=Paper=
{{Paper
|id=Vol-2426/paper7
|storemode=property
|title=Multiscale Modeling of Clusters of Point Defects in Semiconductor Structures
|pdfUrl=https://ceur-ws.org/Vol-2426/paper7.pdf
|volume=Vol-2426
|authors=Karine K. Abgaryan,Ilya V. Mutigullin,Sergey I. Uvarov,Olga V. Uvarova
}}
==Multiscale Modeling of Clusters of Point Defects in Semiconductor Structures==
https://ceur-ws.org/Vol-2426/paper7.pdf
Multiscale Modeling of Clusters of Point Defects in Semiconductor
Structures
Karine K. Abgaryan1,2, Ilya V. Mutigullin1, Sergey I. Uvarov1, Olga V. Uvarova1,2
1
Dorodnitsyn Computing Center FRC CSC RAS, Moscow, Russia
2
Moscow Aviation Institute (NRU) (MAI), Moscow, Russia, kristal83@mail.ru
Abstract
Clusters of point and extended defects, arising in semiconductors as a
result of radiation exposure, allow structures to acquire various properties
that can be used in the manufacture of new generation devices for
nanoelectronics. Numerical simulation of semiconductor materials used to
research such processes is a resource-intensive and multifaceted task. To
solve it, the multiscale modeling complex was created and the multiscale
composition containing instances of basic composition models was set.
An algorithm was developed that allows speeding up calculations for
systems of large dimensions and accounting for a large number of
interacting atoms. The structure of silicon with a complex of point defects
was considered as a model. Molecular dynamics simulation was
performed using the multiparameter potential of Tersoff. For the
calculations, an effective approach to the implementation of parallel
computing was presented, and software for parallel computations was
used, placed on the hybrid high-performance computing complex of the
FRC βComputer Science and Control" of Russian Academy of Science.
To implement the parallel algorithm, the OpenMP standard was used.
This approach has significantly reduced the computational complexity of
the calculations. It was shown that the developed high-performance
software can significantly accelerate molecular dynamics calculations,
such as the calculation of divacancy communication energy, due to the
parallel algorithm.
1 Introduction
Conducting theoretical studies of the formation of clusters of point defects in semiconductor structures is an
important task on the way to improving technologies for obtaining new materials. One of the reasons for the
formation of various defects in the semiconductor structure, including point, extended, their clusters and complexes is
the radiative forcing. As is known from a number of experimental studies [1, 2], as a result of irradiation, such
structures acquire various properties that can be used in the manufacture of new generation devices for
nanoelectronics. In this work, the multiscale approach is used to calculate defects that form in semiconductor
structures as a result of radiation exposure [3, 4]. It is based on:
- selection of the main scale levels, including atomic-crystalline and molecular-dynamic;
- development and application for solving the set tasks of mathematical models and algorithms specific for each
level;
- combining models and algorithms in the general computing process.
Due to the large labor-intensiveness and versatility of the methods used for numerical simulation of semiconductor
materials, a software package was created for multiscale modeling of their structural features, which allowed studying
the formation of clusters of point and extended defects in a computational experiment. The paper presents the results
of calculations obtained using the software for paralleling the computations placed on the hybrid high-performance
computing complex of the FIC "Informatics and Control" of the Russian Academy of Sciences.
At present, a theoretical study of the processes occurring in complex defect structures is a very urgent task. One of
the common approaches to conducting such research, which provides a compromise between the speed of calculations
and the accuracy of the results, is the method of molecular-dynamic calculations. However, the problem of molecular
Copyright Β© 2019 for the individual papers by the papers' authors. Copyright Β© 2019 for the volume as a collection by its
editors. This volume and its papers are published under the Creative Commons License Attribution 4.0 International (CC BY 4.0).
In: Sergey I. Smagin, Alexander A. Zatsarinnyy (eds.): V International Conference Information Technologies and High-
Performance Computing (ITHPC-2019), Khabarovsk, Russia, 16-19 Sep, 2019, published at http://ceur-ws.org
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dynamic modeling of complex defective structures remains resource-intensive due to the need to consider systems of
high dimensionality and to take into account the interaction of a huge number of atoms with each other. In this regard,
it is necessary to develop algorithms that allow accelerating such calculations without sacrificing the size of the
simulated atomic structures.
The task of developing a new computational algorithm for molecular dynamics calculations was solved in the
framework of the study of clusters of point defects in single-crystal silicon. Crystal defects call any violation of the
translational symmetry of a crystal - the ideal periodicity of the crystal lattice. There are several types of defects:
point, linear, flat, bulk. Point defects are a local violation of the crystal structure, the dimensions of which in all three
dimensions are comparable with one or several interatomic distances. These are defects associated with impurities,
with displacement or with the replacement of a small group of atoms. Such defects usually occur during heating
during crystal growth, during radiation exposure, and also as a result of the addition of impurities. One type of point
defects is a vacancy - a free, unoccupied atom, a lattice site.
The occurrence of radiation defects is an inevitable side effect of such a method of modifying materials as ion
implantation. Radiation defects occur due to exposure to the material of neutrons or gamma rays. Such an effect is
characteristic of materials found in a nuclear reactor. In space, the impact on materials of electrons and protons, as
well as heavy ions with low energy, is characteristic.
Theoretical and experimental studies show that defects in silicon can form complex extended structures. For
numerical simulation of such structures and the study of their stability, it is necessary to take into account in the
calculations a large number of interacting atoms. This, in turn, leads to an increase in the computational complexity of
the problem and an increase in the time required to solve it. The use of new approaches to the parallelization of
molecular dynamic calculations on high-performance computer clusters allows us to solve such problems today.
In this paper, a new efficient approach is proposed for parallel computations when solving the problem of the
molecular dynamic description of the structure of silicon with interacting vacancy defects.
2 Multiscale Modeling of Clusters of Point Defects in Silicon
Multiscale approach was applied to calculations of ordered cluster configurations of vacancies and the interstitial
atoms in Si [3.4]. Two large-scale levels (apart from zero) - atomic and crystal and molecular and dynamic were
selected. Within set-theoretic representations it can be set by means of multiscale composition in which are involved:
(0,14;1,1;1,2;2,1;2,2) (ππ)
πΎ0,1,2 = πΎ0,1,2 (1)
such copies of basic models compositions:
ππ ππ ππ ππ
π¬π01 : {π01 , π01 , ππ΄01 }; (2)
ππ ππ ππ ππ
πͺ11 : {π11 , π11 , ππ΄11 };πͺ11 (Β«CRYSTAL β CHEMICAL FORMULAΒ») (3)
ππ ππ ππ ππ
πͺ12 : {π12 , π12 , ππ΄12 };πͺ12 (Β«QUANTUM β MECHANICAL CELLΒ») (4)
ππ ππ ππ ππ
πͺ21 : {π21 , π21 , ππ΄21 }-πͺ12 (Β«NUCLEAR CLUSTER β STATICΒ») (5)
ππ ππ ππ ππ
πͺ22 : {π22 , π22 , ππ΄22 }-πͺ22 (Β«NUCLEAR CLUSTER β DYNAMICSΒ») (6)
In Figure 1 shows the structure of a multiscale composition for calculating ordered cluster configurations of
vacancies and interstitial atoms in Si. Specimens of basic compositions and the sequence of their use in the
computational process are indicated.
Figure 1: Large-scale composition for the calculation of defects in Si
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At the first level, data on the chemical composition and atomic crystal structure of Si (diamond structure), obtained
using the basic composition πͺ11 ("CRYSTAL CHEMICAL FORMULA"), were used. Further, they were used as input
data in the base composition πͺ12 (βQUANTUM-MECHANICAL CELLβ) during the first-principle calculations in the
framework of the electron density functional theory using the VASP software package [5]. In the first-principle
modeling of the structure of ideal silicon, a periodic cell consisting of 64 atoms of dimension (2 Γ 2 Γ 2) was used.
Refined the atomic-crystalline and electronic structure of silicon with defects, was calculated πΈππβ . The
computational resources of the Interdepartmental Supercomputer Center of the Russian Academy of Sciences and
Moscow State University of M. V. Lomonosov were used for the calculations.
At the second scale level, questions were studied of the time variation of the structure of silicon with defects and
with defective clusters. A composition of computational models consisting of basic compositions πͺ12 (βNUCLEAR
CLUSTER β STATICβ) and πͺ22 (βNUCLEAR CLUSTER - DYNAMICSβ) was used. Moreover, when forming the
input data πͺ12 we used the results of first-principle calculations [5], obtained using the basic composition πͺ12 . They
were used as reference. The cohesive energy of the system was the global parameter transmitted from the first to the
second scale πΈππβ .
3 Model Description
For the numerical simulation of silicon single crystal, an elementary silicon cell consisting of 8 atoms was used
(Figure 2). Further, using parallel transfers, the unit cell multiplied to silicon structures containing 616, 1160, and
4504 atoms. A structure was simulated with a complex of point defects, two vacancies located in neighboring lattice
sites (Figure 3), with a selected frequency of defect recurrence β through a cell.
Figure 2: Si crystal lattice without defects
Figure 3: Silicon lattice with divacancy
4 The Solution of the Problem
Molecular dynamics modeling was carried out using the multiparameter potential of Tersoff [6], which proved
well in solving problems of modeling compounds with covalent bonds. The calculation of the cohesive energy of the
system of atoms was carried out as follows:
1
πΈ = β πΈπ = β πππ (7)
2
π π
πππ = ππΆ (πππ )[ππ
(πππ ) + πππ ππ΄ (πππ )] (8)
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1, πππ < π
β π
ππ’π‘
1 π(πππ β π
)
ππΆ (πππ ) = [1 + πππ [ ]], π
β π
ππ’π‘ < πππ < π
+ π
ππ’π‘ (9)
2 2π
ππ’π‘
{ 0, πππ > π
+ π
ππ’π‘ }
ππ
(πππ ) = π΄ππ ππ₯π(βπ
ππ (πππ β π
π )) (10)
ππ΄ (πππ ) = π΅ππ ππ₯π(βπππ (πππ β π
π )) (11)
ππ
β
πππ = πππ (1 + πΎπππ πππππ ) 2 (12)
Potential parameters were selected as a result of solving the optimization problem [7]:
πππ
πΉ(π) = π1 (πΈππβ (π) β πΈππβ )2 + π2 (π(π) β π πππ )2 + π3 (π΅(π) β π΅ πππ )2 +
πππ (13)
+π4 (πΆβ²(π) β πΆβ²πππ )2 + π5 (πΆ44 (π) β πΆ44 )2 + π6 (π(π) β ππππ )2 β πππ
where π = (π1 β¦ ππ ) - parameters of Tersoff potential
πππ πππ
πΈππβ , π πππ , π΅ πππ , πΆβ²πππ , πΆ44 , π πππ - reference values obtained using ab initio calculations and from
publication [8]. Selected values of the potential parameters are given in Table 1.
Table 1: Parameters of Tersoff potential for silicon structure
π«π πΊ π· πΉπ π π
π π πΈ π
2,3631 1,4864 1,4637 2,3436 113074,1153 14,2474 0,9388 -0,4239 1,2466β 10β6 0,2993
Molecular dynamics modeling was a solution to the Cauchy problem for the equation of motion described below.
The coordinates and velocities of each particle were set as the initial conditions for such problem.
ππ’π
ππ = πΉπ (π₯1 , . . , π₯π ),
ππ‘
πππ
ππ = πΉπ (π¦1 , . . , π¦π ),
ππ‘
ππ€π
ππ = πΉπ (π§1 , . . , π§π ),
ππ‘ (14)
ππ₯π
= π’π ,
ππ‘
ππ¦π
= ππ ,
ππ‘
ππ§π
{ = π€π ,
ππ‘
where ππ[1, π];
ππ β mass of the n-th atom, ππ[1, π];
πΉπ β force acting on the particle n.
To integrate the Cauchy problem, we used the Verlet velocity method [9]:
ππ2 ππππ
πππ+1 = πππ + ππ π£ππ β
2 ππππ (15)
π π+1
πππ π
πππ
π£ππ+1 = π£ππ + π ( + )
2 ππππ+1 ππππ (16)
This method is a compromise between accuracy and speed of implementation. The method is stable and accurate, as
well as self-starting due to the fact that its velocity is taken into account to obtain the next position of the particle.
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Figure 4: Block diagram of the molecular dynamics algorithm.
Figure 5: The block diagram of the parallel algorithm.
Two algorithms were developed to simulate defects: serial, which was run on a personal computer (Intel Core i7 4-
core 4 GHz CPU, 16 GB OP), and parallelized to run on the IBM supercomputer (two 8-core IBM Power 8 CPUs, OP
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512 GB) Features of the implementation are associated with the use of the potential of Tersoff, which is difficult to
parallelize due to its complex structure, and is also resource-intensive from the point of view of computation.
To implement the parallelized algorithm, the OpenMP standard was used. To do this, we determined the maximum
available number of threads for the program instance being started, after which the input data were divided into the
number of blocks equal to the number of available threads. Each input block was launched in its own stream. During
the molecular dynamics simulation, at the end of each time step, the blocks exchanged data in order to synchronize
the parameters of atoms that are common to different blocks (Figure 5). This approach has reduced the computational
complexity by reducing the number of atoms processed in each stream. In turn, this made it possible to significantly
accelerate the process of modeling, thanks to which it became possible to take into account a larger number of atoms
in the calculations.
For a visual comparison of the speed of the parallel and sequential algorithms, the modeling process was limited to
10 time steps. The results of the calculations are presented in Table 2. According to the obtained results, the
application of the developed algorithm on a personal computer allows you to significantly speed up the calculations,
and the demonstrated result of acceleration on a supercomputer is more significant than on a quad-core processor.
Table 2: Comparison of the running time of the algorithm on PC and IBM for different amount
Number of atoms Personal Personal IBM IBM supercomputer,
Computer, Computer, supercomputer, 128 threads,
1 thread 4 threads 1 thread, sec
sec sec sec
864 991.664 358.496 1990.230 65.585
1152 1995.660 707.852 3830.310 125.255
2048 7010.740 2873.040 14231.100 464.480
The results obtained using the developed software package were also compared with the results obtained using the
LAMMPS package. A separate program was written to obtain results within the LAMMPS package. In it, the
elementary cell of silicon was modeled from 16 atoms with the help of the Tersoff potential at different temperatures.
The obtained data were compared with a similar experiment set in the developed software package. The bond energy
(E_pair) and system temperature (Temp) were compared.
Table 3: Calculation results for a cell of 16 silicon atoms with a divacancy (the temperature at the beginning of the
simulation is 0 K)
Number of time E_pair MD E_pair Temp MD, Temp LAMMPS,
steps eV LAMMPS, K Π
eV
0 -74.0808 -74.0866 0 0
100 -74.0808 -74.0866 5.8324 β 10β34 9.8751β 10β25
1000 -74.0808 -74.0866 6.0933β 10β32 9.1005β 10β25
10000 -74.0808 -74.0866 7.0054β 10β34 3.1961β 10β25
Table 4: Calculation results for a cell of 16 silicon atoms with a divacancy (the temperature at the beginning of the
simulation is 100 K)
Number of time E_pair MD E_pair Temp MD, Temp LAMMPS,
steps eV LAMMPS, K Π
eV
0 -74.0808 -74.0866 100 100
100 -73.5437 -73.9947 87.5567 52.6309
1000 -74.0808 -74.0120 87.5872 61.5911
10000 -74.0808 -73.9978 87.5872 54.2501
Table 5: Calculation results for a cell of 16 silicon atoms with a divacancy (the temperature at the beginning of the
simulation is 500 K)
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Number of time E_pair MD E_pair Temp MD, Temp LAMMPS,
steps eV LAMMPS, K Π
eV
0 -74.0808 -74.0866 500 500
100 -70.9716 -73.6818 437.8505 291.3985
1000 -74.0808 -73.6169 437.9358 258.1365
10000 -74.0808 -73.6535 437.9360 276.9892
Table 6: Calculation results for a cell of 16 silicon atoms with a divacancy (the temperature at the beginning of the
simulation is 1000 K)
Number of time E_pair MD E_pair Temp MD, Temp LAMMPS,
steps eV LAMMPS, K Π
eV
0 -74.0808 -74.0866 1000 1000
100 -67.8394 -73.1538 875.6751 519.4458
1000 -74.0808 -73.1616 875.8718 523.6768
10000 -74.0808 -73.0931 875.8721 488.4341
From the comparison performed, it can be seen that the binding energy is close to the energy values obtained using
the LAMMPS software, and the temperature is comparable to the results obtained in LAMMPS.
The implemented algorithm made it possible to calculate the characteristics of monocrystalline silicon, in particular,
the value of the binding energy for monocrystalline silicon was calculated (πΈππβ (π) = β4.6314Π΅π). The obtained
πππ
value turned out to be close to the value obtained earlier with the help of ab initio calculations (πΈππβ = β4.6305Π΅π)
[10]. Thus, the developed software using the selected parameters of the Tersof potential allows one to fairly
accurately describe the geometric and energy properties of monocrystalline silicon. This approach can be further
applied to the study of more complex structures of vacancy clusters in a silicon single crystal.
5 Conclusion
In this paper, software was developed that enables molecular dynamics modeling, effectively parallelizing
computational flows. As part of the task of studying the stability of defective clusters in monocrystalline silicon, the
developed software was used to calculate the divacancy binding energy in the structure of monocrystalline silicon.
The proposed algorithm allows us to significantly accelerate molecular dynamics calculations, making it possible to
take into account a larger number of interacting atoms in the simulation. In turn, this will allow us to study the
properties of more complex defective structures in silicon. This approach can be applied further to simulate
interacting atomic systems described by different potentials.
The calculations were performed by Hybrid high-performance computing cluster of FRC CS RAS) [19,20] and
Shared Facility Center βData Center of FEB RASβ (Khabarovsk) [21].
6 Application
The designation of variables used in formulas.
π¬ - total energy of the system, (eV);
π½ππ - potential energy of the interaction of two particles i and j, (eV);
ππͺ (πππ ) - cutoff-function
πππ -distance between two particles i and j, (Γ
);
πΉπππ - cutoff distance (Γ
);
ππΉ β repulsive potential between two atoms, (eV);
ππ¨ β potential of attraction between two atoms, (eV);
Πππ -parameter of attraction between two atoms, (eV);
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π¨ππ -repulsive parameter between two atoms, (eV);
R β parameter of Tersoff potential, (Γ
);
πππ β parameter of Tersoff potential, (Γ
);
πΏππ β parameter of Tersoff potential, (Γ
);
Ξ³ β parameter of Tersoff potential, (dimensionless);
Re β parameter of Tersoff potential, (Γ
);
Ξ» β parameter of Tersoff potential, (Γ
);
n β parameter of Tersoff potential, (dimensionless);
ΞΆ β parameter of Tersoff potential, (dimensionless);
π - parameter of Tersoff potential, (dimensionless);
π¬πππ - cohesive energy of the system, (eV);
π - lattice constant, (Γ
);
π© - bulk modulus, (Mbar);
πͺβ² - shear modulus, (Mbar);
πͺππ - elastic constant, (Mbar);
π» - Kleinman's constant, (dimensionless);
π = (ππ β¦ ππ ) β weights;
π = (ππ β¦ ππ ) - parameter of Tersoff potential;
m β atom mass, (1.66054 * 10-27 kg);
F β the force acting on the molecule, (N);
ππ , ππ , ππ β coordinates of the n-th atom, (Γ
);
ππ , ππ , ππ β the speed of the n-th atom (m/s);
r β atomic coordinates, (Γ
);
v β atom speeds (m/s);
t β time, (s);
U - interaction potential between two atoms, (J);
References
1. Tang, M., Colombo, L., Zhu, J., Diaz, T. de la Rubia: Intrinsic point defects in crystalline silicon: Tight-binding
molecular dynamics studies of self-diffusion, interstitial-vacancy recombination, and formation volumes.
Phys. Rev. B. 1997, vol. 55, iss. 21, pp. 14279β14289. DOI: 10.1103/PhysRevB.55.14279.2. Kolbin I.S.,
Reviznikov D.L.Resheniyezadachmatematicheskoyfiziki s ispolzovanieymnormalizovannikhradialno-
basisnikhsetey.// Β«NeirokompyuteriΒ»: razrabotka,primineniye. β 2012. β β 2 β pp. 12-19. (In Russian)
2. Fedina, L. I., Sheglov, D. V., Gutakovskii, A. K., Kosolobov, S. S., Latyshev, A. V.: Precision measurements of
nanostructure parameters. Optoelectronics, Instrumentation and Data Processing. 2010, vol. 46, no. 4, pp.
301β311.
3. Abgaryan, K. K.: Mnogomasshtabnoe modelirovanie v zadachah strukturnogo materialovedeniya//Monografiya.
M.: Maks Press, 2017 - P. 284. (In Russian)
4. Abgaryan, K. K.: Informacionnaya tekhnologiya postroeniya mnogomasshtabnyh modelej v zadachah
vychislitel'nogo materialovedeniya. // Β«Izdatel'stvo Β«RadiotekhnikaΒ», βSistemy vysokoj dostupnostiβ. 2018.
V. 15. β 2. pp.9-15. (In Russian)
5. VASP β http://cms.mpi.univie.ac.at/vasp/
6. Tersoff, J.: Empirical interatomic potential for silicon with improved elastic properties / J. Tersoff // Phys. Rev. B. -
1988. - V. 38. - P. 9902β9905.
7. Abgaryan, K. K., Posipkin M.A.: Primenenie optimizacionnyh metodov dlya resheniya zadach parametricheskoj
identifikacii potencialov mezhatomnogo vzaimodejstviya. // ZH. vych. mat. i matem. fiz. 2014. V. 54. β 12.
pp.1994-2001. (In Russian)
8. Powell, D.: Elasticity, lattice dynamics and parameterisation techniques for the Tersoff potential applied to
elemental and type IIIβV semiconductors : dis. - University of Sheffield, 2006.
9. Zaliznjak, V.E.; Osnovy vychislitel'noj fiziki. Chast' 2. Vvedenie v metod chastic / Zaliznjak V. E. // Moskva-
Izhevsk: NIC Β«Reguljarnaja i haoticheskaja dinamikaΒ»; Institut komp'juternyh issledovanij, 2006, pp. 26β45.
50
Computer Design of New Materials
______________________________________________________________________________________________
_
10. Abgaryan, K. K.: Mathematical Modeling of Point Defect Cluster Formation in Silicon Based on Molecular
Dynamic Approach / Abgaryan K.K., Volodina O. V., Uvarov S. I.//. News of higher education institutions.
Materials of electronic equipment. 2015 Π³.β1. Page 31-42.
11. Linnik, Yu.V.: Metod naimen'shih kvadratov i osnovy matematiko-statisticheskoj teorii obrabotki nablyudenij β
M.: FIZMATLIT, 1958, P. 336 (In Russian)
12. Ashkroft, N., Mermin, N.: Fizika tverdogo tela. Tom 1 β M.: Mir, 1979. β P. 486 (In Russian)
13. Landau, L.D., Lifshic, Π.M.: Teoreticheskaya fizika. Teoriya uprugosti. 4-e izd., ispr. -M.: Nauka. Gl. red. fiz.-
mat. lit., 1987.β P. 248 (In Russian)
14. Slovar nanotekhnologicheskih i svyazannyh s nanotekhnologiyami terminov / pod red. S. V. Kalyuzhnogo. βM.:
Fizmatlit, 2010. β P. 528 (In Russian)
15. Huk, R., Dzhivs, T.A.: Β«Pryamoj poisk resheniya dlya chislovyh i staticheskih problemΒ», pp. 212β219 1961. (In
Russian)
16. Zefirov, N.S. (gl. red.). Himicheskaya enciklopediya. β Moskva: Bol'shaya Rossijskaya Enciklopediya, 1995. β
V. 4. β P. 55. β pp. 639 (In Russian)
17. Abgaryan, K. K.: Primenenie optimizacionnyh metodov dlya modelirovaniya mnogoslojnyh poluprovodnikovyh
nanosistem // Trudy Instituta sistemnogo analiza Rossijskoj akademii nauk. Dinamika neodnorodnyh sistem.
2010. V. 53(3). (In Russian)
18. Ostrik, A.V.: Metod konechno-razmernyh chastic v yachejke primenyaemyj dlya chislennogo modelirovaniya
vysokoskorostnogo vzaimodejstviya geterogennyh tel // Himicheskaya fizika.β 2008. β V. 27, β 8. β pp.
81β88. (In Russian)
19. Federal Research Center βComputer Science and Controlβ of the Russian Academy of Sciences. Available at:
http://hhpcc.frccsc.ru (accessed 09/12/2018).
20. Zatsarinny A.A., Gorshenin A.K., Kondrashev V.A., Volovich K.I., Denisov S.A. Toward high performance
solutions as services of research digital platform. // Procedia Computer Science. Volume 150 (2019). p. 622-
627.
21. Sorokin, A.A., Makogonov, S.V., Korolev, S.P.: The Information Infrastructure for Collective Scientific Work in
the Far East of Russia // Scientific and Technical Information Processing. 2017. Vol. 44. Number 4. P. 302-
304.
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