An analytical model of thermal mechanical stress induced by through silicon via

doi:10.1088/1674-1056/24/5/056601

中国物理B ›› 2015, Vol. 24 ›› Issue (5): 56601-056601.doi: 10.1088/1674-1056/24/5/056601

• CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES • 上一篇下一篇

An analytical model of thermal mechanical stress induced by through silicon via

董刚, 石涛, 赵颖博, 杨银堂

Microelectronics Institute, Xidian University, Xi'an 710071, China

收稿日期:2014-09-04 修回日期:2015-01-13 出版日期:2015-05-05 发布日期:2015-05-05
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 61334003) and the Kunshan Innovation Institute of Xidian University.

An analytical model of thermal mechanical stress induced by through silicon via

Dong Gang (董刚), Shi Tao (石涛), Zhao Ying-Bo (赵颖博), Yang Yin-Tang (杨银堂)

Microelectronics Institute, Xidian University, Xi'an 710071, China

Received:2014-09-04 Revised:2015-01-13 Online:2015-05-05 Published:2015-05-05
Contact: Dong Gang E-mail:gdong@mail.xidian.edu.cn
About author:66.30.-h; 62.20.-x; 72.15.-v; 84.30.-r
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 61334003) and the Kunshan Innovation Institute of Xidian University.

摘要/Abstract

摘要： We present an accurate through silicon via (TSV) thermal mechanical stress analytical model which is verified by using finite element method (FEM). The results show only a very small error. By using the proposed analytical model, we also study the impacts of the TSV radius size, the thickness, the material of Cu diffusion barrier, and liner on the stress. It is found that the liner can absorb the stress effectively induced by coefficient of thermal expansion mismatch. The stress decreases with the increase of liner thickness. Benzocyclobutene (BCB) as a liner material is better than SiO₂. However, the Cu diffusion barrier has little effect on the stress. The stress with a smaller TSV has a smaller value. Based on the analytical model, we explore and validate the linear superposition principle of stress tensors and demonstrate the accuracy of this method against detailed FEM simulations. The analytic solutions of stress of two TSVs and three TSVs have high precision against the finite element result.

关键词: through silicon via, finite element method (FEM), thermal mechanical stress

Abstract: We present an accurate through silicon via (TSV) thermal mechanical stress analytical model which is verified by using finite element method (FEM). The results show only a very small error. By using the proposed analytical model, we also study the impacts of the TSV radius size, the thickness, the material of Cu diffusion barrier, and liner on the stress. It is found that the liner can absorb the stress effectively induced by coefficient of thermal expansion mismatch. The stress decreases with the increase of liner thickness. Benzocyclobutene (BCB) as a liner material is better than SiO₂. However, the Cu diffusion barrier has little effect on the stress. The stress with a smaller TSV has a smaller value. Based on the analytical model, we explore and validate the linear superposition principle of stress tensors and demonstrate the accuracy of this method against detailed FEM simulations. The analytic solutions of stress of two TSVs and three TSVs have high precision against the finite element result.

Key words: through silicon via, finite element method (FEM), thermal mechanical stress

中图分类号: (Diffusion in solids)

66.30.-h

62.20.-x (Mechanical properties of solids) 72.15.-v (Electronic conduction in metals and alloys) 84.30.-r (Electronic circuits)

董刚, 石涛, 赵颖博, 杨银堂. An analytical model of thermal mechanical stress induced by through silicon via[J]. 中国物理B, 2015, 24(5): 56601-056601.

Dong Gang (董刚), Shi Tao (石涛), Zhao Ying-Bo (赵颖博), Yang Yin-Tang (杨银堂). An analytical model of thermal mechanical stress induced by through silicon via[J]. Chin. Phys. B, 2015, 24(5): 56601-056601.

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An analytical model of thermal mechanical stress induced by through silicon via

An analytical model of thermal mechanical stress induced by through silicon via

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