The Effect of Initial Void Configuration on the Morphological Evolution Under the Action of Normalized Electron Wind For
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THE EFFECT OF INITIAL VOID CONFIGURATION ON THE MORPHOLOGICAL EVOLUTION UNDER THE ACTION OF NORMALIZED ELECTRON WIND FORCES
Ersin Emre Orena) and Tarik Omer Ogurtanib) Department of Metallurgical and Materials Engineering Middle East Technical University, 06531, Ankara, Turkey ABSTRACT In these studies a comprehensive picture of void shape evolution dynamics and its strong dependence on the initial configuration has been thoroughly investigated by utilizing hypocycloid algebra to generate four different shapes of main interest. Our mathematical model on the isotropic diffusion and mass accumulation on void surfaces, under the action of applied electrostatic potential and capillary effects, follows a novel irreversible but discrete thermodynamic formalism of interphases and surfaces. As a result during the intragranual motion, in addition to the crescent–like slit formation, very rich and also unusual void morphological variations such as fragmentations into the daughter voids or inner island generation have been observed under the severe (normalized) electron wind intensities or very long exposure times. In these numerical experiments, the Euler’s method of finite differences with an automatic time step self-adjustment has been utilized in combination with a rather powerful and fast indirect boundary element method (IBEM) for the solution of the Laplace equation. INTRODUCTION The electromigration induced failure of metallic interconnects is a complicated process, which involves flux divergence, vacancy and/or atom accumulation with or without compositional variations, void nucleation, and void growth and shape changes. Electromigration-induced failure processes become more complicated due to the existence of grain boundary diffusion in addition to the surface and bulk diffusion mechanisms.1 Generally in the literature explicitly or implicitly, it has been postulated that all other transport phenomenon such as bulk diffusion is negligibly slow in regards to surface diffusion, but it is rather fast in comparison with the interface reaction taking place at the advancing void front which may be labeled as the growth process. This last requirement, that permits one to use steady state solution of the bulk diffusion boundary value problem in the calculation of atomic fluxes at the reaction front, is a fundamental assumption in the theory of phase transformation advocated by Wagner2 and others.3 This approach can only be justified if one has a growth process where the interfacial reaction is the rate-controlling step. Another extreme case is the one where the interfacial reaction is fast enough to establish the complete physico-chemical equilibrium just at the hypothetical boundary separating the growing phase (void, etc) from the bulk region. In our formulation of the problem through the internal entropy production term, we have not made any assumption in regards to the kinetics of the growth process other than the fundamental postulates of the linear irreversible thermodynamics.4 In the evaluation of the capillary effec
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