Electromigration-Induced Instability of the Interface between Solid Conductors

Аннотация

A model has been developed to describe the influence of vacancy electromigration in the bulk of joined conducting materials under applied electric current on the shape stability of a flat interface between them. A system of equations is formulated and solved to describe the relationship between changes in the interface profile and mechanical stresses arising in it due to ion and vacancy fluxes, induced by a small spatially periodic perturbation of the interface. Criteria of the perturbation amplitude growth with time, i.e., the shape instability conditions for the interface, are determined. A more detailed analysis and estimation are performed for two special cases: in the first case the interface is between two similar materials, and in the other the mobility of ions and vacancies in one of the materials can be neglected. Perturbation wavelength ranges are determined and studied analytically for these cases; within the intervals the bulk vacancy electromigration is the main factor that leads to the growth of perturbation amplitude and mechanical stresses along the interface with time. Conditions for the existence of such ranges and dependences of their boundaries on the current direction and current density are determined. Particular wavelength and current density ranges of the interface instability are estimated. The estimates show that the interface instability due to bulk electromigration is possible under reasonable (experimentally and practically) conditions in terms of temperature (∼100°C), current density (∼10¹⁰ − 10¹² A/m²), and perturbation wavelength (∼10¹ − 10³ μm). The obtained results may be useful, e.g., for improving the reliability and lifetime of micro- and nanoelectronic components.