþ1 and xt obtained from the GSA routine. Here xt is a N -dimensional vector that contains all atomic coordinates ðN Þ to be optimized. For details of our MC approach see Refs. [9,13–17]. We simulated the adhesion process of a boron atom on the tungsten (1 1 0) surface and studied a site occupation preference for the boron atom. The surface was simulated in a cluster approximation with 393 atoms. In Fig. 1 we show the sites that were selected for simulations of the adsorption process. The primary task in our search of wellconverged statistical averages for geometry relaxation process in the model cluster was the selection of the number of GSA loops. The maximum atomic displacement was adjusted to the lattice parameter, a, to ensure its acceptance ratio to a not exceeding 0.5. The many-body interatomic potential Uð~ rÞ and the non-empirical W–B
Fig. 1. A top view on the tungsten (1 1 0) surface: W1 and W2 mark the position of simulated deposition of boron atom on the surface.
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S. Dorfman et al. / Surface Science 566–568 (2004) 676–682
interaction potential, VWB ðrÞ were applied to simulate the adhesion process of a boron atom on tungsten (1 1 0) surface in the selected sites (see Fig. 1). We have placed a trial boron atom in a number of positions selected on the path perpendicular to the surface (1 1 0). Distances from the up to 6 A with surface were changed from )2 A For each of these positions we the step 0.5 A. found an equilibrium spatial structure of the cluster with the boron atom in the trial position. Thus the adhesion process that is simulated in our study is a very slow (compared to the characteristic time of the lattice relaxation) movement of the boron atom to the surface. The cluster was relaxed using the GSA procedure for 106 GSA loops. The GSA procedure was used to simulate the relaxation. The convergence of the relaxation process
Fig. 2. A side view on the relaxed tungsten cluster with (1 1 0) terminated surface with the boron atom in the distance 1.5 A from the surface: (a) a relaxed cluster––a general view, (b) the relaxed surface layer with the boron atom, (c) the relaxed subsurface layer, (d) the third plane from the surface after 106 GSA loops.
was achieved after approximately 106 GSA loops for each position of the boron atom. As an example the equilibrium structures of the selected cluster and three surface layers with the boron from the tungsten surface is shown atom in 1.5 A in Fig. 2.
3. Simulation results In Fig. 2a we have drawn a sketch of the equilibrium structure of the tungsten cluster with from the (1 1 0) surface in the boron atom in 1.5 A W1 position. We have also displayed the spatial structure of the surface and subsurface tungsten planes in Fig. 2b–d. All these layers are completely relaxed in 106 GSA loops. The subsurface layer and the third plane from the surface are shown with an aim to observe expansion of re-arrangement of atoms produced by the boron atom approaching the surface. As it was expected substantial displacements were observed in the surface layer. It is possible to see the damping of the layer distortions inward the cluster from the surface to the third layer initiated by the deposited boron atom. All these distortions are reduced from the surface to the subsurface layers. In Fig. 3 the final structure of the first three planes of the tungsten cluster with the boron atom from the surface is shown. We at the distance 1.5 A selected 11 tungsten atoms and marked them (see Fig. 3). Coordinates of these atoms are shown in
Fig. 3. Three top layers of the cluster after relaxations. The from the surface. The markers in boron atom is located in 1.5 A the circles show the selected tungsten atoms. (For a colour version of the figure see the online paper.)
S. Dorfman et al. / Surface Science 566–568 (2004) 676–682
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Table 1 Cohesive energies in Ry of some selected tungsten atoms (see Fig. 3) from the first three planes of the cluster Layer
Numbers of tungsten atoms according to Fig. 3 and their coordinates
Pairwise potential
Potential with pair and triple interactions
Surface
1 2 3 4 5 6
(4.6320, )1.6680, )1.3480) (3.5200, )0.2880, )3.2960) (1.7440, 1.5520, )4.7120) (0.1040, 3.4960, )3.1080) ()0.2600, 3.2560, 3.4200) (4.6320, )1.6680, )1.3480)
)0.52583 )0.53912 )0.43526 )0.47813 )0.47127 )0.47101
)0.51077 )0.52621 )0.40774 )0.47286 )0.43656 )0.45872
0.01506 0.01291 0.02752 0.00527 0.03471 0.01230
Second plane from the surface
7 (1.4720, )1.4440, )4.7280) 8 (0.0920, )0.1320, 6.6440) 9 (0.0200, 0.1840, 0.3400)
)0.63231 )0.62893 )0.67376
)0.57794 )0.57888 )0.66866
0.05437 0.05005 0.00510
10 ()1.6120, )1.7880, 1.9000) )0.65468 11 ()3.3280, )0.0960, 3.4360) )0.64917 W atom is located on the distance 1.5 A from the tungsten (1 1 0) surface.
)0.62851 )0.60337
0.02618 0.04580
Third plane from the surface
Table 1. Cohesive energies were calculated for the selected tungsten atoms according to the procedure suggested in [17]. Table 1 illustrates the importance of accounting triple interactions for study of cohesive energies. The input of triple interactions is changed from 1% to 5%. Table 1 allows observing that the atom 9 that belongs to the subsurface layer is better connected with the host than any of selected atoms in the third layer. We choose the atoms 3 and 9 as the atoms with the strongest and weakest cohesive energies and calculated the change of cohesive energies for different distances from the surface of the deposited B atom for the selected sites W1 and W2 (see Fig. 4). Dependencies of cohesive energies of these atoms have a number of minima divided by barriers. The minimum on these curves means strengthening of the lattice. Thus the deposition on the site W2 leads to the improving of the cohesive forces in the host (Fig. 4). The results of calculations of the energy of the system for the adhesion path of the boron atom are plotted in Fig. 5. In this figure the change in the energy with respect to the energy of the tungsten cluster with (1 1 0) surface and the boron atom from the surplaced at the distance equal to 6 A face is demonstrated. The same procedure was carried out in the pairwise approximation (the dashed line in Fig. 5) and with the three-body interactions (the solid line). Fig. 5 shows that the pairwise interaction overestimates the value of the
Contributions of triple interactions
Fig. 4. Cohesive energies for a couple of selected atoms for different locations of the deposited boron atom in W1 and W2 positions: square and triangle markers correspond to the data that were obtained in simulations and lines were drawn with the spline method.
adsorption barrier and that the three-body potential is responsible for the shift of adsorption barrier outward the cluster. The position of the energy minimum is situated at the distance close to above the surface for the W1 site and equal to 2A for the W2 site. 2A At the same time, account for the many-body interactions changes sufficiently the local reconstruction of the lattice in the vicinity of the surface. It is obvious from Fig. 5 that the adhesion process
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Fig. 5. Energy profiles of boron deposition for W1 (a) and W2 (b) sites with pairwise and many-body potentials: squares and triangles mark the calculated values and dotted and continuous lines were plotted with the spline method.
starts from the distance approximately equal to 5 The displacements of atoms for the boron at the A. from the surface may be considered as distance 6 A corresponding to the case of the ‘‘pure’’ (1 1 0) surface of tungsten. It is interesting to note that the values of displacements of tungsten atoms in the vicinity of the (1 1 0) surface when the boron atom is moving to the surface along the adsorption path are often lower than those for the ‘‘pure’’ surface. This indicates the existence of complicate balance between W–B and W–W interactions in the adsorption process. This balance defines also the complicated profile of the energy curves in Fig. 5.
4. Discussion In our simulations we used the adiabatic hypothesis and the boron atom slowly moves to the surface of tungsten passing energy equilibrium positions on the deposition way. Several additional comments should be given to clarify the results obtained in our approach in the study of B deposition on W (1 1 0) surface. In the case of chemical vapor deposition in the inert gas atmosphere the mass transfer of the boron atoms occurs with the velocities at least one order smaller as compared with mean-square velocity at room temperature for a boron, which is about 500 m/s.
The velocity of sound in the tungsten has the order of magnitude 103 m/s. In this adiabatic approximation W atoms that oscillate with the period 1012 s may reach the equilibrium relaxed positions at each place of B on its path to the surface. Boron atom serves as a probe to display such response of the substrate on the atom approaching different positions on the surface. For such type of a process as a vapor deposition relaxation of the atoms in the vicinity of W surface in our simulations that include 106 loops are complete at each distance of B from this surface. Obviously it would be of interest to use MD simulations to study the case when the velocity of the B atom that approaches the surface is high: how this atom is stopped by the repulsion interaction and what are the changes in surface relaxations in comparison with so called slow movement of adsorbed atom. W–B interaction forces are rather short-ranged (see Fig. 5) when the [15]. The distance of 5 A approaching B atom starts to ‘‘feel’’ the W (1 1 0) surface is only 15% larger than interplanar distance in W in the direction (1 1 0). As yields from Ref. [15] actually even pairwise part of W–B interaction is much more short-ranged in comparison with W–W interatomic interaction. According to our calculations even very fast decreasing part of W–B interaction nevertheless has a small tail. The origin of this tail is that this interaction is obtained from the recursive procedure for B interstitials in the bulk tungsten. The potentials used in our calculations include both pairwise and three-body angledependent interactions. By the definition these three-body terms in the energy are not additive. The damping of oscillations by three-body interactions (see Fig. 5) is an expected result. At small distances we observe the pronounced angledependent interaction that makes the lattice more stable with respect to the atomic displacements. This result qualitatively corresponds to the numerous papers describing the stabilizing of the lattice by many-body interactions in a phonon spectrum. Keeping this fact in mind, the smoothening of the curve is the relevant result that shows simply that pairwise approximation overestimates the elastic response of W surface on the excitation that comes from the B atom that approaches the surface.
S. Dorfman et al. / Surface Science 566–568 (2004) 676–682
One of the internal parameters in the GSA approach is the radius of some effective sphere surrounding each atom. The treatment of the possible atomic positions for each atom (to find the equilibrium structure) is limited thus by the corresponding volume. The atomic displacements are not allowed to overcome these limits. This is the reason that the oscillations that we see in Fig. 5 may be associated non-directly with some type of cutoff effect in the phonon dispersion. At the same time the chosen radius is large enough to escape the influence of this cutoff effect at least for the case of not extremely high temperatures. Finally, let us discuss the nature and interpretation of the deposition process illustrated by Fig. 5. First of all it should be noted that the actual deposition process might be much more complicated that the one simulated in our work. The adsorption energy profiles presented here are not enough to make the final conclusion about the real trajectory of the boron atom passing to the surface. These trajectories should be considered as the first attempt of mapping the energy surface in the direction normal to the substrate surface and in the plane parallel to this surface. More detailed information on the changes of the energy is obviously needed and a mapping of energy paths in different surface sites with account of relaxations may be helpful. The trajectory of the B movement to the surface may become more complicated and energy barriers may be lower. Nevertheless our results may be considered as the first step in such a modeling that clearly illustrates the complicated character of the adsorption process. We show that adsorption from the atomistic point is a many-step sticking process that is accompanied by the reconstruction of the substrate. The analysis of W atoms displacements shows boron atom that at the distances more than 4 A does not influence the reconstruction of W surface. This allows conclude that the formation of the minimum of the energy curve in Fig. 5 at this distance is the result of the interaction of B atom with already relaxed W (1 1 0) surface. It means that even if B atom moves to the surface with a high velocity it will feel the field of this relaxed surface. At smaller distances to the surface B influences the relaxation of W atoms at the sur-
681
face. If B still has kinetic energy to overcome po for the W1 tential barrier in the vicinity of 3.5 A site or 2.8 A for the W2 site it will interact with W (1 1 0) surface, and this interaction will lead to the additional relaxation of the tungsten atoms in the vicinity of the surface stimulated by boron. Boron atom will loose the most part of its kinetic energy and will start to move slowly towards the surface. The energy profile of its interaction with the surface is displayed in Fig. 5 for the distances less for the W1 site or 2.8 A for the W2 site than 3.5 A and accounts the additional relaxation of W (1 1 0) surface stimulated by this interaction. B atom will be stopped at the distance approximately equal to at relatively deep energy minimum. Another 2A remarkable fact is that the deepest minimum on the both of the curves in Fig. 5 is located in 2 A from the (1 1 0) surface of tungsten. The calculated adsorption energy curves show that the adsorption process is divided in several steps that might be considered as accommodation of adsorbed atom and the further site occupation. The first step corresponds to the case when the adsorbed atom reaches the first small minimum that is well defined in Fig. 5b. Simple estimations show that for W2 site the time that B atom spends in this minimum is only one or two orders higher than the characteristic period of vibrations for W atoms. After the accommodation in the first minimum the atom may overcome the energy barrier, Ubarr 500 meV, just by the activation process due to thermal fluctuations and shifts to the occupation site that is defined by the position of the main minimum. The probability of this process x expðUbarr =kT Þ and a large kinetic energy of B atom is not needed for it. Comparing the data on the relative depth of the main minima on adsorption curves displayed in Fig. 5a and b and keeping in mind the geometry of the substrate surface we can assume that even if the B atom is adsorbed in W2 position and there exists the energy barrier between this position and W1 the atom may jump further to W1 in another activation process directly from W2 to W1 or along more complicated trajectory. Obviously, the mapping of the energy in different surface sites with account of relaxations should be provided to give the detailed description of the adsorption path.
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5. Summary
References
In our paper the results of the non-empirical study of the boron deposition process on the (1 1 0) tungsten surface were presented. A comparative analysis of the fine atomic structure and cohesive energies in the vicinity of the surface clears up the behavior of the system in the simulated deposition process. Existence of a number of energy barriers in the adhesion path of the boron atom demonstrates the dependence of deposition conditions on the energy of the atom approaching the surface. This result also shows that the conditions of the metalloid adhesion are influenced by the directional bonding nature and the structural reconstruction of the substrate surface. We have demonstrated by direct calculations the influence of account for many-body interactions on the calculated energy characteristics of the deposition process. We proved that the directional bonding between tungsten atoms in the vicinity of (1 1 0) surface is a reason to form the favorable energy conditions for absorption of the boron above the surface. Our atom at the distance 2 A results show the changes of the energy of atoms in the system and the tendencies of the propagation of the elastic field in the vicinity of (1 1 0) surface of W induced by the boron deposition process.
[1] H. Ehrhardt, Surf. Coat. Technol. 74/75 (1995) 29. [2] H. Hofs€ass, C. Ronning, In: J. Singh, S. Copley and J. Mazumder (Eds.), International Conference on Beam Processing of Advanced Materials, ASM Int, Materials Park (1996), p. 29. [3] W. Kulisch, S. Ulrich, Thin Solid Films 423 (2003) 183. [4] P. Mirkarimi, K. McCarty, D. Medlin, Mater. Sci. Eng. Rep. 21 (1997) 47. [5] S. Watanabe, S. Miyake, M. Murakawa, Diamond Films Technol. 7 (1997) 139. [6] W. Kulisch, S. Reinke, Diamond Films Technol. 7 (1997) 205. [7] H. Walter, K. Bewilogua, A. Schutze, T. Maassen, Diamond Relat. Mater. 8 (1999) 110. [8] W.T. Geng, A.J. Freeman, R.Q. Wu, Phys. Rev. B 63 (2001) 064427. [9] S. Dorfman, R.R. Braga, K.C. Mundim, D. Fuks, A. Gordon, J. Felsteiner, J. Phys.: Condens. Matter 15 (2003) 17. [10] C. Westphal, Surf. Sci. Rep. 50 (2003) 1. [11] M. B€aumer, H.-J. Freund, Prog. Surf. Sci. 61 (1999) 127. [12] S.H. Overbury, J. Vac. Sci. Technol. A 5 (1987) 694; D.M. Riffe, G.K. Wertheim, P.H. Citrin, Phys. Rev. Lett. 65 (1990) 219; C. Linnsmeier, J. Wanner, Surf. Sci. 454–456 (2000) 305; R.X. Ynzunza et al., Surf. Sci. 459 (2000) 69; M.A. Zaluska-Kotur, S. Krukowski, Z. Romanowski, L.A. Turski, Phys. Rev. B 65 (2002) 045404; N.V. Petrova, I.N. Yakovkin, Y.G. Ptushinskii, Surf. Sci. 497 (2002) 349. [13] S. Dorfman, V. Liubich, D. Fuks, K.C. Mundim, J. Phys.: Condens. Matter 13 (2001) 6719. [14] K.C. Mundim, C. Tsallis, Int. J. Quantum Chem. 58 (1996) 373. [15] K.C. Mundim, L.A.C. Malbouisson, S. Dorfman, D. Fuks, J. Van Humbeeck, V. Liubich, THEOCHEM 539 (2001) 191. [16] D.E. Ellis, K.C. Mundim, D. Fuks, S. Dorfman, A. Berner, Philos. Mag. B 79 (1999) 1615. [17] S. Dorfman, K.C. Mundim, V. Liubich, D. Fuks, J. Appl. Phys. 20 (2001) 705.
Acknowledgements S.D. acknowledges the support of the Israel Ministry of Absorption by the ‘‘KAMEA’’ program and CNPq. S.D. was also supported by the Low Saxony Ministry of Science and Arts.
Simulations of initial stages of boron deposition on (1 1 0) tungsten surface Simon Dorfman a, Ronan R. Braga b, Kleber C. Mundim b, David Fuks
c,*
a
c
Department of Physics, Technion-Israel Institute of Technology, 32000 Haifa, Israel b Inst. Quimica, Uni. Brasilia, C.P. 4478, 70919-970 Brasilia, Brazil Department of Materials Engineering, Ben-Gurion University of the Negev, P.O. Box 653, 84105 Beer Sheva, Israel Available online 11 June 2004
Abstract Non-empirical potentials are employed in atomistic simulations of the deposition process of boron on tungsten (1 1 0) surface in the framework of the generalized simulation annealing formalism. A comparative analysis of the fine atomic structure in the vicinity of the surface clears up the behavior of the system in the simulated deposition process. Existence of a number of energy barriers in the adhesion path of the boron atom demonstrates the dependence of adhesion conditions on the energy of the atom approaching the surface. This result also shows that the conditions of the metalloid adhesion are influenced by the directional bonding nature and the structural reconstruction of the substrate surface. Ó 2004 Elsevier B.V. All rights reserved. Keywords: Adsorption kinetics; Tungsten; Boron; Monte Carlo simulations; Adhesion
1. Introduction The past decade has brought an impressive progress in cubic boron nitride (c-BN) thin film technology. This is true for the development of deposition techniques and processes, theoretical understanding of the underlying mechanisms and the characterization of basic and application-related film properties alike (for recent reviews see [1–6]). c-BN possesses many interesting properties,
* Corresponding author. Tel.: +972-8-6461460; fax: +972-86472946. E-mail addresses: [email protected] (S. Dorfman), [email protected] (D. Fuks).
such as high hardness close to that of diamond, large band gap, small friction coefficient, excellent optical transmission, high thermal conductivity and chemical inertness. Large compressive intrinsic stress and poor adhesion are normally found in these films due to non-stoichiometric boron nitride deposition [7], which results in the delaminating of film from the surface. Problems such as high stress and the poor adhesion of the deposited film with the substrate are commonly observed. The problems obviously prevent c-BN’s variety of technical applications and thus must be solved. Cubic boron nitride film formation usually involves the deposition of boron or boron nitride film from solid or gaseous precursors, and the bombardment of this growing film with either a mixture of nitrogen and inert gas ions or pure inert gas ions [1,3–6].
0039-6028/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2004.05.128
S. Dorfman et al. / Surface Science 566–568 (2004) 676–682
In our work, the study of the interactions of boron atoms with tungsten (1 1 0) surface has been conducted. The study is expected to give useful information on the first step of the direct deposition so as to provide insight on achieving a better adhesion of c-BN films. Investigation of the metalloid deposits on metal surfaces has attracted a lot of attention in recent years [8,9]. Nevertheless, despite of the application importance, and, hence, the very extensive research undertaken in this field over the last decade, there is still a limited knowledge about the underlying physics and chemistry of such systems [10]. In relation to this, it is necessary to perform further investigation on the adsorption of metalloid atoms, clusters and thin films on the surfaces of metals. The microscopic features of metal–metalloid interfaces including the reconstruction of the surface where the metalloid atom is adsorbed are only rarely known from direct measurements [11]. Some aspects of adsorption of O, H, C on low-index W surfaces were studied recently [12] showing the importance of both chemical and structural effects in the binding of adsorbed atoms to the surface. In this communication we illustrate directly the importance of directional bonding in simulations of the deposition process on the tungsten (1 1 0) surface.
2. Methodology Interatomic potentials [9,13] that we use in our simulations do not contain any adjustable parameters to obtain better agreement with experiments and are absolutely ab initio. In the development of these potentials the problem of determination of the tungsten–boron interatomic potential was solved. W–W, W–B, and B–B interacting potentials were derived on the basis of non-empirical calculations of total energies within the recursive procedure. For details we refer to our recent papers [9,13–17]. In atomistic simulations we used the MC methodology in the generalized simulated annealing approach (GSA) (see, for example, Ref. [14] and references therein). GSA is based on the correlation between the minimization of a cost func-
677
tion (conformational energy) and the geometry randomly obtained through slow cooling. In this technique, an artificial temperature is introduced, and the system is gradually cooled in a complete analogy with the annealing technique used in metallurgy when a molten metal reaches its crystalline state (the global minimum of the thermodynamic energy). In our case the temperature plays the role of an external noise. The artificial temperature (or a set of temperatures) acts as a convenient stochastic source for eventual detraining from local minima. The procedure of searching the minima (global and local) or mapping the energy hypersurface consists of comparing the energies of two consecutive random geometries xtþ1 and xt obtained from the GSA routine. Here xt is a N -dimensional vector that contains all atomic coordinates ðN Þ to be optimized. For details of our MC approach see Refs. [9,13–17]. We simulated the adhesion process of a boron atom on the tungsten (1 1 0) surface and studied a site occupation preference for the boron atom. The surface was simulated in a cluster approximation with 393 atoms. In Fig. 1 we show the sites that were selected for simulations of the adsorption process. The primary task in our search of wellconverged statistical averages for geometry relaxation process in the model cluster was the selection of the number of GSA loops. The maximum atomic displacement was adjusted to the lattice parameter, a, to ensure its acceptance ratio to a not exceeding 0.5. The many-body interatomic potential Uð~ rÞ and the non-empirical W–B
Fig. 1. A top view on the tungsten (1 1 0) surface: W1 and W2 mark the position of simulated deposition of boron atom on the surface.
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S. Dorfman et al. / Surface Science 566–568 (2004) 676–682
interaction potential, VWB ðrÞ were applied to simulate the adhesion process of a boron atom on tungsten (1 1 0) surface in the selected sites (see Fig. 1). We have placed a trial boron atom in a number of positions selected on the path perpendicular to the surface (1 1 0). Distances from the up to 6 A with surface were changed from )2 A For each of these positions we the step 0.5 A. found an equilibrium spatial structure of the cluster with the boron atom in the trial position. Thus the adhesion process that is simulated in our study is a very slow (compared to the characteristic time of the lattice relaxation) movement of the boron atom to the surface. The cluster was relaxed using the GSA procedure for 106 GSA loops. The GSA procedure was used to simulate the relaxation. The convergence of the relaxation process
Fig. 2. A side view on the relaxed tungsten cluster with (1 1 0) terminated surface with the boron atom in the distance 1.5 A from the surface: (a) a relaxed cluster––a general view, (b) the relaxed surface layer with the boron atom, (c) the relaxed subsurface layer, (d) the third plane from the surface after 106 GSA loops.
was achieved after approximately 106 GSA loops for each position of the boron atom. As an example the equilibrium structures of the selected cluster and three surface layers with the boron from the tungsten surface is shown atom in 1.5 A in Fig. 2.
3. Simulation results In Fig. 2a we have drawn a sketch of the equilibrium structure of the tungsten cluster with from the (1 1 0) surface in the boron atom in 1.5 A W1 position. We have also displayed the spatial structure of the surface and subsurface tungsten planes in Fig. 2b–d. All these layers are completely relaxed in 106 GSA loops. The subsurface layer and the third plane from the surface are shown with an aim to observe expansion of re-arrangement of atoms produced by the boron atom approaching the surface. As it was expected substantial displacements were observed in the surface layer. It is possible to see the damping of the layer distortions inward the cluster from the surface to the third layer initiated by the deposited boron atom. All these distortions are reduced from the surface to the subsurface layers. In Fig. 3 the final structure of the first three planes of the tungsten cluster with the boron atom from the surface is shown. We at the distance 1.5 A selected 11 tungsten atoms and marked them (see Fig. 3). Coordinates of these atoms are shown in
Fig. 3. Three top layers of the cluster after relaxations. The from the surface. The markers in boron atom is located in 1.5 A the circles show the selected tungsten atoms. (For a colour version of the figure see the online paper.)
S. Dorfman et al. / Surface Science 566–568 (2004) 676–682
679
Table 1 Cohesive energies in Ry of some selected tungsten atoms (see Fig. 3) from the first three planes of the cluster Layer
Numbers of tungsten atoms according to Fig. 3 and their coordinates
Pairwise potential
Potential with pair and triple interactions
Surface
1 2 3 4 5 6
(4.6320, )1.6680, )1.3480) (3.5200, )0.2880, )3.2960) (1.7440, 1.5520, )4.7120) (0.1040, 3.4960, )3.1080) ()0.2600, 3.2560, 3.4200) (4.6320, )1.6680, )1.3480)
)0.52583 )0.53912 )0.43526 )0.47813 )0.47127 )0.47101
)0.51077 )0.52621 )0.40774 )0.47286 )0.43656 )0.45872
0.01506 0.01291 0.02752 0.00527 0.03471 0.01230
Second plane from the surface
7 (1.4720, )1.4440, )4.7280) 8 (0.0920, )0.1320, 6.6440) 9 (0.0200, 0.1840, 0.3400)
)0.63231 )0.62893 )0.67376
)0.57794 )0.57888 )0.66866
0.05437 0.05005 0.00510
10 ()1.6120, )1.7880, 1.9000) )0.65468 11 ()3.3280, )0.0960, 3.4360) )0.64917 W atom is located on the distance 1.5 A from the tungsten (1 1 0) surface.
)0.62851 )0.60337
0.02618 0.04580
Third plane from the surface
Table 1. Cohesive energies were calculated for the selected tungsten atoms according to the procedure suggested in [17]. Table 1 illustrates the importance of accounting triple interactions for study of cohesive energies. The input of triple interactions is changed from 1% to 5%. Table 1 allows observing that the atom 9 that belongs to the subsurface layer is better connected with the host than any of selected atoms in the third layer. We choose the atoms 3 and 9 as the atoms with the strongest and weakest cohesive energies and calculated the change of cohesive energies for different distances from the surface of the deposited B atom for the selected sites W1 and W2 (see Fig. 4). Dependencies of cohesive energies of these atoms have a number of minima divided by barriers. The minimum on these curves means strengthening of the lattice. Thus the deposition on the site W2 leads to the improving of the cohesive forces in the host (Fig. 4). The results of calculations of the energy of the system for the adhesion path of the boron atom are plotted in Fig. 5. In this figure the change in the energy with respect to the energy of the tungsten cluster with (1 1 0) surface and the boron atom from the surplaced at the distance equal to 6 A face is demonstrated. The same procedure was carried out in the pairwise approximation (the dashed line in Fig. 5) and with the three-body interactions (the solid line). Fig. 5 shows that the pairwise interaction overestimates the value of the
Contributions of triple interactions
Fig. 4. Cohesive energies for a couple of selected atoms for different locations of the deposited boron atom in W1 and W2 positions: square and triangle markers correspond to the data that were obtained in simulations and lines were drawn with the spline method.
adsorption barrier and that the three-body potential is responsible for the shift of adsorption barrier outward the cluster. The position of the energy minimum is situated at the distance close to above the surface for the W1 site and equal to 2A for the W2 site. 2A At the same time, account for the many-body interactions changes sufficiently the local reconstruction of the lattice in the vicinity of the surface. It is obvious from Fig. 5 that the adhesion process
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Fig. 5. Energy profiles of boron deposition for W1 (a) and W2 (b) sites with pairwise and many-body potentials: squares and triangles mark the calculated values and dotted and continuous lines were plotted with the spline method.
starts from the distance approximately equal to 5 The displacements of atoms for the boron at the A. from the surface may be considered as distance 6 A corresponding to the case of the ‘‘pure’’ (1 1 0) surface of tungsten. It is interesting to note that the values of displacements of tungsten atoms in the vicinity of the (1 1 0) surface when the boron atom is moving to the surface along the adsorption path are often lower than those for the ‘‘pure’’ surface. This indicates the existence of complicate balance between W–B and W–W interactions in the adsorption process. This balance defines also the complicated profile of the energy curves in Fig. 5.
4. Discussion In our simulations we used the adiabatic hypothesis and the boron atom slowly moves to the surface of tungsten passing energy equilibrium positions on the deposition way. Several additional comments should be given to clarify the results obtained in our approach in the study of B deposition on W (1 1 0) surface. In the case of chemical vapor deposition in the inert gas atmosphere the mass transfer of the boron atoms occurs with the velocities at least one order smaller as compared with mean-square velocity at room temperature for a boron, which is about 500 m/s.
The velocity of sound in the tungsten has the order of magnitude 103 m/s. In this adiabatic approximation W atoms that oscillate with the period 1012 s may reach the equilibrium relaxed positions at each place of B on its path to the surface. Boron atom serves as a probe to display such response of the substrate on the atom approaching different positions on the surface. For such type of a process as a vapor deposition relaxation of the atoms in the vicinity of W surface in our simulations that include 106 loops are complete at each distance of B from this surface. Obviously it would be of interest to use MD simulations to study the case when the velocity of the B atom that approaches the surface is high: how this atom is stopped by the repulsion interaction and what are the changes in surface relaxations in comparison with so called slow movement of adsorbed atom. W–B interaction forces are rather short-ranged (see Fig. 5) when the [15]. The distance of 5 A approaching B atom starts to ‘‘feel’’ the W (1 1 0) surface is only 15% larger than interplanar distance in W in the direction (1 1 0). As yields from Ref. [15] actually even pairwise part of W–B interaction is much more short-ranged in comparison with W–W interatomic interaction. According to our calculations even very fast decreasing part of W–B interaction nevertheless has a small tail. The origin of this tail is that this interaction is obtained from the recursive procedure for B interstitials in the bulk tungsten. The potentials used in our calculations include both pairwise and three-body angledependent interactions. By the definition these three-body terms in the energy are not additive. The damping of oscillations by three-body interactions (see Fig. 5) is an expected result. At small distances we observe the pronounced angledependent interaction that makes the lattice more stable with respect to the atomic displacements. This result qualitatively corresponds to the numerous papers describing the stabilizing of the lattice by many-body interactions in a phonon spectrum. Keeping this fact in mind, the smoothening of the curve is the relevant result that shows simply that pairwise approximation overestimates the elastic response of W surface on the excitation that comes from the B atom that approaches the surface.
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One of the internal parameters in the GSA approach is the radius of some effective sphere surrounding each atom. The treatment of the possible atomic positions for each atom (to find the equilibrium structure) is limited thus by the corresponding volume. The atomic displacements are not allowed to overcome these limits. This is the reason that the oscillations that we see in Fig. 5 may be associated non-directly with some type of cutoff effect in the phonon dispersion. At the same time the chosen radius is large enough to escape the influence of this cutoff effect at least for the case of not extremely high temperatures. Finally, let us discuss the nature and interpretation of the deposition process illustrated by Fig. 5. First of all it should be noted that the actual deposition process might be much more complicated that the one simulated in our work. The adsorption energy profiles presented here are not enough to make the final conclusion about the real trajectory of the boron atom passing to the surface. These trajectories should be considered as the first attempt of mapping the energy surface in the direction normal to the substrate surface and in the plane parallel to this surface. More detailed information on the changes of the energy is obviously needed and a mapping of energy paths in different surface sites with account of relaxations may be helpful. The trajectory of the B movement to the surface may become more complicated and energy barriers may be lower. Nevertheless our results may be considered as the first step in such a modeling that clearly illustrates the complicated character of the adsorption process. We show that adsorption from the atomistic point is a many-step sticking process that is accompanied by the reconstruction of the substrate. The analysis of W atoms displacements shows boron atom that at the distances more than 4 A does not influence the reconstruction of W surface. This allows conclude that the formation of the minimum of the energy curve in Fig. 5 at this distance is the result of the interaction of B atom with already relaxed W (1 1 0) surface. It means that even if B atom moves to the surface with a high velocity it will feel the field of this relaxed surface. At smaller distances to the surface B influences the relaxation of W atoms at the sur-
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face. If B still has kinetic energy to overcome po for the W1 tential barrier in the vicinity of 3.5 A site or 2.8 A for the W2 site it will interact with W (1 1 0) surface, and this interaction will lead to the additional relaxation of the tungsten atoms in the vicinity of the surface stimulated by boron. Boron atom will loose the most part of its kinetic energy and will start to move slowly towards the surface. The energy profile of its interaction with the surface is displayed in Fig. 5 for the distances less for the W1 site or 2.8 A for the W2 site than 3.5 A and accounts the additional relaxation of W (1 1 0) surface stimulated by this interaction. B atom will be stopped at the distance approximately equal to at relatively deep energy minimum. Another 2A remarkable fact is that the deepest minimum on the both of the curves in Fig. 5 is located in 2 A from the (1 1 0) surface of tungsten. The calculated adsorption energy curves show that the adsorption process is divided in several steps that might be considered as accommodation of adsorbed atom and the further site occupation. The first step corresponds to the case when the adsorbed atom reaches the first small minimum that is well defined in Fig. 5b. Simple estimations show that for W2 site the time that B atom spends in this minimum is only one or two orders higher than the characteristic period of vibrations for W atoms. After the accommodation in the first minimum the atom may overcome the energy barrier, Ubarr 500 meV, just by the activation process due to thermal fluctuations and shifts to the occupation site that is defined by the position of the main minimum. The probability of this process x expðUbarr =kT Þ and a large kinetic energy of B atom is not needed for it. Comparing the data on the relative depth of the main minima on adsorption curves displayed in Fig. 5a and b and keeping in mind the geometry of the substrate surface we can assume that even if the B atom is adsorbed in W2 position and there exists the energy barrier between this position and W1 the atom may jump further to W1 in another activation process directly from W2 to W1 or along more complicated trajectory. Obviously, the mapping of the energy in different surface sites with account of relaxations should be provided to give the detailed description of the adsorption path.
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5. Summary
References
In our paper the results of the non-empirical study of the boron deposition process on the (1 1 0) tungsten surface were presented. A comparative analysis of the fine atomic structure and cohesive energies in the vicinity of the surface clears up the behavior of the system in the simulated deposition process. Existence of a number of energy barriers in the adhesion path of the boron atom demonstrates the dependence of deposition conditions on the energy of the atom approaching the surface. This result also shows that the conditions of the metalloid adhesion are influenced by the directional bonding nature and the structural reconstruction of the substrate surface. We have demonstrated by direct calculations the influence of account for many-body interactions on the calculated energy characteristics of the deposition process. We proved that the directional bonding between tungsten atoms in the vicinity of (1 1 0) surface is a reason to form the favorable energy conditions for absorption of the boron above the surface. Our atom at the distance 2 A results show the changes of the energy of atoms in the system and the tendencies of the propagation of the elastic field in the vicinity of (1 1 0) surface of W induced by the boron deposition process.
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Acknowledgements S.D. acknowledges the support of the Israel Ministry of Absorption by the ‘‘KAMEA’’ program and CNPq. S.D. was also supported by the Low Saxony Ministry of Science and Arts.