Vacancy Model for Threshold Electromigration in Thin Metallic Films

摘要

The problem of threshold electromiration in thin metallic films is described in the framework of the thermodynamics of irreversible processes. The main idea of the model consists in supposition that the phenomenon is caused by inefficient operation of vacancy sources and sinks located at the film surface. In this case the electric power would be expended for a creation of vacancy concentration deviation from the equilibrium caused by concentration inertness of internal vacancy sources and sinks. Such a deviation of vacancy concentration from the equilibrium leads to the gradient in the vacancy concentration along the metallic film. By this means the necessary condition is produced to "switch on" internal vacancy sources and sinks at the film ends, which provide atomic transport. It is shown that the gradient in the vacancy concentration along the film is in direct proprotion to the electric current density. The value of the threshold current density is determined by the concentration inertness of the internal vacancy source which is in operation. The role of grain boundaries during electromigration in thin metallic films is discussed.