Chapter 5
Phase-Field-Crystal Model: A Tool
for Probing Atoms in TSV
Jinxin Liu, Zhiheng Huang, Paul Conway, and Yang Liu
5.1 Introduction
Following Chap. 4 on atomistically-informed reliability modeling of TSVs, the PFC
model will be derived in detail in this chapter. The basis for the PFC model, i.e.,
approximations from the classic density functional theory (CDFT) is reviewed first.
The derivation of model parameters, the governing equation for microstructural evolution, recent progress on the extension of PFC model to multi-component and multiphase material systems and coupling with external fields in PFC models are then
introduced in detail. Finally, the development and exploration of PFC models for
potential applications in TSVs. are discussed.
Electronic supplementary material The online version of this chapter
(https://doi.org/10.1007/978-981-15-7090-2_5) contains supplementary material, which is
available to authorized users.
J. Liu · Z. Huang (B)
School of Materials Science and Engineering, Sun Yat-sen University,
135 West Xingang Road, Guangzhou 510275, China
e-mail: hzh29@mail.sysu.edu.cn
P. Conway
Electrical and Manufacturing Engineering, The Wolfson School of Mechanical,
Loughborough University, Loughborough, Leicestershire LE11 3TU, UK
Y. Liu
School of Electronics and Information Technology, Sun Yat-sen University,
Xiaoguwei Island, Panyu District, Guangzhou 510006, China
© The Editor(s) (if applicable) and The Author(s), under exclusive
license to Springer Nature Singapore Pte Ltd. 2021
Y. Li and D. Goyal (eds.), 3D Microelectronic Packaging,
Springer Series in Advanced Microelectronics 64,
https://doi.org/10.1007/978-981-15-7090-2_5
107
Phase-Field-Crystal Model: A Tool
for Probing Atoms in TSV
Jinxin Liu, Zhiheng Huang, Paul Conway, and Yang Liu
5.1 Introduction
Following Chap. 4 on atomistically-informed reliability modeling of TSVs, the PFC
model will be derived in detail in this chapter. The basis for the PFC model, i.e.,
approximations from the classic density functional theory (CDFT) is reviewed first.
The derivation of model parameters, the governing equation for microstructural evolution, recent progress on the extension of PFC model to multi-component and multiphase material systems and coupling with external fields in PFC models are then
introduced in detail. Finally, the development and exploration of PFC models for
potential applications in TSVs. are discussed.
Electronic supplementary material The online version of this chapter
(https://doi.org/10.1007/978-981-15-7090-2_5) contains supplementary material, which is
available to authorized users.
J. Liu · Z. Huang (B)
School of Materials Science and Engineering, Sun Yat-sen University,
135 West Xingang Road, Guangzhou 510275, China
e-mail: hzh29@mail.sysu.edu.cn
P. Conway
Electrical and Manufacturing Engineering, The Wolfson School of Mechanical,
Loughborough University, Loughborough, Leicestershire LE11 3TU, UK
Y. Liu
School of Electronics and Information Technology, Sun Yat-sen University,
Xiaoguwei Island, Panyu District, Guangzhou 510006, China
© The Editor(s) (if applicable) and The Author(s), under exclusive
license to Springer Nature Singapore Pte Ltd. 2021
Y. Li and D. Goyal (eds.), 3D Microelectronic Packaging,
Springer Series in Advanced Microelectronics 64,
https://doi.org/10.1007/978-981-15-7090-2_5
107