А. R. Honda, V. V. Morozovych, Ya. D. Korol, Yu. О. Lyashenko


The Cu-Sn phase formation process is influenced by the structural structure of the copper layer and its roughness. The structural structure of the copper layer depends primarily on the technology of pre-treatment of copper plates.

The purpose of this work is to study the fractal dimension of the rough surfaces of copper layers, which are obtained as a result of the action of stationary and non-stationary regimes of electrodeposition of copper on copper plates. Copper coatings obtained by different regimes of electrodeposition were examined using a scanning electron microscope. In the course of the work, the fractal structure of electrodeposited copper layers after the solid-state reaction of copper with tin was analysed. The electrodeposited copper samples were  immersed then briefly in molten tin and subjected to long-term solid-state annealing. As a result, the features of the fractal structure of the interface of copper layers before and after the solid-state reaction, depending on the regime of copper electrodeposition, were identified.

The influence of the structure of copper layers obtained under different regimes of electrodeposition - stationary, reverse impulse and stochastic on the result of solid-phase reactions with tin was compared. Stochastic modes of electrodeposition were obtained on the basis of the Chua random oscillation generator model with two stationary points. The stationary states were selected from the analysis of the polarization curve according to the conditions of the electrodeposition. As a result, it was shown that copper electrodeposition onto copper plates in stochastic modes leads to the formation of rough surfaces with fractal dimension. It is shown that the fractal dimension of the copper interface before and after the solid-state reaction depends on the regime of electrodeposition and characterizes the features of the roughness of the obtained interfaces. It is established that under stochastic regimes of electrodeposition, the obtained fractality of copper interface is quite significant and changes slightly after solid-state reaction with tin, unlike the use of stationary mode of electrodeposition with high overpotential.


copper/tin; electrodeposition; solid-state reaction; fractal dimension; Chua generator model; roughness of the interface


Tu K. N. (2010). Electronic thin-film reliability. Cambridge University Press. Retrieved from

Tu K. N. (2007). Solder joint technology. New York: Springer. Retrieved from

Gusak A. M., Tu K. N. (2002). Kinetic theory of flux-driven ripening. Physical Review B, 66(11), 115403. Retrieved from

Tu K. N., Gusak A. M., Li M. (2003). Physics and materials challenges for lead-free solders. Journal of applied Physics, 93(3), 1335-1353. Retrieved from

Suh J. O., Tu K. N., Lutsenko G. V., Gusak A. M. (2008). Size distribution and morphology of Cu6Sn5 scallops in wetting reaction between molten solder and copper. Acta Materialia, 56(5), 1075-1083. Retrieved from

Liashenko O. Y., Hodaj F. (2015). Differences in the interfacial reaction between Cu substrate and metastable supercooled liquid Sn–Cu solder or solid Sn–Cu solder at 222° C: Experimental results versus theoretical model calculations. Acta Materialia, 99, 106-118. Retrieved from

Liashenko O. Y., Lay S., Hodaj F. (2016). On the initial stages of phase formation at the solid Cu/liquid Sn-based solder interface. Acta Materialia, 117, 216-227. Retrieved from

Liashenko O. Y., Gusak A. M., Hodaj F. (2015). Spectrum of heterogeneous nucleation modes in crystallization of Sn-0.7 wt% Cu solder: experimental results versus theoretical model calculations. Journal of Materials Science: Materials in Electronics, 26(11), 8464-8477. Retrieved from

Gusak A. M., Zaporozhets T. V., Janczak-Rusch, J. (2017). Kinetic pinning versus capillary pinning of voids at the moving interface during reactive diffusion. Philosophical Magazine Letters, 97(1), 1-10. Retrieved from

Morozovych V. V., Honda A. R., Lyashenko Yu. O., Korol Ya. D., Liashenko O. Yu., Cserháti С., and Gusak A. M. (2018) Influence of Copper Pretreatment on the Phase and Pore Formations in the Solid Phase Reactions of Copper with Tin. Metallofiz. Noveishie Tekhnol., 40(12): 1649-1673. Retrieved from

Nіkolenko Yu. V., Diduk V. A., Korol Ya. K., Lyashenko Yi. O. (2016). Development and application of the hardware and software complex in the board by the process of electrolytic deposition of copper in the mode of stochastic oscillations. Visnyk Cherkaskoho Universytetu. Seriia «Fizyko-Matematychni Nauky» (Bulletin of Cherkasy University. Series "Physics and Mathematics"), 1, 27-29. Retrieved from

Tiutenko, V. M., Morozovych, V. V., Diduk, V. A., Kolinko, S., & Lyashenko, Y. O. (2018). The influence of SMAT processing on microstructure of copper films electroplated in steady-state, reversed impulse and stochastic regimes. Visnyk Cherkaskoho Universytetu. Seriia «Fizyko-Matematychni Nauky» (Bulletin of Cherkasy University. Series "Physics and Mathematics"), 1, 63-78. Retrieved from

Belenkyi M. A., Ivanov A. F. (1985). Electrodeposition of metal coatings: Handbook. Moscow: Metallurgy (in Rus).

Popov K. I. Djokic S. S., Nikolic N. D., Jovic V. D. (2016). Morphology of electrochemically and chemically deposited metals. Switzerland: Springer. Retrieved from

Hrynchenko V. T., Matsypura V. T., Snarskyy A. A. (2007) Introduction to nonlinear dynamics. Chaos and Fractals. Moscow: LKI (in Rus) Retrieved from ISBN 978-5-9710-6410-7

Chua L. (1980). Dynamic nonlinear networks: State-of-the-art. IEEE Transactions on Circuits and Systems, 27(11), 1059-1087. Retrieved from

Matsumoto T. (1984). A chaotic attractor from Chua's circuit. IEEE Transactions on Circuits and Systems, 31(12), 1055-1058. Retrieved from 10.1109/TCS.1984.1085459

Nayak S. R., Mishra J., Jena P. M. (2018). Fractal dimension of grayscale images. In Progress in Computing, Analytics and Networking. Springer, Singapore. 710, 225-234. Retrieved from

Sarkar N., Chaudhuri B. B. (1994). An efficient differential box-counting approach to compute fractal dimension of image. IEEE Transactions on systems, man, and cybernetics, 24(1), 115-120. Retrieved from

Chen W. S., Yuan S. Y., Hsieh C. M. (2003). Two algorithms to estimate fractal dimension of gray-level images. Optical Engineering, 42(8), 2452-2465. Retrieved from

Full Text: PDF (Українська)
2013 16
2014 16
2015 16
2016 1
2017 1
2018 1




Journal Content