MODELING OF VOID FORMATION DURING THE PROCESS OF REACTION DIFFUSION IN A BINARY SYSTEM
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Numerous experiments demonstrate that processes of reaction diffusion are followed by void formation quite often. 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 causes an appearance of areas in a diffusion zone with supersaturation and deficiency in vacancies, where sinks / sources of non-equilibrium vacancies act. Dislocations, interphase and grain borders, microvoids may be sinks / sources of non-equilibrium vacancies. Therefore voids may be considered as a sinks of non-equilibrium vacancies that act in the area of a diffusion zone where there is vacancy supersaturation during modeling of reaction diffusion. The model of void formation for a binary system during the process of reaction diffusion is suggested. This model allows to investigate the kinetics of void growth, and their motion in a volume of sample. The model takes into account the effect of sources / sinks of non-equilibrium vacancies on void formation in different parts of diffusion zone. The numerical modeling has shown that the better work effectivity of vacancies sources/sinks, the more rapid growth of voids. At the same time the cube of void radius has linear dependence on time. Maximal size of void also depends on efficiency of vacancies sources / sinks.
Tu K. N. (2003). Recent advances on electromigration in very-large-scale-integration of interconnects. Journal of Applied Physics. 94, 5451-5473.
Choi W. J., Yeh E. C. C., Tu K. N. (2003). Mean-time-to-failure study of flip chip solder joints on Cu/Ni(V)/Al thin-film under bump metallization. Journal of Applied Physics. 90, 56655671.
Gan H., Tu K. N. (2005). Polarity effect of electromigration on kinetics of intermetallic compound formation in Pb-free solder V-groove samples. Journal of Applied Physics. 97, 063514.
Huang M., Zhou S., and Chen L. (2014). Stress relaxation and failure of Cu-3.0Ag-0.5Cu flipchip solder bumps undergoing electromigration. J.Mater.Res. 29(21), 2556-2564.
An R. (2015). Electromigration-induced intermetallic growth and voids formation in symmetrical Cu/Sn/Cu and Cu/Intermetallic compounds (IMCs)/Cu joints. J Mater Sci:Mater.Electron. 26, 2674 – 2681.
Hurov K. P., Husak A. M. (1985). Description of mutual diffusion in alloys with arbitrary power of vacancy sinks. Fyzyka metallov y metallovedenye (Physics of metals and Metallography). 59(6), 1062-1066.
Husak A. M. (1992). Linear phase growth and non-equilibrium vacancies. Metallofizika i Noveishie Tekhnologii. (Physics of Metals and Advanced Technologies). 14(9), 3-6.
Kornienko S. V. (2010) Vplyv dzherel ta stokiv vakansii u materynskii fazi na kinetyku reaktsiinoi dyfuzii u binarnii systemi. Visnyk Cherkaskoho universytetu, seriia fizyko – matematychni nauky. (Bulletin of Cherkasy University), 185, 39-47.
Kornienko S. V. (2013). Model of reaction diffusion in a binary system, taking into account the effect of sources and sinks of vacancies in the mother phases. Metallofizika i Noveishie Tekhnologii. (Physics of Metals and Advanced Technologies) 35(12), 1685-1696.
Kornyenko S. V., Husak A. M. (2015). Influence of sources and sinks of vacancies on the kinetics of reaction diffusion in a binary system. Metallofizika i Noveishie Tekhnologii. (Physics of Metals and Advanced Technologies), 37(10), 1001-1016.
Storozhuk N. V., Husak A. M. (2014). Competition of Kirkendall and Fraenkel effects during mutual diffusion. Metallofizika i Noveishie Tekhnologii. 36(3), 367-374.
Zaporozhets T. V., Storozhuk N. V., Gusak A. M. (2016). Competition of Voiding and Kirkendall Shift during Compound Growth in Reactive Diffusion–Alternative Models. Metallofizika i Noveishie Tekhnologii. (Physics of Metals and Advanced Technologies) 38(10), 1279-1292.