Modelling void growth and failure of passivated metal lines under stress and electromigration conditions

Abstract

Failure of interconnect metal lines by stress‐ and electromigration‐induced voiding is examined theoretically. By calculating the rate of growth of a single void in a passivated line subjected to an initial hydrostatic tension stress and by assuming that failure occurs when the void reaches a critical size, a model for failure of encapsulated interconnect lines by stress voiding can be developed. The model leads to a failure law for aluminum lines of the form tfσ2/d=1019.2 exp(Q/RT), where tf is the failure time in seconds, σ is the initial hydrostatic tension stress in the line in Pa, d is the grain size in meters and the activation energy, Q=80.9 kJ/mol, is close to that for grain boundary diffusion in aluminum.The effects of electromigration on void growth are also considered. It is shown that only limited void growth can occur by the sweeping of vacancies from other parts of the line. The amount of void growth by this process is too small to account for interconnect failures, unless very widely spaced ‘‘blocking’’ grain are assumed to exist in the line. Void growth by the migration and coalescence of small voids is shown to be more likely mechanism of electromigration failure.