Computer simulation of grain boundary grooving by anisotropic surface drift diffusion due to capillary, electromigration and elastostatic forces

Akyıldız, Öncü
The aim of this study is to develop a theoretical basis and to perform computational experiments for understanding the grain boundary (GB) grooving in polycrystalline thin film metallic conductors (interconnects) by anisotropic surface diffusion due to capillary, electromigration and elastostatic forces. To this end, irreversible thermo–kinetics of surfaces and interfaces with triple junction singularities is elaborated, and the resulting well-posed moving boundary value problem is solved using the front–tracking method. To simulate the strain conditions of the interconnects during service, the problem is addressed within the framework of isotropic linear elasticity in two dimensions (plane strain condition). In the formulation of stress induced surface diffusion, not only the contribution due to elastic strain energy density (ESED) but also that of the elastic dipole tensor interactions (EDTI) between the stress field and the mobile atomic species (monovacancies) is considered. In computation of the elastostatic and electrostatic fields the indirect boundary element method (IBEM) with constant and straight boundary elements is utilized. The resulted non–linear partial differential equation is solved numerically by Euler’s method of finite differences. The dynamic computer simulation experiments identify well known GB groove shapes and shed light on their growing kinetics. They also allow generating some scenarios under several conditions regarding to the applied force fields and/or physicochemical parameters. The destruction of groove symmetry, termination of the groove penetration with isotropic surface diffusivity, ridge/slit formations with anisotropic diffusivity and the role played by the wetting parameter are all identified for electromigration conditions. The kinetics of accelerated groove deepening with an applied tensile stress is examined in connection with GB cavity growth models in the literature and a diffusive micro-crack formation is reported at the groove tip for high stresses. On the other hand, the use of EDTI provided a means to dynamically simulate GB ridges under compressive stress fields with surface diffusion. An incubation time for hillock growth and a crossover depth over which GB migration becomes energetically favorable is defined and discussed in this context.


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Citation Formats
Ö. Akyıldız, “Computer simulation of grain boundary grooving by anisotropic surface drift diffusion due to capillary, electromigration and elastostatic forces,” Ph.D. - Doctoral Program, Middle East Technical University, 2010.