MODELING OF VOID FORMATION UNDER REACTION DIFFUSION IN BINARY SYSTEM

Main Article Content

S. V. Kornienko

Abstract

The proposed model of void formation takes into account existence two types of sinks/sources of non-equilibrium vacancies, depending on their location: in the phase volume and at the interfacial boundaries. At the interdiffusion and reaction diffusion which happens on the vacancy atomic diffusion mechanism, the inequality of atoms fluxes is caused by their differential mobility, give rise to a directional flux of vacancies. This flux of vacancies cause an appearance of areas in a diffusion zone with supersaturation and deficiency in vacancies, where sinks/sources of non-equilibrium vacancies act. It is believed that the voids arise with a certain periodicity near the interfacial boundary, where there is a vacancy supersaturation due to the different mobility of the components. The voids move in volume of growing phase, their sizes change. The void radius increases as long as void is in the region of the diffusion zone where there is a vacancy supersaturation. The void radius begins to decrease if the void is in the area of the diffusion zone, where there is a negative vacancy supersaturation (the concentration of vacancies is less than the equilibrium) until it disappears. The study of the influence on the kinetics of void formation during reaction diffusion in the binary system of sinks/sources of vacancies was carried out by computer simulation. In the case of efficient operation of vacancies sinks/sources only at the borders (vacancies sinks/sources do not work in the phase volume) we get a significant saturation of vacancies in the diffusion zone, which leads to rapid voids growth and the existence of significant pore size differences. If the vacancies sinks/sources in the volume work well (the efficiency of their work at the interfacial boundaries does not affect the result in this case), then almost everywhere in the system an equilibrium concentration of vacancies is established, as a result of which the vast majority of pores have the same (maximum) size. The pore sizes are much smaller than with the previous case.

Article Details

Section
Materials Physics
Author Biography

S. V. Kornienko, The Bohdan Khmelnytsky National University of Cherkasy

Candidate of Physical and Mathematical Sciences, docent,

Educational and Scientific Institute of Information and Educational Technologies,

The Bohdan Khmelnytsky National University of Cherkasy, Cherkasy, Ukraine

References

Tu K. N. Recent advances on electromigration in very-large-scale-integration of interconnects // Journal of Applied Physics. – 2003. – Vol. 94. – Р. 5451 – 5473. Retrieved from https://doi.org/10.1063/1.1611263

Chang, Y. W. et al. Study of electromigration-induced formation of discrete voids in flip-chip solder joints by in-situ 3D laminography observation and finite-element modeling // Acta Materialia. – 2016. – Vol. 117. – Р. 100–110. Retrieved from https://doi.org/10.1016/j.actamat.2016.06.059

Yuan-Wei Chang, Yin Cheng, Lukas Helfen, Feng Xu, Tian Tian, et al. Electromigration Mechanism of Failure in Flip-Chip Solder Joints Based on Discrete Void Formation// Scientific Reports. - 2017. – Vol. 7. – Р. (17950)1-16. Retrieved from https://doi.org/10.1038/s41598-017-06250-8

R. An, Y. Tian, R. Zhang, C. Wang Electromigration-induced intermetallic growth and voids formation in symmetrical Cu/Sn/Cu and Cu/Intermetallic compounds (IMCs)/Cu joints//J Mater Sci:Mater.Electron – 2015. – Vol.26. – P. 2674 – 2681. Retrieved from https://doi.org/10.1007/s10854-015-2736-6

Hsuan-Ling Hsu, Hsuan Lee,Chi-Wei Wang,Chenju Liang,Chih-MingChen Impurity evaporation and void formation in Sn/Cu solder joints// Materials Chemistry and Physics. -2019. – Vol. 225. – P. 153-158. Retrieved from https://doi.org/10.1016/j.matchemphys.2018.12.036

Gusak, A. M. Moving interphase interfaces as vacancy generators, vacancy gradients, nonparabolic growth and all that // The Minerals, Metals & Materials Society. – 1994. – P. 1133-1138. Retrieved from http://eprints.cdu.edu.ua/id/eprint/2169

Gusak A., Kornienko S., Lutsenko G. Nonequilibrium vacancies in nanosystems // Defect and Diffusion Forum – 2007. – Vol.264. – P. 109-116 Retrieved from https://doi.org/10.4028/www.scientific.net/DDF.264.109

Gusak, A., Kornienko S., Storozhuk N., Zaporozhets T. Influence of Limited Efficiency and Competition of Vacancy Sinks/Sources on the Diffusion-Controlled Intermediate Phase Growth // Diffusion Foundations – 2014. –2.- P. 141-158 Retrieved from https://doi.org/10.4028/www.scientific.net/DF.2.141

Kornienko S.V. Model of reaction diffusion in a binary system, considering action of sources and sinks of vacancies in parent phases // Металлофизика и новейшие технологи. – 2013. – Т.35, №12. – С.1685-1696 Retrieved from http://dspace.nbuv.gov.ua/handle/123456789/104268

Kornienko S.V., Gusak A.M. Influence of vacancy sources and sinks on the kinetics of the reaction diffusion in a binary system // Металлофизика и новейшие технологи. – 2015. – Т.37, №10, – С.1001-1016. Retrieved from https://doi.org/10.15407/mfint.37.10.1297

Storozhuk N.V., Gusak A.M. Competition of the kirkendall and frenkel effects at reaction diffusion // Металлофизика и новейшие технологии. – 2014. – Т. 36, № 3. – С. 367-374. Retrieved from http://dspace.nbuv.gov.ua/handle/123456789/104131

Zaporozhets T.V., Storozhuk N.V., Gusak A.M. Competition of Voiding and Kirkendall Shift during Compound Growth in Reactive Diffusion–Alternative Models // Металлофизика и новейшие технологии. — 2016. — Т. 38, № 10. — С. 1279-1292. Retrieved from https://doi.org/10.15407/mfint.38.10.1279

Kolisnyk L.I., Kornienko C.V. Modeling of void formation during the process of reaction diffusion in a binary system // Visnyk Cherkaskoho Universytetu. Seriia «Fizyko-Matematychni Nauky» (Bulletin of Cherkasy University. Series "Physics and Mathematics"). – 2018. – № 1. – P.21 – 28. Retrieved from https://doi.org/10.31651/2076-5851-2018-1-21-28

Chuvtaiev Yu.V.,Kornienko S.V. Modeling of void distribution by size at the diffusion zone// Visnyk Cherkaskoho Universytetu. Seriia «Fizyko-Matematychni Nauky» (Bulletin of Cherkasy University. Series "Physics and Mathematics"). – 2019.- №1. - P. 96-106. Retrieved from https://doi.org/10.31651/2076-5851-2019-1-96-106