Accounting for heat release in small volumes of matter on the example of the growth of ZnO micro-rods: search for a modeling technique

Using examples of an exothermic chemical reaction and self-heating of the region of a conducting filament of a memristor, heat-induced phase transitions, disadvantages of applying the classical Fourier approach on the nanoscale, and advantages of the molecular mechanics method at modeling the temperature factor are discussed. The correction for Arrhenius relationship, taking into account that the temperature becomes a random variable is proposed. Based on the introduced concepts (elementary act of heat release, distance and region of thermal impact) method for taking into account the thermal factor, is proposed.

The correction is based on splitting the entire pool of particles into several, each of which corresponds to a fixed temperature value taken from a certain range. Although continuous and discrete correction options are given both, but the discrete option is more preferable. This is due to the fact that the methodology focuses on the application of methods of molecular mechanics, and, intentionally, in the most primitive version. The role of amorphization is noted as an example of the structural restructuring of matter in nano-volumes. It is indicated that the phonon spectra themselves, which determine heat transfer, depend on temperature. The technique is consistent with the ideology of multiscale modeling. The integral temperature increase is calculated outside the region of thermal exposure, where nonequilibrium effects are significant, by solving the standard equation of thermal conductivity.

1. Stempkovsky A.L., Gavrilov S.V., Matyushkin I.V., Teplov G.S. On the issue of application of cellular automata and neural networks methods in VLSI design. Optical Memory and Neural Networks. 2016; 25(2): 72–78. https://doi.org/10.3103/S1060992X16020065; https://www.elibrary.ru/wvvldl

2. Sidorenko K.V., Gorshkov O.N., Kasatkin A.P. Application of the kinetic Monte Carlo method for calculating the CVC and heat transfer in memristive structures based on stabilized zirconia. Proc. of the XXI Inter. symposium "Nanophysics and Nanoelectronics". March 13–16, 2017, Nizhny Novgorod. In 2 vol. Nizhny Novgorod: Nizhni Novgorod University Press (NNUP); 2017. Vol. 2. P. 716–717. (In Russ.)

3. Menzel S., Waters M., Marchewka A., Böttger U., Dittmann R., Waser R. Origin of the ultra-nonlinear switching kinetics in oxide-based resistive switches. Advanced Functional Materials. 2011; 21(23): 4487–4492. https://doi.org/10.1002/adfm.201101117

4. Guseinov D.V., Korolev D.S., Belov A.I., Okulich E.V., Okulich V.I., Tetelbaum D.I., Mikhaylov A.N. Flexible Monte-Carlo approach to simulate electroforming and resistive switching in filamentary metal-oxide memristive devices. Modelling and Simulation in Materials Science and Engineering. 2020; 28(1): 015007–015023. https://doi.org/10.1088/1361-651X/ab580e

5. Zhang X., Yang Sh., Tu Ch.-G., Kiang Y.-W., Yang C.C. Growth model of a GaN nanorod with the pulsed-growth technique of metalorganic chemical vapor deposition. Crystal Growth & Design. 2018; 18(7): 3767–3773. https://doi.org/10.1021/acs.cgd.7b01605

6. Sharapov A.A., Matyushkin I.V. Simulation of the growth process of an array of one-dimensional ZnO single-crystal structures. In: Mathematical modeling in materials science of electronic component. Proc. of the Inter. сonf. ICM3SEC–2021. October 25–27, 2021, Moscow. Moscow: Maks Press; 2021. P. 150–151. (In Russ.). https://doi.org/10.29003/m2497.MMMSEC-2021/150-151; https://www.elibrary.ru/tgzahm

7. Redkin A.N., Ryzhova M.V., Yakimov E.E., Gruzintsev A.N. Aligned arrays of zinc oxide nanorods on silicon substrates. Semiconductors. 2013; 47(2): 252–258. (In Russ.). https://journals.ioffe.ru/articles/viewPDF/4898; https://www.elibrary.ru/rcqwit

8. Nosenko T.N., Sitnikova V.E., Strel'nikova I.E., Fokina M.I. Workshop on vibrational spectroscopy. St. Petersburg: Universitet ITMO; 2021. 173 p. (In Russ.)

9. Nedoseikina T.I., Shuvaev A.T., Vlasenko V.G. Investigation of the anharmonic pair potential of Zn-O bonds in ZnO and Zn0,1Mg0,9O. Issledovano v Rossii. 1999; 2: 1–9. (In Russ.)

10. Vorob'eva N.A. Nanocrystalline ZnO(M) (M = Ga, In) for gas sensors and transparent electrodes. Diss. Cand. Sci. (Chem.). Moscow; 2015. 180 p. (In Russ.)

11. Lu X., Fang D., Ito S., Okamoto Y., Ovchinnikov V., Cui Q. QM/MM free energy simulations: recent progress and challenges. Molecular Simulation. 2016; 42(13): 1052–1078. https://doi.org/10.1080/08927022.2015.1132317

12. Burkert U., Allinger N.L. Molecular mechanics. Washington, D.C.: American Chemical Society; 1982. 339 p. (Russ. Transl.: Burkert U., Allinger N.L. Molekulyarnaya mekhanika. Moscow: Mir; 1986. 364 p.)

13. Zhang Y., Chen H.X., Duan L., Fan J.-B. The electronic structures, elastic constants, dielectric permittivity, phonon spectra, thermal properties and optical response of monolayer zirconium dioxide: A first-principles study. Thin Solid Films. 2021; 721: 138549–138556. https://doi.org/10.1016/j.tsf.2021.138549; https://www.elibrary.ru/rimzwe

14. Abgaryan K.K., Kolbin I.S. Ab initio Calculation of the effective thermal conductivity coefficient of a superlattice using the Boltzmann transport equation. Russian Microelectronics. 2020; 49(8): 594–599. https://doi.org/10.1134/S1063739720080028; https://www.elibrary.ru/powoad

15. Abgaryan K.K. Multiscale modeling in problems of structural materials science. Moscow: MAKS Press; 2017. 280 p. (In Russ.). https://www.elibrary.ru/xuntmd

16. Matushkin I.V., Telminov O.A. Formal and philosophical issuesof connectionism and actual problems of neuromorphic systems design. Electronic Engineering. Series 3. Microelectronics. 2022; (2(186)): 49–59. (In Russ.). https://doi.org/10.7868/S2410993222020099

17. Matyushkin I.V., Tel'minov O.A., Mikhailov A.N. Accounting for heat release in small volumes of matter on the example of the growth of ZnO microrods: search for a modeling technique. In: Mathematical modeling in materials science of electronic components ICM3SEC–2022. Proc. of the International conference. October 24–26, 2022, Moscow. Moscow: Maks Press 2022. P. 68–71. https://doi.org/10.29003/m3070.ММMSEC-2022/68-71

18. Hu Y., Chen Ch., Wen Y., Xue Zh., Zhou X., Shi D., Hu G., Xie X. Novel micro-nano epoxy composites for electronic packaging application: Balance of thermal conductivity and processability. Composites Science and Technology. 2021; 209(4): 108760. https://doi.org/10.1016/j.compscitech.2021.108760

19. Manavendra P. Singh, Ryntathiang S., Krishnan S., Nayak P. Study of thermal conductivity in two-dimensional Bi2Te3 from micro-Raman spectroscopy. Current Chinese Science. 2021; 1(4): 453–459. https://doi.org/10.2174/2210298101666210412101104

20. Wang X., An M., Ma W., Zhang X. Tunable Anisotropic lattice thermal conductivity in one-dimensional superlattices from molecular dynamics simulations. Journal of Thermal Science. 2022; 31(1): 1068–1075. https://doi.org/10.1007/s11630-022-1661-2

21. Fernandes H., Cerqueira N., Sousa S., Melo A. A molecular mechanics energy partitioning software for biomolecular systems. Molecules. 2022; 27(17): 5524. https://doi.org/10.3390/molecules27175524

22. Kostyukov V. Molecular mechanics of biopolymers. Moscow: INFRA-M; 2020. 140 p. (In Russ.). https://doi.org 10.12737/1010677

23. Wang Yu., Fass J., Kaminow B., Herr J., Rufa D., Zhang I., Pulido I., Henry M., Macdonald H., Takaba K., Chodera J. End-to-end differentiable construction of molecular mechanics force fields. Chemical Science. 2022; 13: 12016–12033. https://doi.org/1010.1039/D2SC02739A

24. Pei Zh., Mao Y., Shao Y., Liang W. Analytic high-order energy derivatives for metal nanoparticle-mediated infrared and Raman scattering spectra within the framework of quantum mechanics / molecular mechanics model with induced charges and dipoles. The Journal of Chemical Physics. 2022; 157(16): 164110. https://doi.org/10.1063/5.0118205

25. Yang X., Feng T., Li J., Ruan X. Evidence of fifth-and higher-order phonon scattering entropy of zone-center optical phonons. Physical Review B. 2022; 105(11): 115205–115206. https://doi.org/10.1103/PhysRevB.105.115205