A Complete Model of Lifetime Distribution for Electromigration Failure Including Grain Boundary and Lattice Diffusions in Submicron Thin Film Metallization

Abstract

A complete model of electromigration failure lifetime distribution is illustrated in detail in this paper. The proposed theory can be divided into two portions: the physical model and the statistical model. As a result of the combination of these models, the electromigration lifetime distribution as a function of line width and temperature is generally predicted. Experiments have been conducted to verify the validity of this model and reported previously. Various theoretical aspects and implications of this model are discussed in this paper. Empirically, it is found that a significant portion of the increase in the shape factor with the decrease in line width can be attributed to the increase in the temperature standard deviation for narrower lines. Based on this model and coupled with the experimental observations, it is shown that the design rule scaling suffers a steep drop with line width in the deep submicron region. As a result, it will be difficult for the bamboo structure in practice to salvage thin film metallization from electromigration susceptibility for deep submicron microchip technologies. In order to meet the reliability specification for deep submicron devices, other alternatives are considered and discussed.