#### Vol. 13, No. 3, 2018

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Effect of interconnect linewidth on the evolution of intragranular microcracks due to surface diffusion in a gradient stress field and an electric field

### Linyong Zhou, Peizhen Huang and Qiang Cheng

Vol. 13 (2018), No. 3, 365–378
##### Abstract

Based on the weak formulation for combined surface diffusion and evaporation/condensation, we derive the governing equation of the finite-element induced both by stressmigration and electromigration. The corresponding program is developed for simulating the evolution of the intragranular microcracks caused by surface diffusion in copper interconnect lines under a gradient stress field and an electric field. Unlike previously published works, this paper is focused on how the interconnect linewidth influences the microcrack evolution. Numerical analysis results show that there exists a critical value of the linewidth ${ĥ}_{c}$. When $ĥ>{ĥ}_{c}$, the microcrack will drift along the direction of the electric field by a stable form. When $ĥ\le {ĥ}_{c}$, it will split into two small microcracks and the decrease of the linewidth is beneficial for the microcrack splitting. Besides, the critical linewidth increases with the increase of the electric field and the aspect ratio, and the critical linewidth first increases and then decreases with the increase of the stress gradient. That is, the increase of the electric field and the aspect ratio is beneficial for the microcrack to split. In addition, all of the critical values of the electric field, the aspect ratio and the stress gradient decrease with the decrease of the linewidth. The microcrack has a stronger dependence on the linewidth when $ĥ<25$.

##### Keywords
linewidth, stress gradient, surface diffusion, stressmigration, electromigration, finite-element method
##### Milestones
Revised: 2 April 2018
Accepted: 11 May 2018
Published: 31 August 2018
##### Authors
 Linyong Zhou State Key Laboratory of Mechanics and Control of Mechanical Structures Nanjing University of Aeronautics and Astronautics 29 Yudao Street Nanjing, 210016 China Peizhen Huang State Key Laboratory of Mechanics and Control of Mechanical Structures Nanjing University of Aeronautics and Astronautics 29 Yudao Street Nanjing, 210016 China Qiang Cheng State Key Laboratory of Mechanics and Control of Mechanical Structures Nanjing University of Aeronautics and Astronautics 29 Yudao Street Nanjing, 210016 China