Thermomechanical effects of radiation origin in microelectronics products
Matematičeskoe modelirovanie, Tome 34 (2022) no. 2, pp. 58-70.

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A mathematical model of the thermomechanical effect of penetrating radiation on a microelectronic product is presented. The model is based on the thermoelasticity equations, which are a consequence of the quantum kinetic equations for phonons. Heat transport is described by the law of conservation of energy and the Cattaneo equation, which takes into account the finite rate of heat propagation. Lattice vibrations are considered in the approximation of the linear theory of elasticity. In general, the model determines the distribution of temperature, energy flow, deformation and stress. Difference schemes have been developed for solving the model equations. The effectiveness of the developed model was tested by solving the problem of thermal shock.
Keywords: penetrating radiation, thermomechanical effect, thermoelasticity, thermal conductivity, difference scheme, thermal shock.
Mots-clés : phonons
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Yu. A. Volkov; M. Yu. Vyrostkov; M. B. Markov; I. A. Tarakanov. Thermomechanical effects of radiation origin in microelectronics products. Matematičeskoe modelirovanie, Tome 34 (2022) no. 2, pp. 58-70. http://geodesic.mathdoc.fr/item/MM_2022_34_2_a4/

[1] V. E. Fortov, Extreme States of Matter. High Energy Density Physics, Springer Series in Material Science, 2016 | DOI | Zbl

[2] L. D. Landau, E. M. Lifshitz, The Classical Theory of Fields, v. 2, 4th Ed., Butterworth-Heinemann, 1975

[3] W. Heitler, The Quantum Theory of Radiation, Clarendon Press, Oxford, 1954 | Zbl

[4] H. Davies, H. A. Bethe, L. C. Maximon, “Theory of bremsstrahlung and pair production. Integral cross section for pair production”, Phys. Rev., 93 (1954), 788–795 | DOI | MR

[5] N. F. Mott, H. S. W. Massey, The theory of atomic collisions, Clarendon Press, Oxford, 1965

[6] H. S. W. Massey, E. H. S. Burhop, Electronic and Ionic Impact Phenomena, Clarendon Press, Oxford, 1969

[7] M. Gryzinski, “Classic Theory of Electronic and Ionic Inelastic Collisions”, Phys. Rev., 115 (1959), 374–383 | DOI | MR | Zbl

[8] Yong-Ki Kim, M. E. Rudd, “Theory for Ionization of Molecules by Electrons”, Phys. Rev., 50 (1994), 3954–3967 | DOI

[9] A. I. Anselm, Vvedenie v teoriiu poluprovodnikov, Nauka, M., 1978, 616 pp.

[10] M. V. Fischetti, W. G. Vandenberghe, Edvanced Physics of Electron. Transport in Semiconductors and Nanostructures, Springer, 2016, 474 pp.

[11] P. Yu, M. Cardona, Fundamentals of Semiconductors, Springer Science Business Media, 2010, 795 pp.

[12] R. E. Peierls, Quantum Theory of Solids, Clarendon Press, Oxford, 1955

[13] P. G. Klemens, “Thermal conductivity and lattice vibration modes”, Encyclopedia of Physics, v. 14, Springer-Verlag, Berlin, 1956, 198

[14] J. Callaway, “Model for lattice thermal conductivity at low temperatures”, Phys. Rev., 113:3 (1959), 1046–1051 | DOI | Zbl

[15] M. G. Holland, “Analysis of lattice thermal conductivity”, Phys. Rev., 132:6 (1963), 2461–2471 | DOI

[16] A. A. Vlasov, Nelokalnaia statisticheskaia mekhanika, Nauka, M., 1978, 264 pp.

[17] A. S. Dmitriev, Vvedenie v nanoteplofiziku, Binom, Laboratoriia znaniy, M., 2015, 790 pp.

[18] Yu. A. Volkov, M. B. Markov, “Priblizhenie Vlasova dlia gaza fononov”, Keldysh Institute preprints, 2019, 083, 15 pp.

[19] C. Cattaneo, “On a form of heat equation which eliminates the paradox of instantaneous propagation”, C. R. Acad. Sci. Paris, 1958, 431–433 | Zbl

[20] R. A. Guyer, J. A. Krumhansl, “Solution of the linearized Phonon Boltzmann equation”, Phys. Rev., 148:2 (1966), 766–778 | DOI

[21] W. Nowacki, Thermoelasticity, Pergamon Press, New-York, 1986, 578 pp. | Zbl

[22] D. S. Chandrasekharaiah, “Thermoelasticity with second sound: A review”, Appl. Mech. Rev., 39:3 (1986), 355–375 | DOI

[23] D. S. Chandrasekharaiah, “Hyperbolic thermoelasticity: A review of recent literature”, Appl. Mech. Rev., 51:12 (1986), 705–729 | DOI

[24] P. Van et al, “Gayer-Krumhansl-type heat conduction at room temperature”, EPL, 118 (2017), 50005, 7 pp. | DOI

[25] Yu. A. Volkov, K. K. Inozemtseva, M. B. Markov, I. A. Tarakanov, “Algoritm modelirovaniia radiatsionnykh termomekhanicheskikh effektov v priblizhenii Kattaneo”, Preprinty IPM im. M.V. Keldysha, 2018, 108, 12 pp.

[26] V. I. Danilovskaia, “Temperaturnye napriazheniia v uprugom poluprostranstve, voznikaiushchie vsledstvie vnezapnogo nagreva granitsy”, PMM, 16:3 (1952), 341–344 | MR | Zbl