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6
POWER
05.14.00
POWER STATIONS ON THE BASIS OF RENEWABLE ENERGY 05.14.08
DOI: 10.33693/2313-223X-2019-6-2-160-163
COMPUTER MODELING THIN FILM GROWTH ON THE SURFACE BY LOW ENERGY CLUSTER DEPOSITION
MuminovRamizullaAbdullaevich, doctor of physical and mathematical sciences, academican of the Akademy sciences of the Republic Uzbekistan, Physico-Technical Institute of the SPA "Physics-Sun", Akademy of sciences of Uzbekistan. Tashkent, Uzbekistan. E-mail: detector@uzsci.net
Rasulov Akbarali Mahamatovich, doctor of physical and mathematical sciences, professor, Tashkent University of Information Technologies Ferghana branch. Ferghana, Uzbekistan. E-mail: arasulov59@mail.ru
Ibragimov Nodir Ikromjonovich, Senior teacher, Ferghana Polytechnic Institute. Ferghana, Uzbekistan, E-mail: n_ibrohimov@mail.ru
Annotation. A report is presented about progress in the understanding of the properties of bi-metallic nanoparticles, their interaction with surfaces subsequent to low energy slowing down and the properties of nanostructured materials formed with these particles. A nanoparticle contains from a few atoms for the smallest ones to several thousand for the largest ones considered here. The properties of an atom result from quantization and the same is true for the molecules they form. The same is thus true for the smallest nanoparticles. At the other edge, many of the properties of macroscopic materials are well described by a classical approach and nanoparticles appear as objects at the fringing field between quantum and classical behaviors. In the study of their properties, using either a quantum or a classical approach, atomic scale methods appear as naturally well-suited. Atoms are considered as individual objects interacting via their outer shell electrons only. However even with such an approximation, solving the Schrödinger equation becomes quickly prohibitively heavy as the number of atoms involved increases. For the heaviest elements, relativistic effects make the problem even heavier.
Key words: computer simulation, low energy, cluster, deposition, slowing down, Molecular Dynamics, parallelization, Embedded Atom Model.
1. Introduction
Nanoclusters on surfaces are interesting for a wide range of chemical, magnetic, electronic and optical properties. Bimetallic particles can be produced displaying either core-shell structures [1-3] or forming alloys with, eventually, a segregated surface [4; 5]. The possibilities of synthesis outside equilibrium conditions widely increase the range of possible cluster composition and structure [6; 7]. Such particles can be modelled at the atomic scale [8-11] allowing detailed comparison with experiment. Such studies are facilitated either by depositing the clusters on surface or embedding them into a matrix. Deposited and embedded particles can be modelled on their turn, at the atomic scale [12-16]. By accumulating them, it is possible to synthesised nanostructured layers with specific properties. Cluster assembled films are formed by deposition on a surface [17] and such films could be modelled as well [18-21]. Specifically, clusters on surfaces can be obtained by atomic deposition followed by thermal diffusion. This method applies for atomic species forming islands rather then wetting the surface. Such a method was used, for instance, to produce cobalt clusters on a silver surface [22]. These clusters precipitate preferentially on pre-existing defects, or the atoms form defects at landing, themselves acting as sinks for cluster growth. Clusters in the gas phase are produced by laser ablation [23] or by condensation [24] and then extracted into a supersonic beam directed toward the substrate surface. By the latter method, clusters at thermodynamic equilibrium are formed while clusters outside equilibrium can be synthesised with the former. These both techniques allow mass selection so that homogeneous populations of deposited clusters can be formed, with identical
deposition conditions. It is well known from both experiment [23] and modelling [14] that clusters slowing down at supersonic velocities do not fragment upon impact. Whether they remain intact or undergo restructuring upon impact is still an open issue which merits attention. In particular, the question to know to which extent clusters retain their original characteristics needs an answer when the clusters are considered as possible building blocks for transferring their specific properties to the macroscopic scale.
For study of characteristics of low energy cluster beam deposition (LECBD) processes one of best methods is the computer simulation using Molecular Dynamics. However, in this case the calculation time is dramatically increased with increasing the number of atoms in the studied system. The parallelization of algorithm for simulation of LECBD characteristics results in considerable decreasing the calculation time. The parallelization strategy adopted is a multidimensional domain decomposition of the simulation box using a link cell method and a Verlet list method for each sub-domain independently. The program paradigm is based on explicit massage passing, and the standard Message-Passing Interface (MPI) was chosen in order to achieve portability.
2. MD Simulations. Model
The MD model employed is already described elsewhere [20] and will only be briefly summarised. The equations of motion of the atoms in the system are integrated stepwise in time with the algorithm in [25]. Forces are derived from a Embedded Atom Model potential (EAM) proposed in [26] and account, in addition, for a contribution of electron-phonon coupling.
COMPUTER MODELING THIN FILM GROWTH ON THE SURFACE BY LOW ENERGY CLUSTER DEPOSITION
Muminov R.A., Rasulov A.M., Ibroximov N.I.
This is done by means of a friction term which governs the exchange of energy between the ionic and the electronic systems, assuming a constant electronic temperature. It is shown in [20] how an approximate model can be established to evaluate the strength of the coupling with no adjustable parameters. The physical quantities needed are known from experiment in the case of pure elements, and it is assumed that the electronic density at the Fermi level is one electron per atom. The electron-phonon coupling contributes to dissipate the energy brought by the cluster in the impact and enhances the local cooling of the system. As compared to elemental systems, more complexity occurs in the present case as we have to deal with two different metallic elements that are not homogeneously distributed. The approximated electron-phonon coupling model employed is unsuitable to correctly describe the transport of heat by the electronic system through an interface between two elemental subsystems as in a core-shell structured cluster. It is considered here that, since the substrate is pure silver, it will be sufficient to model the electron-phonon coupling for pure silver and to neglect the difference with cobalt. The major parameter which governs the interatomic interactions in the system is, of course, the potential. Its assessment for the Co—Ag system is thoroughly discussed in [12; 10] and this discussion will not be repeated. This potential was used to discuss the equilibrium properties of Co clusters embedded in Ag and Co—Ag free clusters. The difference with the present case is the impact of the clusters on a surface, involving energies up to 1.5 eV per atom, which is much higher than those involved at thermal equilibrium. However, at this energy, the shortest Ag—Ag separation distance involved in the simulations presented below is 2.124 A at 1.5 eV/at. It is similar for Co—Co and Ag—Co pairs at the same energy. Such distances are still of the order of the first neighbour distance for which the EAM potential is designed.
In order to evaluate the modification of the clusters as a result of their impact on a Ag substrate surface, a set of characterisation functions is used.
A structure factor is used to measure the epitaxial accommodation of the clusters with the substrate. It is measured inside the cluster and gives information about the periodicity in one direction.
1 N S = - X i
M ¿-I
(1)
' i = -
In this expression, k is the wave vector, r. is the position of the atom j and N is the total number of atoms in the cluster. If the periodicity in the direction of k corresponds to the inverse of |k|, then the value of |5|2 is unity. If there is no such periodicity in this direction, 1512 is zero. In order to measure the epitaxial accommodation of the deposited cluster with the substrate, substrate lattice wave vectors are used
k =—(h, k, l), an
(2)
where a0 is the substrate lattice parameter, and h, k and l are Miller indices of lattice directions.
A pair correlation function is used to characterise short-range order in the clusters,
- N -1 N
'ir «¡¡b ig, 5,s( - ' >•
(3)
Where 5 is the Dirac function, N is the number of atoms in the cluster and r the distance between atoms i and j
a j
in the cluster. The pair correlation function gives the number of atomic pairs separated by a given distance, r. This function is calculated separately for the different kinds of pairs: Co—Co, Ag—Ag and Ag—Co. It is characteristic of the lattice structure.
3. Thin Film Growth
by Low Energy Cluster Deposition
Using Parallel Programming with MPI the AgnCom clusters with n = m (where n = 100, 250, 500, 750, 1000, 1250 and 1500) have been deposited on a Ag (100) surface at energies of 0.5 eV per atom for the studying the thin film growth processes by LECBD. In this case the Ag Co clusters with number
nm
of atoms 200, 500, 1000, 1500, 2000, 2500 and 3000 are deposited consequently with randomize choosing the next cluster from mentioned list of clusters. The slowing down of each cluster is followed for 150 ps and then next one. The substrate has a size 148.2 x 148.2 x 98.8 A which consists of 124 416 atoms. The calculation has been performed at room temperature with taking into account the periodic boundary condition on two dimensions and the electron-phonon coupling [28].
If one defines the impact characteristic time as the time needed for the cluster to convert its centre of mass kinetic energy into potential energy, and this potential energy to convert into kinetic energy into the whole system, it can be estimated as of the order of 5 ps, which is smaller than the electron-phonon coupling time at room temperature (20 ps). The slowing down of a cluster is followed during 150 ps in order to track possible thermally activated processes. At the end of these 150 ps MD evolution, particle trajectories are fully decor related from the initial trajectories and the system is in a thermal equilibrium state which may be metastable. Whether this state has a sufficiently long lifetime to be observed is not known and this question needs comparison with experiment to be settled. However, if an incident cluster undergoes modifications because of the impact, the probability to retrieve its initial state once deposited is vanishingly small. These modifications may thus be considered as permanent, whatever further thermally activated modifications are still possible.
Each cluster impacts on the crystal surface at normal incidence with a given initial kinetic energy, selecting the impact points on the surface and its orientations with respect to the surface at random. Each impact is followed during 150 ps at room temperature. Within the 150 ps evolution time considered, thermally stimulated configuration modifications may have a sufficiently high probability to take place. The slowing down is characterised by several significant features. These can be illustrated with the help of Fig. 1 which represents a cut in the cluster before its deposition and in the cluster-substrate system after 150 ps evolution. For example, the Co285Ag301 cluster is represented and the slowing down energy is 0.5 eV/atom. The final system is characterised by a limited penetration of the cluster into the substrate.
It undergoes some deformation accompanied by structural accommodation of the cluster with the substrate, which is limited in the case of Fig. 1. At the same time, the upper part of the cluster may retain its initial atomic arrangement. In the case of Fig. 1, some damage is created in the substrate and the Ag cluster shell tends to spread on the substrate surface. While the Co core is only moderately affected by the slowing down, the Ag lattice, which is already distorted initially, undergoes further deformation as a consequence of the impact.
ISSN 2313-223X
T. 6, № 2, 2019
Computational nanotechnology
161
POWER
POWER STATIONS ON THE BASIS OF RENEWABLE ENERGY
05.14.00 05.14.08
• ................................ . . . . . ... • • •
. .................................................. .... « » • •> • . . .
• •.••'.'.•.•••■.»••m'................................................•>*
Fig. 1. Initial and final configuration of a Co Ag cluster slowing down at 0.5 eV/atom kinetic energy
Fig. 2. Thin film growth by low energy cluster deposition
In Fig. 2 the film grown by deposition of 0.5 eV/atom AgnCom clusters with number of atoms 200, 500, 1000, 1500, 2000, 2500 and 3000 is presented after deposition of 65 clusters.
step = 500 (after 1 ps) and step = 73500 (after 147 ps) step= 500
TOTAL NUMBER OF ATOMS= 139 444
TOTAL NUMBER OF TYPE 1&2 ATOMS= 111 194 28 250
number of atom in each box
1153 921 850
1913 2173 814
973 1331 1159
7932 7043 7845
8127 7883 7884
8067 7641 7591
6470 6444 6457
6488 6407 6418
6478 6500 6482
number of clusters 65
step= 73500
TOTAL NUMBER OF ATOMS= 139444
TOTAL NUMBER OF TYPE 1&2 ATOMS= 111194 28250
number of atom in each box
1149 918 836
1929 2147 813
965 1329 1163
7931 7052 7876
8121 7863 7882
8057 7637 7616
6467 6458 6434
6490 6449 6426
6485 6508 6443
number of clusters 65
From figure 2 it is seen that some clusters are strongly deformed in result of thin film growth. Obtained results show that the parallelisation in Mеssage Passing of the classical MD code with EAM potentials gives good results on a cluster of personal computers.
4. Conclusion
By this brief review of our present research program, it is hoped to illustrate to which extent classical modeling at the atomic scale may contribute to the understanding of the properties of nanoparticles and the nanostructured materials formed by them.
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1992. 96, 2411; Henglein A, Mulvaney P., Holzwarth A, Sosebee T.E.,
Busenges B. Phys. Chem. 1992. 96, 754.
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КОМПЬЮТЕРНОЕ МОДЕЛИРОВАНИЕ РОСТА ТОНКИХ ПЛЕНОК НА ПОВЕРХНОСТИ МЕТОДОМ НИЗКОЭНЕРГЕТИЧЕСКОГО КЛАСТЕРНОГО ОСАЖДЕНИЯ Муминов Р.А., Расулов А.М., Иброксимов Н.И.
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DOI: 10.33693/2313-223X-2019-6-2-160-163
КОМПЬЮТЕРНОЕ МОДЕЛИРОВАНИЕ РОСТА ТОНКИХ ПЛЕНОК НА ПОВЕРХНОСТИ МЕТОДОМ НИЗКОЭНЕРГЕТИЧЕСКОГО КЛАСТЕРНОГО ОСАЖДЕНИЯ
Муминов Рамизулла Абдуллаевич, доктор физико-математических наук, академик Академии наук Республики Узбекистан, физико-технический институт НПО»Физика-Солнце», Академия наук Узбекистана, Ташкент, Узбекистан. Е-mail: detector@uzsci.net
Расулов Акбарали Махаматович, доктор физико-математических наук, профессор, Ферганский филиал Ташкентского университета информационных технологий, Фергана, Узбекистан. Е-mail: arasulov59@mail.ru Ибрагимов Нодир Икромжонович, старший преподаватель, Ферганский Политехнический институт, Фергана, Узбекистан. Е-mail: n_ibrohimov@mail.ru
Аннотация. Представлен доклад о прогрессе в понимании свойств биметаллических наночастиц, их взаимодействии с поверхностями, последующем за замедлением низкой энергии, и свойств наноструктурированных материалов, образующихся с этими частицами. Наночастица содержит от нескольких атомов для самых маленьких до нескольких тысяч для самых больших, рассмотренных здесь. Свойства атома являются результатом квантования, и то же самое верно для молекул, которые они образуют. То же самое, таким образом, верно и для мельчайших наночастиц. С другой стороны, многие свойства макроскопических материалов хорошо описываются классическим подходом, и наночастицы появляются как объекты на границе поля между квантовым и классическим поведением. При изучении их свойств, используя либо квантовый, либо классический подход, методы атомного масштаба оказываются естественно хорошо подходящими. Атомы рассматриваются как отдельные объекты, взаимодействующие только через электроны внешней оболочки. Однако даже при таком приближении решение уравнения Шредингера быстро становится непомерно тяжелым, поскольку число участвующих атомов увеличивается. Для самых тяжелых элементов релятивистские эффекты делают проблему еще более тяжелой.
Ключевые слова: компьютерное моделирование, низкая энергия, кластер, осаждение, замедление, молекулярная динамика, распараллеливание, модель встроенного атома.
flumepamypa
1. Henglein A. J. Phys. Chem. 1979. 83, 2858.
2. Henglein A., Mulvaney P., Linnert T., Holzwarth A. J. Phys. Chem. 1992. 96, 2411; Henglein A, Mulvaney P., Holzwarth A., Sosebee T.E., Busenges B. Phys. Chem. 1992. 96, 754.
3. Henglein A., Giersig M. J. Phys. Chem. 1994. 98, 6931.
4. Torigoe K., Nakajima Y., Esumi K. J. Phys. Chem. 1993. 97, 8304.
5. Liz-Marzan L.M., Philips A.P. J. Phys. Chem. 1995. 99, 15120.
6. Rousset J.L., Cadrot A.M., Aires F.S., Renouprez A., Mélinon P., Perez A, Pellarin M., Vialle J.L., Broyer M. Surf. Rev. Lett. 1996. 3, 1171.
7. Rousset J.L., Renouprez A., Cadrot A.M. Phys. Rev. 1998. B58, 2150.
8. Rousset J.L., Bertolini J.C., Miegge P. Phys. Rev. 1996. B53, 4947.
9. Zhurkin E.E., Hou M. J. Phys. Condens. Matter. 2000. 12, 6735.
10. Van Hoof T., Hou M. Appl. Surf. Sci. 2004. 226, 94.
11. Van Hoof T., Hou M. Eur. Phys. J. 2004. D29, 33.
12. Hou M., El Azzaoui M., Pattyn H., Verheyden J., Koops G., Zhang G. Phys. Rev. 2000. B62, 5117.
13. Hsieh H., Averback R.S., Sellers H., Flunn C.P. Phys. Rev. 1992. B45, 4417.
14. Hou M. Nucl. Instr. and Methods. 1998. B135, 501.
15. Pauwels B., Van Tendeloo G., Zhurkin E.E., Hou M., Verschoren G., Theil Kuhn L., Bouwen W., Lievens P. Phys. Rev. 2001. B63, 165406-1.
16. Kharlamov WS., Zhurkin E.E., Hou M. Nucl. Instr. Methods. 2002. B193, 538.
17. Bardotti L., Prével B., Mélinon P., Perez A., Hou Q., Hou M. Phys. Rev. 2000. B62, 2835.
18. Müller K.-H. J. Apll. Phys. 1987. 61, 2516.
19. Hou Q., Hou M., Bardotti L., Prével B., Mélinon P., Perez A. Phys. Rev. 2000. B62, 2825.
20. Hou M., Kharlamov WS., Zhurkin E.E. Phys. Rev. 2002. B66, 195408-1.
21. Dekoster J., Degroote B., Pattyn H., Langouche G., Vantomme A., Degroote S. Appl. Phys. Lett. 1999. 75, 938.
22. Mélinon P., Paillard V., Dupuis V., Perez A., Jensen P., Hoareau A., Perez J.P., Tuaillon J., Broyer M., Vialle J.L., Pellarin M., Baguenard B., Lerme J. Int. J. Mod. Phys. 1995. B139, 339.
ISSN 2313-223X
Т. 6, № 2, 2019
Computational nanotechnology
163
