Atomistic and computer modeling of metallization failure of integrated circuits by electromigration

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Abstract
Nonstationary and stationary concentration profiles of vacancies in a grain boundary are calculated for the case of electromigration and various conditions of vacancy formation and annihilation. If supersaturation of vacancies is assumed for void formation, current densities necessary for voiding have to be larger than a critical value jcrit, which is related to the length l of the grain boundary by the relation ljcrit=const. An estimation of the value of the constant in the last equation is in agreement with experimental values. An approximate equation for the median time to failure (MTF) is derived from the model for grain boundaries conducting the flux of matter parallel or in series. The results explain many features of experimental studies. First values of MTF for a network of grain boundaries obtained by computer simulations are presented as well, and the effect of resistance heating and nonstationarity on the current exponent is discussed in some detail.