Computer Simulations on the Grain Boundary Grooving and Cathode Edge Displacement in Bamboo-like Metalic Interconnects
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0914-F09-22
Computer Simulations on the Grain Boundary Grooving and Cathode Edge Displacement in Bamboo-like Metalic Interconnects Tarik Omer Ogurtani, and Oncu Akyildiz Metallurgical and Materials Engineering, Middle East Technical University, Ankara, Turkey
ABSTRACT The process of grain boundary (GB) grooving and cathode edge displacement invoked by the surface drift-diffusion along the sidewalls in sandwich type thin film bamboo lines are simulated by introducing a new mathematical model. In the absence of the electric field, the computer studies on the triple junction kinetics show that it obeys the first order reaction kinetics at early transient stage, which is followed by the familiar time law as t 1/ 4 , at the steady state regime. The applied electric field (EF) in constant current experiments modifies this time law drastically above the well-defined electron wind intensity (EWI) threshold, and puts an upper limit for the groove depth, which decreases monotonically with EWI. Below the threshold level, the capillary regime predominates, and EF has little effect on the general kinetics of GB grooving, other then the linear increase in total elapsed time with EWI. INTRODUCTION In the early 1950s, a solid quantitative framework emerged in the field of capillary-driven morphological evolution of surfaces and interfaces of condensed matter, by the classical works of Herring [1], and Mullins [2]. Their efforts relied strictly on the equilibrium thermodynamics, including Gibbs’ description of interfaces and surfaces. The earliest analytical study was Mullins’ [2] treatment of the grooving of a GB. Mullins ignored grain boundary diffusion and considered the triple junction (TJ) to have the equilibrium capillarity configuration satisfying the Young relationship. Klinger et al. [3] have extended Mullins’s theory by taking into account the effect of electromigration on GB sliding. Averbuch et al. [4] utilized highly sophisticated numerical procedures in their studies, but they still assumed that there is an equilibrium configuration at the triple junction. By relying only on the fundamental postulates of linear irreversible thermodynamics for the bulk phases, as advocated by Prigogine [5], Ogurtani [6] has obtained a compact and rigorous analytical theory of a network of interfaces that are interconnected by triple junctions and embedded in bulk phases by utilizing the more realistic monolayer model of Verschaffelt [7] and Guggenheim [8] for the description of interfaces and surfaces rather then the more abstract Gibbs model. Ogurtani and Oren [9], Ogurtani and Akyildiz [10] have performed numerous computer simulations of critical-asymmetric initial void shape with respect to the direction of electron wind with and without the surface diffusion anisotropy. These numerical experiments show that the twofold symmetry in the anisotropic diffusion coefficient becomes a main factor in the development of a straight advancing slit, which accelerates the early open circuit failure.
MATHEMATICAL MODELING The present irrevers
