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7 - Analysis of Electromigration-Induced Stress Evolution and Voiding in Cu Damascene Lines with Microstructure

Published online by Cambridge University Press:  05 May 2022

Paul S. Ho ,
Chao-Kun Hu ,
Martin Gall  and
Valeriy Sukharev
Paul S. Ho
Affiliation:
University of Texas, Austin
Chao-Kun Hu
Affiliation:
IBM T J Watson Research Center, New York
Martin Gall
Affiliation:
GlobalFoundries
Valeriy Sukharev
Affiliation:
Siemens Business
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Summary

An accurate analysis of the stress evolution in a metal line loaded with an electric current requires solution of a number of coupled partial differential equations (PDEs). The continuity equations, describing the evolution of concentrations of vacancies and plated atoms along the line, are linked with the force balance equation yielding the elastic stress evolution due to interaction of the metal line volumetric deformation with the rigid confinement. The electric current density distribution is found by solving the corresponding Laplace equation. Accounting for the polycrystalline structure of the metals used as conductors in on-chip interconnects, and proper consideration of a variety of venues for diffusion of vacancies, such as grain boundaries and interfaces with liners and capping layers, requires a comprehensive 2D or 3D analysis. Following void nucleation, which happens when the tensile stress reaches a critical value, the void shape and size are described by a combination of the Cahn–Hilliard and Allen–Kahn equations with the phase-field formalism. Detailed description of these coupled PDEs and results of their solution for a number of cases using finite element analysis (FEA) are demonstrated in this chapter. A good fit between simulation results and measurements is demonstrated throughout the chapter.

Keywords

mass transportvacancystressstrainvoidfree energygrain boundariesPDEphase-field methodsharp interface approximation
Type
Chapter
Information
Electromigration in Metals
Fundamentals to Nano-Interconnects
 , pp. 251 - 337
Publisher: Cambridge University Press
Print publication year: 2022

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