An analytical open-failure lifetime model for stress-induced voiding in aluminum lines

An analytical model is derived for determining the time before which LSI aluminum (Al) lines with a bamboo-grain structure undergo open failures caused by stress-induced voiding. Derivations are based on the following assumptions: that the driving force for void growth is relaxation of Al-line tensile stress, that the mass transport rate is proportional to the nth power of Al-line stress, and that the void will maintain its prism shape throughout its growth. The critical minimum initial tensile stress value for producing open failure is calculated, as are the respective dependencies of lifetime on void tip angle, temperature, line dimensions, and line tensile stress. By adjusting the values of certain parameters within the model, it is possible to derive temperature, line-dimension, and tensile-stress dependencies that fall within the range of experimentally obtained results