The short-length effect was investigated by testing a 2-level structure with Ti/AlCu/Ti stripes and inter-level W stud vias. Lifetime measurements and resistance changes, as a function of time, were used to monitor the phenomenon and provided new insights into the electromigration behavior of multi-layered metallizations. A linear increase in resistance was followed by a resistance change, with time, that approached zero. For a given product of current density and stripe length, longer stripes increased (in resistance) to higher values than did shorter stripes. The sigma-value of the log-normal distribution increased as the current density decreased and/or as the maximum allowed resistance change increased. The lifetime at relatively low current densities did not obey Black’s empirical equation. Instead, the lifetime data obeyed a modified version of this equation which included a critical current density. As an alternative approach to quantification of the short-length effect, a new method for determining the critical current density was proposed which took account of an apparent saturation of the resistance increase with time of the W stud chains. Unlike the modified Black model, the resistance saturation approach permitted the estimation of lower bounds on the critical current density. The threshold product of length and current density was deduced from the modified Black model, and from the resistance saturation model, for stripe lengths of 50, 70 and 100. Both models indicated that the critical current density depended strongly upon the failure criterion, or upon the magnitude of the resistance change, but was independent of temperature between 175 and 250C. No evidence was found for a threshold product, of length and current density, below which no electromigration-induced damage occurred.

R.G.Filippi, G.A.Biery, R.A.Wachnik: Journal of Applied Physics, 1995, 78[6], 3756-68