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Combining multi-phase field simulation with neural network analysis to unravel thermomigration accelerated growth behavior of Cu6Sn5 IMC at cold side Cu–Sn interface

Kunwar, Anil ; Hektor, Johan LU ; Nomoto, Sukeharu ; Coutinho, Yuri Amorim and Moelans, Nele (2020) In International Journal of Mechanical Sciences 184.
Abstract

In Pb-free solder alloys used in solder balls of diameter of 50 µm or smaller, larger proportion of Cu6Sn5 intermetallics formation is a major reliability concern, and this is aggravated in presence of external thermal gradient. A complete understanding of the mechanism for intermetallics compound (IMC) growth under thermomigration is essential for devising solder materials resistant to degradation under thermal gradient. This work integrates neural network analysis with multi-phase field method to quantify the mechanism of thermomigration at the cold side of a solder-substrate system. At hot side temperature of 523.15 K, 1D multi-phase field model is built for a combined driving force of bulk diffusion and... (More)

In Pb-free solder alloys used in solder balls of diameter of 50 µm or smaller, larger proportion of Cu6Sn5 intermetallics formation is a major reliability concern, and this is aggravated in presence of external thermal gradient. A complete understanding of the mechanism for intermetallics compound (IMC) growth under thermomigration is essential for devising solder materials resistant to degradation under thermal gradient. This work integrates neural network analysis with multi-phase field method to quantify the mechanism of thermomigration at the cold side of a solder-substrate system. At hot side temperature of 523.15 K, 1D multi-phase field model is built for a combined driving force of bulk diffusion and thermomigration, and is solved using finite element method (FEM). The free energy density function for the thermomigration driving force is introduced, and coupled with the functions for bulk and interfacial free energy density of each phase. Data of heats of transport, temperature difference and growth rate constant of IMC are obtained from multiple FEM simulations, and the FEM-generated dataset is employed in the neural network. The machine learning predicted growth rate constant is tallied with experimental value, and heat of transport of Cu in IMC phase (QCuimc) is determined from the inverse method. The obtained value of optimized QCuimc is +35.10 kJ/mol. 2D IMC grain growth simulations are performed with hot-side at 523.15 K and the cold side lowered to 523.0817 K and 522.0 K respectively, thereby revealing that the accelerated grain growth for larger temperature difference is noticed within the first 20 s of the simulations.

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organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Finite element method, Heat of transport, Intermetallic compound, Multi-phase field method, Neural network, Thermomigration
in
International Journal of Mechanical Sciences
volume
184
article number
105843
publisher
Elsevier
external identifiers
  • scopus:85086382965
ISSN
0020-7403
DOI
10.1016/j.ijmecsci.2020.105843
language
English
LU publication?
yes
id
c28405df-4851-4a91-be91-eedb8ee4854f
date added to LUP
2020-06-29 10:36:09
date last changed
2022-07-06 15:22:50
@article{c28405df-4851-4a91-be91-eedb8ee4854f,
  abstract     = {{<p>In Pb-free solder alloys used in solder balls of diameter of 50 µm or smaller, larger proportion of Cu<sub>6</sub>Sn<sub>5</sub> intermetallics formation is a major reliability concern, and this is aggravated in presence of external thermal gradient. A complete understanding of the mechanism for intermetallics compound (IMC) growth under thermomigration is essential for devising solder materials resistant to degradation under thermal gradient. This work integrates neural network analysis with multi-phase field method to quantify the mechanism of thermomigration at the cold side of a solder-substrate system. At hot side temperature of 523.15 K, 1D multi-phase field model is built for a combined driving force of bulk diffusion and thermomigration, and is solved using finite element method (FEM). The free energy density function for the thermomigration driving force is introduced, and coupled with the functions for bulk and interfacial free energy density of each phase. Data of heats of transport, temperature difference and growth rate constant of IMC are obtained from multiple FEM simulations, and the FEM-generated dataset is employed in the neural network. The machine learning predicted growth rate constant is tallied with experimental value, and heat of transport of Cu in IMC phase (Q<sub>Cu</sub><sup>imc</sup>) is determined from the inverse method. The obtained value of optimized Q<sub>Cu</sub><sup>imc</sup> is +35.10 kJ/mol. 2D IMC grain growth simulations are performed with hot-side at 523.15 K and the cold side lowered to 523.0817 K and 522.0 K respectively, thereby revealing that the accelerated grain growth for larger temperature difference is noticed within the first 20 s of the simulations.</p>}},
  author       = {{Kunwar, Anil and Hektor, Johan and Nomoto, Sukeharu and Coutinho, Yuri Amorim and Moelans, Nele}},
  issn         = {{0020-7403}},
  keywords     = {{Finite element method; Heat of transport; Intermetallic compound; Multi-phase field method; Neural network; Thermomigration}},
  language     = {{eng}},
  publisher    = {{Elsevier}},
  series       = {{International Journal of Mechanical Sciences}},
  title        = {{Combining multi-phase field simulation with neural network analysis to unravel thermomigration accelerated growth behavior of Cu<sub>6</sub>Sn<sub>5</sub> IMC at cold side Cu–Sn interface}},
  url          = {{http://dx.doi.org/10.1016/j.ijmecsci.2020.105843}},
  doi          = {{10.1016/j.ijmecsci.2020.105843}},
  volume       = {{184}},
  year         = {{2020}},
}