Date of Award
Open Access Dissertation
Doctor of Philosophy in Materials Science and Engineering (PhD)
Administrative Home Department
Department of Materials Science and Engineering
Committee Member 1
Committee Member 2
Committee Member 3
With the miniaturization of microelectronic devices, the reliability of solder interconnects is a significant concern. As size is reduced, the current density flowing through an interconnect becomes larger and exacerbates electromigration leading to microstructural changes and failure. Since most solder alloys are required to be lead-free over toxicity concerns, there are additional challenges to interconnect performance. Nearly all solder alloys are comprised with its majority component being tin due to its low melting temperature and economical cost. The typical metallic white tin phase has a body-centered tetragonal crystal structure which exhibits strong anisotropy in its physical properties. In particular, the electrical/thermal conductivity and elastic modulus are highly anisotropic. For this reason, the performance of solder bumps that contain only a few grains are sensitive to the orientation of each individual grain. Quantitative description of electromigration at such scales is required to understand the microstructure behavior impacting performance and degradation of interconnects. Electromigration induced microstructure evolution in solder interconnects involves complicated multiphysical processes. It involves the diffusion of atoms driven by charge conduction which is also strongly affected by concurrent heat conduction and mechanical processes. A multiphysics phase field model is developed to investigate the diffusional processes in tin solder interconnects. The driving forces for electromigration are obtained solving for current density and electric field in microstructures with inhomogeneous and anisotropic electrical conductivity using microscopic Ohm's law. Similarly, the driving forces caused by temperature gradients are obtained solving for heat flux using Fourier's law of conduction that accounts for inhomogeneous and anisotropic thermal conductivity. The model is capable of accounting for the generation of heat through Joule heating. Simulations of conduction driven pore and inclusion migration are discussed in terms of volume and surface diffusion mechanisms. Finally, the contribution of stress and its gradient are obtained through microelasticity modeling. From Hooke's law of elasticity, the modeling allows different external loading conditions to be considered and is capable of solving for internal stress concentrations in microstructures with structural and elastic property mismatches near defects including grain boundaries, voids, and precipitates. These internal stresses generated contribute to the diffusional processes through its gradient.
Morgan, Zachary, "Multiphysics phase field modeling of electromigration", Open Access Dissertation, Michigan Technological University, 2020.