On void nucleation and growth in metal interconnect lines under electromigration conditions
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DEDICATION I T is an honor for us to contribute to a volume of work dedicated to the memory of Professor G. Marshall Pound. It was my privilege to know Marsh personally and to work with him at Stanford for some 15 years. Although I never took a course from him, I always considered myself to be one of his students. Indeed, what little I know about thermodynamics and kinetics I learned from him. His enthusiasm for understanding the fundamentals of kinetic processes was absolutely contagious. Those of us who worked and studied with him are still guided by his lessons. There is not sufficient space here to tell even a small fraction of the "Marsh Pound ~ stories that are known to his friends and colleagues. I will recall just one. I remember going to Marsh sometime in the late 1960's being very confused about the nature of a mole and the chemical entities to which a mole might refer. In the course of straightening me out on this, Marsh told me that we could have a mole of chairs, if we wished! I found that to be a most vivid image and one that I will never forget. It freed me from thinking about statistical mechanics in terms of "chemical" things only. Marsh must have helped thousands of students and colleagues in this way. To my mind, it is one of the main reasons we are dedicating this work to his memory. WDN.
W.D. NIX, Lee Otterson Professor of Engineering, is with the Department of Materials Science and Engineering, Stanford University, Stanford, CA 94305. E. ARZT, Professor, is with the Max-PlanckInstitut fiir Metallforschung, Institut fiir Werkstoffwissenshaft, D-7000 Stuttgart, Federal Republic of Germany. This paper is based on a presentation made in the "G. Marshall Pound Memorial Symposium on the Kinetics of Phase Transformations" presented as part of the 1990 fall meeting of TMS, October 8-12, 1990, in Detroit, MI, under the auspices of the ASM/MSD Phase Transformations Committee. METALLURGICAL TRANSACTIONS A
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INTRODUCTION
Current densities of the order of 10 ~~ A / m 2 or higher can be found in the metal interconnection lines used in integrated circuits, mainly because these interconnects have such small cross-sectional areas. The high current densities produce an "electron wind" that causes the migration of matter to occur, primarily through the drift of vacancies and voids in the line. tll This form of mass transport can lead to void growth and metal cracking at points of atomic flux divergence and to hillock formation and passivation cracking where the atomic flux converges. ~2] Thus, understanding electromigration failures in interconnection lines involves not only understanding the effect of the "electron wind" on the motion of defects in the line but also the various causes of flux divergence. Here we focus our attention primarily on those flux divergences that are caused by microstructural inhomogeneities. Other sources of flux divergence, such as geometrical irregularities or temperature gradients in the line, will not be considered here. In the present article, we follow the approach of Blech
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