Electromigration theory

Defect configurations in dilute alloys, studied up to now in the framework of multiple scattering theory, are such that a one-to-one correspondence exists between the atoms in the alloy and the reference system, the latter system regularly being the unperturbed host system. This one-to-one correspondence does not apply to the defect studied in substitutional electromigration, in which a host atom or an impurity can move to a neighbouring vacancy. 

Today, these theories of solutions and of electrolytic solutions are used in the analysis of the solvent development of exposed resists, lithographic mask degradation due to corrosion, electromigration of chromium ions, etc. 

Equation (8) is the basic transport equation. To describe the transport in an electrolyte system, the number of transport equations is equal to the number of substances present in the given system. The first integrals of the simplified transport equations have great importance for better understanding of the theory of electromigration [12]. 

I liked the NG (Nazarov-Gurov) approach but reahzed that its predictions of the KirkendaU shift were far from experimental. So, my aim was to somehow combine Darken s scheme and the NG theory. My main idea was to introduce the hierarchy of time-space scales. In nanoscale (when the size of a physicaUy small volume is less than the free-waUc distance of a vacancy to the sink) and in the corresponding time scale, the NG theory holds. In macroscale we come back to Darken. Evidently, in nanosystems the characteristic size is often less than the typical mean free path length for vacancies. Thus, nonequiUbrium vacancies generated by interdiffusion obtain a second life in application to nanoshell formation and coUapse, initial stages of SSR, electromigration, coarsening of nanoalloys, spinodal decomposition and so on. 

Migration and coalescence of voids as weU as their interactions with grain boundaries (GBs) in the presence of the electric wind force is crucial for understanding the failure mechanism. The first fundamental theory of void migration was developed by Krivoglaz [34] for an isolated spherical void and was later modified by Ho [35] for voids in the vicinity of an external surface. At that, the theory of electron wind force [36, 37] was used to demonstrate a (l/R)-size dependence of void velocity. However, the interaction of a void with GBs during electromigration (EM) was not considered. 

J.M. VALLETON, Theorie des systemes en diffusion-electromigration-reaction. Application aux cinetiques enzymatiques, These d Etat, Universite de Rouen, (1984). 

P. Kosobucki and B. Buszewski, Isotachophoresis, in Electromigration Techniques Theory and Practice, ed. B. Buszewski, E. Dziubakiewicz and M. Szumski, Springer Series in Chemical Physics, Springer GmbH, 2013, vol. 105, p. 93. 

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