- Email: [email protected]
A molecular dynamics evidence for enhanced cluster beam epitaxy
Nuclear Instruments and Methods in Physics Research B 135 (1998) 501±506
A molecular dynamics evidence for enhanced cluster beam epitaxy M. Hou
1
Physique des Solides Irradi es, CP234, Universit e Libre de Bruxelles, Boulevard du Triomphe, B-1050 Brussels, Belgium
Abstract The interaction between a copper cluster of several hundred atoms and a copper single crystal surface is modelled and analysed in detail by means of classical molecular dynamics with a semi-empirical tight binding potential. Deposition with no incident momentum (soft landing), with translation velocities of the order of the velocity of sound (Low Energy Cluster Deposition, LECBD) and higher velocities (Ionised Cluster Beam Deposition, ICBD) are simulated and particular attention is paid to the mechanism of epitaxy. After an interaction time of 0.1 ns, the model predicts soft landing leads to islands which, generally, accommodate with the substrate by partial epitaxy and extended defects. This result is not signi®cantly temperature dependent. When incident energies are of the order of 0.5 eV per atom (LECBD) and more, the cluster undergoes full epitaxy. Depending on the incident energy, the deposited cluster displays facets of dierent kinds, except for the ICBD regime where no facet is anymore produced and the cluster spreads over the surface, forming a ®lm of several monolayers thickness. Ó 1998 Elsevier Science B.V.
1. Introduction The cluster±solid interaction is studied in a wide range of dierent conditions from ``soft landing'' where clusters are smoothly deposited on surfaces, generally at very low temperatures [1,2] to very high energy cluster beams where damage is mostly produced via electron±phonon coupling [3,4]. In between these two extremes, modelling was used to investigate the state of implanted clusters and damage production in the vicinity of the surface by ion cluster beam deposition (ICBD) [5±19]. The preliminary stage of the cluster±substrate interface formation in the soft landing regime was already modelled in [20]. It was not analysed in full detail however over long enough 1
E-mail: [email protected].
periods of time to reach equilibrium. Experiments focused on cluster deposition in view of producing cluster assembled new materials by means of Low energy Cluster-Deposition (LECBD) [21±23]. In the present paper, we look at the cluster±surface interaction driven either by thermal interactions or by deposition with translation energies no more than 1 eV per atom high. In the latter regime, no damage is produced to the substrate, but the interaction has a strong in¯uence on the ®nal state of the deposited cluster. It is shown how low but non-zero cluster momentum has the eect to enhance epitaxy and in¯uence the cluster morphology. The Molecular Dynamics method (MD) used therefore is brie¯y sketched in Section 2. The simulation method is then described and the results are shown and discussed in Section 3.
0168-583X/98/$19.00 Ó 1998 Elsevier Science B.V. All rights reserved. PII S 0 1 6 8 - 5 8 3 X ( 9 7 ) 0 0 6 5 6 - 3
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M. Hou / Nucl. Instr. and Meth. in Phys. Res. B 135 (1998) 501±506
2. The model In the present case study, both the substrate and the cluster are made of elemental copper. It thus represents a situation where there is no other mismatch between the cluster and the substrate lattice parameters than due to relaxation. Little is known about the overall structure of large clusters. No particular assumption is made in the present model and a cluster containing 440 atoms is arbitrarily constructed as a spherical single crystal from which surface atoms mobile at high temperature (above 750 K) are removed by hand. The substrate is a cubic box of 12 ´ 12 ´ 12 lattice unit cells with two (0 0 1) free surfaces. Periodic boundary conditions are applied in the h1 0 0i directions parallel to the surfaces. The forces are derived from a non-local tight binding approximate potential as described in [24]. Its repulsive part is splined to a familiar Moliere screened Coulomb potential [25] at small distances and the spline parameters are given in [26]. The contribution of the screened Coulomb interaction is however minor in the present study. Newton's equations of motion of all particles are integrated stepwise in time. Force evaluation makes use of Verlet neighbour lists combined with a linked cell algorithm. Prior to modelling the cluster±substrate interaction, both systems are brought to thermal equilibrium independently. The initial orientation and position of the cluster with respect to the (0 0 1) substrate surface are selected at random. The cluster initial distance of the surface plane is however chosen in such a way that the distance between the cluster atoms closest to the surface and the surface plane is somewhat shorter than the potential cut-o distance. In addition to the thermal motion, an initial translation kinetic energy may be assigned to the cluster with momentum perpendicular to the substrate surface. In addition to 3D visualisation graphics, a static structure factor is used S k eÿik:r
1
with k-vectors parallel to the low index substrate directions [h,k,l] in order to identify directions common to the cluster and the substrate. All direc-
tions are considered such that the magnitude of the Miller indices is zero or unity. This limitation is arbitrary. By selecting jkj 4p=a where a is the lattice unit, the square of the structure factor is unity for full order and zero for full lack of correlation with the h1 0 0i, h1 1 0i and h1 1 1i substrate directions. This way, the magnitude of the structure factor at 0 K is initially 1 for the substrate and close to 0 for the cluster since its orientation is not correlated with that of the substrate. Since the two systems are thermalised, the initial values are smaller than unity and the expected eect of epitaxy is to increase the magnitude of the structure factor measured in the cluster. Simulations of 100 ps duration were repeated for several cluster initial positions, orientations and translation energies between 0 and 1 eV per atom. The same overall expitaxial behaviour is observed in most of the cases and the results are commented in the next section. 3. The results 3.1. Thermal eects The initial position and relative orientation of the cluster are selected at random, in such a way that, owing to the potential cut-o, only the atoms closest to the surface interact with the substrate. When the cluster has zero initial translation energy (soft landing regime), at 500 K, comparisons with simulations at 0 K shows that the evolution of the system is driven essentially by the temperature and to a lesser extent by the mechanical interaction energy. The state of the system after 100 ps is illustrated in Fig. 1. The cluster±surface mechanical interaction does not modify the temperature by more than 5%. The ordering with respect to the substrate is striking. An examination of snapshots during the evolution of the system shows that the cluster quickly forms one or two epitaxial layers inducing a solid rotation of the remaining part. A grain boundary then forms in the cluster which accommodates the growing epitaxial fragment to the misoriented one. Fig. 1(a) shows that about two-thirds of the cluster is epitaxial with the substrate and this part of the cluster is separated from
M. Hou / Nucl. Instr. and Meth. in Phys. Res. B 135 (1998) 501±506
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thermally, letting the epitaxial fragment grow. The dislocation quickly annealed at the surface, leaving the cluster fully epitaxed with the substrate. This is the only case among the ten runs where full epitaxy was found. Since the excess energy associated to a {1 1 1} twin boundary is close to zero in bulk fcc metals, it is expected that the con®guration in Fig. 1 is almost as stable as a perfectly crystalline deposited cluster. The tilt angle of this grain boundary is about 40°, which is however two-thirds of the tilt angle in a bulk twin boundary. This illustrates the strength of the constraint induced by the cluster surface. The way surface excess energy can be minimised is shown in Fig. 1(b) which represents the same cluster as in Fig. 1(a), viewed along a [1 0 0] direction. The epitaxial fragment tends to form {1 0 0} facets perpendicular to the surface plane. From Fig. 1(a), it is seen that, although the non-epitaxial fragment orientation does not match the orientation of the epitaxial one, it does have strong direction correlation with the substrate. Fig. 2 shows the square of the structure factor as a function of time, measured with wave vector (4p=a; 0; 0). The results in Fig. 2 are typical of those obtained with the other k-vector orientations considered, except for k-vectors parallel to common directions to the cluster fragments and the substrate. The substrate values are constant in time, indicating no signi®cant damage. They are Fig. 1. Con®guration of a copper cluster with respect to the substrate after 100 ps free evolution of the system. The orientation of the axes given in the insets refer to substrate directions. Both the cluster and the substrate are at 500 K equilibrium temperature. (a) [1 1 0] viewing direction; (b) [1 0 0] viewing direction. The twin grain boundary plane is shown in (a). It is a {1 1 1} plane common to the two cluster fragments and to the substrate. The viewing direction in (a) is also common to the fragments and the substrate.
the other by a {1 1 1} plane twin boundary. The simulation was repeated with ten dierent initial cluster positions and orientations selected at random, and the same sequence was found. In one case only, the epitaxial atomic layer accommodates the rotated fragment with a dislocation. This was however found very unstable and migrated
Fig. 2. Squared modulus of the structure factor measured as a function of time with respect to a k-vector parallel to the substrate [1 0 0] direction. Solid line: results for the substrate; dashed line: results for the cluster.
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M. Hou / Nucl. Instr. and Meth. in Phys. Res. B 135 (1998) 501±506
less than unity, because of temperature. In contrast, the results for the cluster are time dependent. The magnitude of the structure factor starts to increase smoothly from zero and undergoes a sharp increase after about 50 ps. It then keeps constant through all the simulation at some smaller value than the substrate. The structure factor for the cluster get the same value as for the substrate when the k-vector is parallel to a common direction to the cluster fragment and the substrate, like the viewing direction in Fig. 1(a). This [1 1 0] direction, together with the [1 1 2] direction inside the plane of the Fig. 1(a) both belong to the (1 1 1) plane of the twin boundary. Since this [1 1 2] direction is also common with the substrate, the whole (1 1 1) planes are common to the whole cluster and the substrate. An examination of intermediate snapshots similar to Fig. 1 shows that the smooth increase of the structure factor with time in the early stage of the interaction corresponds to limited epitaxy at the cluster±substrate interface, as described above. Once some fraction of the cluster atoms is ordered with respect to the substrate, the remaining part of the cluster undergoes a sudden partial reorganisation and remains in the state shown in Fig. 1. 3.2. Impact eect The interaction mechanism between the cluster and the surface when the cluster has some momentum is quite dierent and the ®nal state of the cluster depends on its initial translation energy. To illustrate this, the same event as just described in the previous section is modelled again, and repeated for several cluster initial translation kinetic energy per atom 0 to 1.04 eV. This energy range is typical of LECBD experiments and the highest energies considered (around 1 eV per atom) may already be suggested to belong to the ICBD regime, according to a criterion given below. The time evolution of the structure factor is given in Fig. 3 in the case of the 1.04 eV per atom. The features are similar for all the other k-vectors considered they are also representative of the case of lower energies, down to about 0.25 eV per atom. At the early stage of the interaction, the structure factor for the cluster is zero because of its random orien-
Fig. 3. Same as Fig. 2 when the initial translation energy of the cluster is 1.04 eV per atom. The other initial conditions are identical.
tation with respect to the substrate and the structure factor for the substrate displays a steep minimum in the early interaction. Its magnitude then levels o at a value slightly lower than its initial value. Epitaxy of the cluster starts earlier than that for soft landing and full epitaxy is obtained after 20 ps interaction. This is attested by the fact that the structure factor measured in the cluster reaches the same magnitude as in the substrate whatever the k-vector is. Since the simulation box is isolated, part of the initial translation energy is converted to heat and, since the model system is limited in size, the additional heat results in a raise of the temperature. In the case presented in Fig. 4, the equilibrium temperature raises from 500 to 720 k. Therefore, the structure factor was measured for a perfect simulation box at thermodynamic equilibrium at 720 K and its magnitude was found the same as the ®nal value in Fig. 3. This demonstrates that the temperature raise fully accounts for the slight decrease of the magnitude of the structure factor and, subsequently, that no detectable damage is produced. The ®nal cluster morphology is found to be dependent on the initial translation energy. This is illustrated in Fig. 4. The snapshots are taken after 100 ps free evolution, using the same [1 1 0] viewing direction as in Fig. 1(a). There are no {1 0 0} walls to be found anymore perpendicular to the surface. Instead, {1 1 0} facets are produced in the case of initial translation energy of 0.52 eV, thus forming a truncated pyramid. It spreads al-
M. Hou / Nucl. Instr. and Meth. in Phys. Res. B 135 (1998) 501±506
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within a few picoseconds, without any indication that the system passes through a transient liquid state. It thus looks convenient to distinguish these conditions from LECBD, and to consider them associated to the ICBD. The distinction suggested between the three regimes is thus based on a morphology criterion, which applicability for other systems still needs to be assessed. One ambiguity still remains. Since, because of the impact, the system heats up, it is not yet clear whether epitaxy and morphological evolution are caused by temperature or by mechanical momentum conversion. In order to lift this ambiguity, the same simulation is repeated once more, at 720 K equilibrium temperature and a zero initial cluster translation energy. The cluster only undergoes partial epitaxy. Exactly as shown in Fig. 1 for a temperature of 500 K, it displays a similar twin grain boundary, similar {1 0 0} facets and it does not spread over the surface. 4. Conclusion
Fig. 4. Same as Fig. 1 when the cluster has an initial translation energy of: (a) 0.52 eV per atom; and (b) 1.04 eV per atom.
most isotropically on the substrate surface, over a range about twice as large as in Fig. 1. The initial cluster velocity is in the range of 1000 m/s, typical of LECBD experiments. In the case of initial energy per atom 1.04 eV, it still spreads further. No facet is anymore apparent as if the solid cluster would wet the surface although, as attested by Fig. 3, it undergoes no solid±liquid phase transition. Indeed, the squared modulus of the structure factor raises from zero to the substrate value monotonically
To summarise, at a temperature of 500 K, copper cluster epitaxy on a (0 0 1) copper surface takes place anyway. It is only partial when the cluster is deposited on the substrate with no momentum and the misorientation of the fragments is accommodated by a twin grain boundary. The epitaxial fragment displays facets perpendicular to the substrate surface. Full epitaxy takes place when the cluster has some initial velocity normal to the substrate surface and its morphology is signi®cantly dependent on the incident energy. Facets does not appear when the energy is of the order of 1 eV or higher. It thus turns out that the energy of a cluster beam can be used to monitor some of the deposited cluster properties. The three ®nal states observed for the three initial conditions used naturally suggest a distinction between soft landing, low energy cluster beam deposition and ionised cluster beam deposition. The present study focuses on an epuilibrium temperature of 500 K. Indication is given however that the same partial epitaxy is found at 720 K. Spot simulations were performed at 0 and 300 K showing the same feature. More systematic work,
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M. Hou / Nucl. Instr. and Meth. in Phys. Res. B 135 (1998) 501±506
involving statistics, is necessary in order to con®rm that partial epitaxy occurs over the whole temperature range where the cluster is solid. The role of incident momentum also needs to be characterised at dierent temperatures. Other parameters may also play a role in the process, as the cluster size and its initial morphology. Although similar results may be expected for metals where cohesion is of the same nature, checks are necessary. Finally, the behaviour of heterogeneous systems may display dierent features related to lattice mismatch, solubility and segregation. The topic is rather huge, but the present work indicates that many of the problems raised can be elucidated leading to a comprehensive model for cluster deposition and deposited cluster assemblies. Acknowledgements It is a pleasure to acknowledge stimulating discussions with many colleagues and, in particular with Z.Y. Pan within the frame of a long standing cooperation. This work is sponsored by the Federal Belgian government under contract PAI/IUAP P4/10. References [1] W. Harbisch, S. Fedrigo, J. Buttet, J. Chem. Phys. 96 (11) (1992) 8104. [2] P. Blandin, C. Massobrio, J. Buttet, Z. Phys. D 26 (1/4) (1993) 236. [3] H. Dammak, A. Dunlop, Y. Le Beyec, Phys. Rev. Lett. 74 (7) (1995) 1135. [4] A. Hallen, P. Kanasson, Y. Le Beyec, Nucl. Instr. and Meth. 106 (1/4) (1995) 233.
[5] R. Smith, K. Beardmore, R. Webb, Nucl. Instr. and Meth. B 102 (1/4) (1995) 211. [6] H. Haberland, Z. Insepov, M. Kairias, Nucl. Instr. and Meth. B 80/81 (1993) 2. [7] H. Haberland, Z. Insepov, M. Moseler, Z. Phys. D 26 (1/4) (1993). [8] H. Hsieh, T. Diaz de la Rubia, R.S. Averback, R. Benedek, Phys. Rev. B 40 (1989) 9986. [9] H. Hsieh, R.S. Averback, H. Sellers, C.P. Flynn, Phys. Rev. B 45 (1992) 4417. [10] R.W. Lee, Z.Y. Pan, Y.K. Huo, Phys. Rev. B 53 (1996) 4156. [11] V.I. Shulga, P. Sigmund, Nucl. Instr. and Meth. B 62 (1991) 23. [12] Z.Y. Pan, Nucl. Instr. and Meth. B 66 (1992) 325. [13] Y. Yamamura, T. Muramoto, Radiat. E. 130/131 (1994) 225. [14] Y. Yamamura, Nucl. Instr. and Meth. B 45 (1992) 4417. [15] R.S. Averback, M. Ghaly, H. Zhu, Radiat. E. 130/131 (1994) 211. [16] M. Ghali, R.S. Averback, T. Diaz de la Rubia, Nucl. Instr. and Meth. B 102 (1995) 51. [17] Y. Yamamura, I. Yamada, T. Takagi, Nucl. Instr. and Meth. B 37/38 (1989) 902. [18] Z.Y. Pan, M. Hou, Nucl. Instr. and Meth. B 102 (1995) 317. [19] R.W. Lee, Z.Y. Pan, M. Hou, Nucl. Instr. and Meth. B 115 (1996) 536. [20] M. Yeadon, J.C. Yang, M. Ghaly, D.L. Olyck, R.S. Averback, J.M. Gibson, Mat. Res. Symp. Proc. 457 (1997) 179. [21] P. Melinon, V. Paillard, V. Dupuis, A. Perez, P. Jensen, A. Noareau, J.P. Perez, J. Tuaillon, M. Broyer, J.L. Vialle, M. Pellarin, B. Baguenard, J. Lerme, Int. J. Modern Phys. B 9 (4/5) (1995) 339. [22] L. Bardotti, P. Jensen, P. Melinon, A. Hoareau, B. Cabau, M. Treilleux, Surf. Rev. Lett. 3 (1996) 987. [23] S.J. Caroll, P. Weibel, B. von Issendor, L. Kuipers, R. Palmer, J. Phys. C 8 (1996) L617. [24] G.J. Ackland, V. Vitek, Phys. Rev. B 41 (1990) 10324. [25] G. Moliere, Z. Naturforsch. 2a (1947) 133. [26] M. Hou, Z.Y. Pan, Radiat. E. 142 (1997) 483.
A molecular dynamics evidence for enhanced cluster beam epitaxy M. Hou
1
Physique des Solides Irradi es, CP234, Universit e Libre de Bruxelles, Boulevard du Triomphe, B-1050 Brussels, Belgium
Abstract The interaction between a copper cluster of several hundred atoms and a copper single crystal surface is modelled and analysed in detail by means of classical molecular dynamics with a semi-empirical tight binding potential. Deposition with no incident momentum (soft landing), with translation velocities of the order of the velocity of sound (Low Energy Cluster Deposition, LECBD) and higher velocities (Ionised Cluster Beam Deposition, ICBD) are simulated and particular attention is paid to the mechanism of epitaxy. After an interaction time of 0.1 ns, the model predicts soft landing leads to islands which, generally, accommodate with the substrate by partial epitaxy and extended defects. This result is not signi®cantly temperature dependent. When incident energies are of the order of 0.5 eV per atom (LECBD) and more, the cluster undergoes full epitaxy. Depending on the incident energy, the deposited cluster displays facets of dierent kinds, except for the ICBD regime where no facet is anymore produced and the cluster spreads over the surface, forming a ®lm of several monolayers thickness. Ó 1998 Elsevier Science B.V.
1. Introduction The cluster±solid interaction is studied in a wide range of dierent conditions from ``soft landing'' where clusters are smoothly deposited on surfaces, generally at very low temperatures [1,2] to very high energy cluster beams where damage is mostly produced via electron±phonon coupling [3,4]. In between these two extremes, modelling was used to investigate the state of implanted clusters and damage production in the vicinity of the surface by ion cluster beam deposition (ICBD) [5±19]. The preliminary stage of the cluster±substrate interface formation in the soft landing regime was already modelled in [20]. It was not analysed in full detail however over long enough 1
E-mail: [email protected].
periods of time to reach equilibrium. Experiments focused on cluster deposition in view of producing cluster assembled new materials by means of Low energy Cluster-Deposition (LECBD) [21±23]. In the present paper, we look at the cluster±surface interaction driven either by thermal interactions or by deposition with translation energies no more than 1 eV per atom high. In the latter regime, no damage is produced to the substrate, but the interaction has a strong in¯uence on the ®nal state of the deposited cluster. It is shown how low but non-zero cluster momentum has the eect to enhance epitaxy and in¯uence the cluster morphology. The Molecular Dynamics method (MD) used therefore is brie¯y sketched in Section 2. The simulation method is then described and the results are shown and discussed in Section 3.
0168-583X/98/$19.00 Ó 1998 Elsevier Science B.V. All rights reserved. PII S 0 1 6 8 - 5 8 3 X ( 9 7 ) 0 0 6 5 6 - 3
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M. Hou / Nucl. Instr. and Meth. in Phys. Res. B 135 (1998) 501±506
2. The model In the present case study, both the substrate and the cluster are made of elemental copper. It thus represents a situation where there is no other mismatch between the cluster and the substrate lattice parameters than due to relaxation. Little is known about the overall structure of large clusters. No particular assumption is made in the present model and a cluster containing 440 atoms is arbitrarily constructed as a spherical single crystal from which surface atoms mobile at high temperature (above 750 K) are removed by hand. The substrate is a cubic box of 12 ´ 12 ´ 12 lattice unit cells with two (0 0 1) free surfaces. Periodic boundary conditions are applied in the h1 0 0i directions parallel to the surfaces. The forces are derived from a non-local tight binding approximate potential as described in [24]. Its repulsive part is splined to a familiar Moliere screened Coulomb potential [25] at small distances and the spline parameters are given in [26]. The contribution of the screened Coulomb interaction is however minor in the present study. Newton's equations of motion of all particles are integrated stepwise in time. Force evaluation makes use of Verlet neighbour lists combined with a linked cell algorithm. Prior to modelling the cluster±substrate interaction, both systems are brought to thermal equilibrium independently. The initial orientation and position of the cluster with respect to the (0 0 1) substrate surface are selected at random. The cluster initial distance of the surface plane is however chosen in such a way that the distance between the cluster atoms closest to the surface and the surface plane is somewhat shorter than the potential cut-o distance. In addition to the thermal motion, an initial translation kinetic energy may be assigned to the cluster with momentum perpendicular to the substrate surface. In addition to 3D visualisation graphics, a static structure factor is used S k eÿik:r
1
with k-vectors parallel to the low index substrate directions [h,k,l] in order to identify directions common to the cluster and the substrate. All direc-
tions are considered such that the magnitude of the Miller indices is zero or unity. This limitation is arbitrary. By selecting jkj 4p=a where a is the lattice unit, the square of the structure factor is unity for full order and zero for full lack of correlation with the h1 0 0i, h1 1 0i and h1 1 1i substrate directions. This way, the magnitude of the structure factor at 0 K is initially 1 for the substrate and close to 0 for the cluster since its orientation is not correlated with that of the substrate. Since the two systems are thermalised, the initial values are smaller than unity and the expected eect of epitaxy is to increase the magnitude of the structure factor measured in the cluster. Simulations of 100 ps duration were repeated for several cluster initial positions, orientations and translation energies between 0 and 1 eV per atom. The same overall expitaxial behaviour is observed in most of the cases and the results are commented in the next section. 3. The results 3.1. Thermal eects The initial position and relative orientation of the cluster are selected at random, in such a way that, owing to the potential cut-o, only the atoms closest to the surface interact with the substrate. When the cluster has zero initial translation energy (soft landing regime), at 500 K, comparisons with simulations at 0 K shows that the evolution of the system is driven essentially by the temperature and to a lesser extent by the mechanical interaction energy. The state of the system after 100 ps is illustrated in Fig. 1. The cluster±surface mechanical interaction does not modify the temperature by more than 5%. The ordering with respect to the substrate is striking. An examination of snapshots during the evolution of the system shows that the cluster quickly forms one or two epitaxial layers inducing a solid rotation of the remaining part. A grain boundary then forms in the cluster which accommodates the growing epitaxial fragment to the misoriented one. Fig. 1(a) shows that about two-thirds of the cluster is epitaxial with the substrate and this part of the cluster is separated from
M. Hou / Nucl. Instr. and Meth. in Phys. Res. B 135 (1998) 501±506
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thermally, letting the epitaxial fragment grow. The dislocation quickly annealed at the surface, leaving the cluster fully epitaxed with the substrate. This is the only case among the ten runs where full epitaxy was found. Since the excess energy associated to a {1 1 1} twin boundary is close to zero in bulk fcc metals, it is expected that the con®guration in Fig. 1 is almost as stable as a perfectly crystalline deposited cluster. The tilt angle of this grain boundary is about 40°, which is however two-thirds of the tilt angle in a bulk twin boundary. This illustrates the strength of the constraint induced by the cluster surface. The way surface excess energy can be minimised is shown in Fig. 1(b) which represents the same cluster as in Fig. 1(a), viewed along a [1 0 0] direction. The epitaxial fragment tends to form {1 0 0} facets perpendicular to the surface plane. From Fig. 1(a), it is seen that, although the non-epitaxial fragment orientation does not match the orientation of the epitaxial one, it does have strong direction correlation with the substrate. Fig. 2 shows the square of the structure factor as a function of time, measured with wave vector (4p=a; 0; 0). The results in Fig. 2 are typical of those obtained with the other k-vector orientations considered, except for k-vectors parallel to common directions to the cluster fragments and the substrate. The substrate values are constant in time, indicating no signi®cant damage. They are Fig. 1. Con®guration of a copper cluster with respect to the substrate after 100 ps free evolution of the system. The orientation of the axes given in the insets refer to substrate directions. Both the cluster and the substrate are at 500 K equilibrium temperature. (a) [1 1 0] viewing direction; (b) [1 0 0] viewing direction. The twin grain boundary plane is shown in (a). It is a {1 1 1} plane common to the two cluster fragments and to the substrate. The viewing direction in (a) is also common to the fragments and the substrate.
the other by a {1 1 1} plane twin boundary. The simulation was repeated with ten dierent initial cluster positions and orientations selected at random, and the same sequence was found. In one case only, the epitaxial atomic layer accommodates the rotated fragment with a dislocation. This was however found very unstable and migrated
Fig. 2. Squared modulus of the structure factor measured as a function of time with respect to a k-vector parallel to the substrate [1 0 0] direction. Solid line: results for the substrate; dashed line: results for the cluster.
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M. Hou / Nucl. Instr. and Meth. in Phys. Res. B 135 (1998) 501±506
less than unity, because of temperature. In contrast, the results for the cluster are time dependent. The magnitude of the structure factor starts to increase smoothly from zero and undergoes a sharp increase after about 50 ps. It then keeps constant through all the simulation at some smaller value than the substrate. The structure factor for the cluster get the same value as for the substrate when the k-vector is parallel to a common direction to the cluster fragment and the substrate, like the viewing direction in Fig. 1(a). This [1 1 0] direction, together with the [1 1 2] direction inside the plane of the Fig. 1(a) both belong to the (1 1 1) plane of the twin boundary. Since this [1 1 2] direction is also common with the substrate, the whole (1 1 1) planes are common to the whole cluster and the substrate. An examination of intermediate snapshots similar to Fig. 1 shows that the smooth increase of the structure factor with time in the early stage of the interaction corresponds to limited epitaxy at the cluster±substrate interface, as described above. Once some fraction of the cluster atoms is ordered with respect to the substrate, the remaining part of the cluster undergoes a sudden partial reorganisation and remains in the state shown in Fig. 1. 3.2. Impact eect The interaction mechanism between the cluster and the surface when the cluster has some momentum is quite dierent and the ®nal state of the cluster depends on its initial translation energy. To illustrate this, the same event as just described in the previous section is modelled again, and repeated for several cluster initial translation kinetic energy per atom 0 to 1.04 eV. This energy range is typical of LECBD experiments and the highest energies considered (around 1 eV per atom) may already be suggested to belong to the ICBD regime, according to a criterion given below. The time evolution of the structure factor is given in Fig. 3 in the case of the 1.04 eV per atom. The features are similar for all the other k-vectors considered they are also representative of the case of lower energies, down to about 0.25 eV per atom. At the early stage of the interaction, the structure factor for the cluster is zero because of its random orien-
Fig. 3. Same as Fig. 2 when the initial translation energy of the cluster is 1.04 eV per atom. The other initial conditions are identical.
tation with respect to the substrate and the structure factor for the substrate displays a steep minimum in the early interaction. Its magnitude then levels o at a value slightly lower than its initial value. Epitaxy of the cluster starts earlier than that for soft landing and full epitaxy is obtained after 20 ps interaction. This is attested by the fact that the structure factor measured in the cluster reaches the same magnitude as in the substrate whatever the k-vector is. Since the simulation box is isolated, part of the initial translation energy is converted to heat and, since the model system is limited in size, the additional heat results in a raise of the temperature. In the case presented in Fig. 4, the equilibrium temperature raises from 500 to 720 k. Therefore, the structure factor was measured for a perfect simulation box at thermodynamic equilibrium at 720 K and its magnitude was found the same as the ®nal value in Fig. 3. This demonstrates that the temperature raise fully accounts for the slight decrease of the magnitude of the structure factor and, subsequently, that no detectable damage is produced. The ®nal cluster morphology is found to be dependent on the initial translation energy. This is illustrated in Fig. 4. The snapshots are taken after 100 ps free evolution, using the same [1 1 0] viewing direction as in Fig. 1(a). There are no {1 0 0} walls to be found anymore perpendicular to the surface. Instead, {1 1 0} facets are produced in the case of initial translation energy of 0.52 eV, thus forming a truncated pyramid. It spreads al-
M. Hou / Nucl. Instr. and Meth. in Phys. Res. B 135 (1998) 501±506
505
within a few picoseconds, without any indication that the system passes through a transient liquid state. It thus looks convenient to distinguish these conditions from LECBD, and to consider them associated to the ICBD. The distinction suggested between the three regimes is thus based on a morphology criterion, which applicability for other systems still needs to be assessed. One ambiguity still remains. Since, because of the impact, the system heats up, it is not yet clear whether epitaxy and morphological evolution are caused by temperature or by mechanical momentum conversion. In order to lift this ambiguity, the same simulation is repeated once more, at 720 K equilibrium temperature and a zero initial cluster translation energy. The cluster only undergoes partial epitaxy. Exactly as shown in Fig. 1 for a temperature of 500 K, it displays a similar twin grain boundary, similar {1 0 0} facets and it does not spread over the surface. 4. Conclusion
Fig. 4. Same as Fig. 1 when the cluster has an initial translation energy of: (a) 0.52 eV per atom; and (b) 1.04 eV per atom.
most isotropically on the substrate surface, over a range about twice as large as in Fig. 1. The initial cluster velocity is in the range of 1000 m/s, typical of LECBD experiments. In the case of initial energy per atom 1.04 eV, it still spreads further. No facet is anymore apparent as if the solid cluster would wet the surface although, as attested by Fig. 3, it undergoes no solid±liquid phase transition. Indeed, the squared modulus of the structure factor raises from zero to the substrate value monotonically
To summarise, at a temperature of 500 K, copper cluster epitaxy on a (0 0 1) copper surface takes place anyway. It is only partial when the cluster is deposited on the substrate with no momentum and the misorientation of the fragments is accommodated by a twin grain boundary. The epitaxial fragment displays facets perpendicular to the substrate surface. Full epitaxy takes place when the cluster has some initial velocity normal to the substrate surface and its morphology is signi®cantly dependent on the incident energy. Facets does not appear when the energy is of the order of 1 eV or higher. It thus turns out that the energy of a cluster beam can be used to monitor some of the deposited cluster properties. The three ®nal states observed for the three initial conditions used naturally suggest a distinction between soft landing, low energy cluster beam deposition and ionised cluster beam deposition. The present study focuses on an epuilibrium temperature of 500 K. Indication is given however that the same partial epitaxy is found at 720 K. Spot simulations were performed at 0 and 300 K showing the same feature. More systematic work,
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involving statistics, is necessary in order to con®rm that partial epitaxy occurs over the whole temperature range where the cluster is solid. The role of incident momentum also needs to be characterised at dierent temperatures. Other parameters may also play a role in the process, as the cluster size and its initial morphology. Although similar results may be expected for metals where cohesion is of the same nature, checks are necessary. Finally, the behaviour of heterogeneous systems may display dierent features related to lattice mismatch, solubility and segregation. The topic is rather huge, but the present work indicates that many of the problems raised can be elucidated leading to a comprehensive model for cluster deposition and deposited cluster assemblies. Acknowledgements It is a pleasure to acknowledge stimulating discussions with many colleagues and, in particular with Z.Y. Pan within the frame of a long standing cooperation. This work is sponsored by the Federal Belgian government under contract PAI/IUAP P4/10. References [1] W. Harbisch, S. Fedrigo, J. Buttet, J. Chem. Phys. 96 (11) (1992) 8104. [2] P. Blandin, C. Massobrio, J. Buttet, Z. Phys. D 26 (1/4) (1993) 236. [3] H. Dammak, A. Dunlop, Y. Le Beyec, Phys. Rev. Lett. 74 (7) (1995) 1135. [4] A. Hallen, P. Kanasson, Y. Le Beyec, Nucl. Instr. and Meth. 106 (1/4) (1995) 233.
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