Modeling of the coelescence of micro-voids under the influence of elastic stresses and electromigration

Peng Zhou; Jie Wang

doi:10.1109/ICEPT.2014.6922825

Modeling of the coelescence of micro-voids under the influence of elastic stresses and electromigration

Peng Zhou^*
, Jie Wang

^*Corresponding author for this work

School of Astronautics

Harbin Institute of Technology

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

Void growth and coalescence usually cause reliability concerns to solder joints in integrated circuits. In this paper, a diffuse interface model is developed to simulate the coalescence of micro-voids under the influence of elastic stresses and electromigration. A variable c stands for the composition of vacancies, with c=1.0 indicating the void phase and c=1.0×10⁴ indicating the bulk phase. A double well potential is used to describe the chemical free energy density of the thermodynamic system. In this model, a modified Cahn-Hilliard type equation was solved with a nonlinear multi-grid method to determine the composition field c; the Cauchy-Navier equations for the elastic displacements u and v were solved with a linear multi-grid method to determine the elastic energy density; a steady state equation of electric potential was solved to determine the effective driving force for electromigration. Simulation results show that the applied stresses have significant effects on the coalescence of micro-voids. For the given initial configuration, the tensile stresses accelerate the coalescence of micro-voids; on contrast, the shear and the combined stresses interrupt the coalescence of micro-voids and steady states are eventually achieved under the influence of these stresses. Under the influence of tensile stresses, a simulated 'failure' which leads to an opening is also shown.

Original language	English
Title of host publication	2014 15th International Conference on Electronic Packaging Technology, ICEPT 2014
Editors	Keyun Bi, Zhong Tian, Ziqiang Xu
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1047-1051
Number of pages	5
ISBN (Electronic)	9781479947072
DOIs	https://doi.org/10.1109/ICEPT.2014.6922825
State	Published - 13 Oct 2014
Event	2014 15th International Conference on Electronic Packaging Technology, ICEPT 2014 - Chengdu, China Duration: 12 Aug 2014 → 15 Aug 2014

Publication series

Name	Proceedings of the Electronic Packaging Technology Conference, EPTC

Conference

Conference	2014 15th International Conference on Electronic Packaging Technology, ICEPT 2014
Country/Territory	China
City	Chengdu
Period	12/08/14 → 15/08/14

Keywords

Diffuse interface model
Elastic stresses
Void coaelscence

Access to Document

10.1109/ICEPT.2014.6922825

Cite this

Zhou, P., & Wang, J. (2014). Modeling of the coelescence of micro-voids under the influence of elastic stresses and electromigration. In K. Bi, Z. Tian, & Z. Xu (Eds.), 2014 15th International Conference on Electronic Packaging Technology, ICEPT 2014 (pp. 1047-1051). Article 6922825 (Proceedings of the Electronic Packaging Technology Conference, EPTC). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICEPT.2014.6922825

Zhou, Peng ; Wang, Jie. / Modeling of the coelescence of micro-voids under the influence of elastic stresses and electromigration. 2014 15th International Conference on Electronic Packaging Technology, ICEPT 2014. editor / Keyun Bi ; Zhong Tian ; Ziqiang Xu. Institute of Electrical and Electronics Engineers Inc., 2014. pp. 1047-1051 (Proceedings of the Electronic Packaging Technology Conference, EPTC).

@inproceedings{14f7ecf1403b4cb88970bb411788a108,

title = "Modeling of the coelescence of micro-voids under the influence of elastic stresses and electromigration",

abstract = "Void growth and coalescence usually cause reliability concerns to solder joints in integrated circuits. In this paper, a diffuse interface model is developed to simulate the coalescence of micro-voids under the influence of elastic stresses and electromigration. A variable c stands for the composition of vacancies, with c=1.0 indicating the void phase and c=1.0{\texttimes}104 indicating the bulk phase. A double well potential is used to describe the chemical free energy density of the thermodynamic system. In this model, a modified Cahn-Hilliard type equation was solved with a nonlinear multi-grid method to determine the composition field c; the Cauchy-Navier equations for the elastic displacements u and v were solved with a linear multi-grid method to determine the elastic energy density; a steady state equation of electric potential was solved to determine the effective driving force for electromigration. Simulation results show that the applied stresses have significant effects on the coalescence of micro-voids. For the given initial configuration, the tensile stresses accelerate the coalescence of micro-voids; on contrast, the shear and the combined stresses interrupt the coalescence of micro-voids and steady states are eventually achieved under the influence of these stresses. Under the influence of tensile stresses, a simulated 'failure' which leads to an opening is also shown.",

keywords = "Diffuse interface model, Elastic stresses, Void coaelscence",

author = "Peng Zhou and Jie Wang",

note = "Publisher Copyright: {\textcopyright} 2014 IEEE.; 2014 15th International Conference on Electronic Packaging Technology, ICEPT 2014 ; Conference date: 12-08-2014 Through 15-08-2014",

year = "2014",

month = oct,

day = "13",

doi = "10.1109/ICEPT.2014.6922825",

language = "英语",

series = "Proceedings of the Electronic Packaging Technology Conference, EPTC",

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pages = "1047--1051",

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booktitle = "2014 15th International Conference on Electronic Packaging Technology, ICEPT 2014",

address = "美国",

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Zhou, P & Wang, J 2014, Modeling of the coelescence of micro-voids under the influence of elastic stresses and electromigration. in K Bi, Z Tian & Z Xu (eds), 2014 15th International Conference on Electronic Packaging Technology, ICEPT 2014., 6922825, Proceedings of the Electronic Packaging Technology Conference, EPTC, Institute of Electrical and Electronics Engineers Inc., pp. 1047-1051, 2014 15th International Conference on Electronic Packaging Technology, ICEPT 2014, Chengdu, China, 12/08/14. https://doi.org/10.1109/ICEPT.2014.6922825

Modeling of the coelescence of micro-voids under the influence of elastic stresses and electromigration. / Zhou, Peng; Wang, Jie.
2014 15th International Conference on Electronic Packaging Technology, ICEPT 2014. ed. / Keyun Bi; Zhong Tian; Ziqiang Xu. Institute of Electrical and Electronics Engineers Inc., 2014. p. 1047-1051 6922825 (Proceedings of the Electronic Packaging Technology Conference, EPTC).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Modeling of the coelescence of micro-voids under the influence of elastic stresses and electromigration

AU - Zhou, Peng

AU - Wang, Jie

PY - 2014/10/13

Y1 - 2014/10/13

N2 - Void growth and coalescence usually cause reliability concerns to solder joints in integrated circuits. In this paper, a diffuse interface model is developed to simulate the coalescence of micro-voids under the influence of elastic stresses and electromigration. A variable c stands for the composition of vacancies, with c=1.0 indicating the void phase and c=1.0×104 indicating the bulk phase. A double well potential is used to describe the chemical free energy density of the thermodynamic system. In this model, a modified Cahn-Hilliard type equation was solved with a nonlinear multi-grid method to determine the composition field c; the Cauchy-Navier equations for the elastic displacements u and v were solved with a linear multi-grid method to determine the elastic energy density; a steady state equation of electric potential was solved to determine the effective driving force for electromigration. Simulation results show that the applied stresses have significant effects on the coalescence of micro-voids. For the given initial configuration, the tensile stresses accelerate the coalescence of micro-voids; on contrast, the shear and the combined stresses interrupt the coalescence of micro-voids and steady states are eventually achieved under the influence of these stresses. Under the influence of tensile stresses, a simulated 'failure' which leads to an opening is also shown.

AB - Void growth and coalescence usually cause reliability concerns to solder joints in integrated circuits. In this paper, a diffuse interface model is developed to simulate the coalescence of micro-voids under the influence of elastic stresses and electromigration. A variable c stands for the composition of vacancies, with c=1.0 indicating the void phase and c=1.0×104 indicating the bulk phase. A double well potential is used to describe the chemical free energy density of the thermodynamic system. In this model, a modified Cahn-Hilliard type equation was solved with a nonlinear multi-grid method to determine the composition field c; the Cauchy-Navier equations for the elastic displacements u and v were solved with a linear multi-grid method to determine the elastic energy density; a steady state equation of electric potential was solved to determine the effective driving force for electromigration. Simulation results show that the applied stresses have significant effects on the coalescence of micro-voids. For the given initial configuration, the tensile stresses accelerate the coalescence of micro-voids; on contrast, the shear and the combined stresses interrupt the coalescence of micro-voids and steady states are eventually achieved under the influence of these stresses. Under the influence of tensile stresses, a simulated 'failure' which leads to an opening is also shown.

KW - Diffuse interface model

KW - Elastic stresses

KW - Void coaelscence

UR - https://www.scopus.com/pages/publications/84908093312

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DO - 10.1109/ICEPT.2014.6922825

M3 - 会议稿件

AN - SCOPUS:84908093312

T3 - Proceedings of the Electronic Packaging Technology Conference, EPTC

SP - 1047

EP - 1051

BT - 2014 15th International Conference on Electronic Packaging Technology, ICEPT 2014

A2 - Bi, Keyun

A2 - Tian, Zhong

A2 - Xu, Ziqiang

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2014 15th International Conference on Electronic Packaging Technology, ICEPT 2014

Y2 - 12 August 2014 through 15 August 2014

ER -

Zhou P, Wang J. Modeling of the coelescence of micro-voids under the influence of elastic stresses and electromigration. In Bi K, Tian Z, Xu Z, editors, 2014 15th International Conference on Electronic Packaging Technology, ICEPT 2014. Institute of Electrical and Electronics Engineers Inc. 2014. p. 1047-1051. 6922825. (Proceedings of the Electronic Packaging Technology Conference, EPTC). doi: 10.1109/ICEPT.2014.6922825

Modeling of the coelescence of micro-voids under the influence of elastic stresses and electromigration

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