STRESS AND ELECTROMIGRATION IN AL-LINES OF INTEGRATED-CIRCUITS

The generation of tensile and compressive stresses by the annihilation and production of vacancies which are subject to driving forces due to electromigration and due to the developing stress gradient is calculated. The rate of the stress changes is related to the deviation of the vacancy concentration from its equilibrium concentration. Depending on the magnitude of the rate constant different mechanisms of annihilation and production of vacancies (i.e. in the grain boundary itself, in adjacent grain boundaries or at dislocations) are covered. The resulting differential equations are solved numerically and analytically for some limiting cases. A quasi steady state concentration profile is established within a short initial period of time, which is determined by one of the three processes diffusion, electromigration or rate of vacancy annihilation. During the quasi steady state the stresses increase linearly with time. When stresses are large enough to change the equilibrium vacancy concentration deviation from the linear increase occur and a rather long period follows where the true steady state is approached. If the time to failure, t(f), of an Al-line is defined as the time necessary to reach a critical stress, t(f) is proportional to j(-n) where the current exponent changes from 1 at low critical stresses to 2 at higher stresses. The theoretical results are in excellent agreement with recent measurements of compressive stresses both with respect to the dependence on time and position.