Research Papers

Electromigration Simulation for Metal Lines

[+] Author and Article Information
JianPing Jing1

State Key Laboratory of Mechanical System and Vibration, Shanghai Jiaotong University, Shanghai 200240, P. R. Chinajianpj@gmail.com, jianpj@sjtu.edu.cn

Lihua Liang

 Zhejiang University of Technology, Hangzhou 310014, China

Guang Meng

State Key Laboratory of Mechanical System and Vibration, Shanghai Jiaotong University, Shanghai 200240, P. R. China


Correspondent author.

J. Electron. Packag 132(1), 011002 (Mar 04, 2010) (7 pages) doi:10.1115/1.4000716 History: Received August 22, 2008; Revised September 27, 2009; Published March 04, 2010; Online March 04, 2010

As the electronics industry continues to push for high performance and miniaturization, the demand for higher current densities, which may cause electromigration failures in an IC, interconnects. Electromigration is a phenomenon that metallic atoms constructing the line are transported by electron wind. The damage induced by electromigration appears as the formation of voids and hillocks. A numerical simulation method for electromigration void incubation, and afterwards, void propagation, based on commercial software ANSYS Multiphysics and FORTRAN code, is presented in this paper. The electronic migration formulation considering the effects of the electron wind force, stress gradients, temperature gradients, and the atomic concentration gradient has been developed for the electromigration failure mechanisms. Due to introducing the atomic concentration gradient driving force in atomic flux formulations, the conventional atomic flux divergence method is no longer valid in electromigration (EM) simulation. Therefore, the corresponding EM atomic concentration redistribution algorithm is proposed using FORTRAN code. Finally, the comparison of voids generation through the numerical example of a standard wafer electromigration accelerated test (SWEAT) structure with the measurement result is discussed.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

Normalized atomic concentration as normalized time τ=a2Dt for various conductor lengths with blocking boundary condition

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Figure 2

Computational procedure for numerical simulation of the failure process: (a) procedure for the simulation of the incubation period and (b) procedure for the simulation of the void propagation period

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Figure 3

SWEAT structure and its mesh

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Figure 4

Temperature and current density distributions under 14.8×10+10 A/m2 current density at initial time: (a) temperature distribution and (b) current density distribution

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Figure 5

Hydrostatics stress distribution under 14.8×10+10 A/m2 current density at room temperature and initial time of stressing current load: (a) at room temperature and (b) at initial time of stressing current load

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Figure 6

Atomic density distribution of the SWEAT structure at different time: (a) at time=1×105 s, (b) at time=5×105 s, and (c) at time=1×106 s

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Figure 7

Void observed in the experiment (9): (a) 1/2 in element edge length, (b) 1/4 in element edge length, (c) 1/8 in element edge length, and (d) 1/12 in element edge length

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Figure 8

Mesh densities with 1/2, 1/4, 1/8, and 1/12 of element edge length along the edge length of cross section

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Figure 9

Comparison of EM TTF with different mesh density under 20×10+10 A/m2 current density

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Figure 10

Comparison of the simulation results for TTF and the previous experimental test results obtained in Ref. 9



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