Stress-driven diffusive voiding of aluminum conductor lines

The trend to miniaturize silicon integrated circuits has brought with it a thermal stress-induced void formation problem in the aluminum conductor lines of these circuits. Here, local stress relaxation has been included quantitatively in the construction of a wedge-like void growth model. It is shown that under stress relaxation conditions, the stress-induced grain boundary diffusion equation transforms into the diffusion equation. With the use of appropriate boundary conditions and the initial conductor line stress profile, the diffusion equation is solved numerically. This solution yields the temporal history of void size and local stress. It is shown that two types of stress relaxation moderate and limit the growth of voids. From this analysis, a useful expression which relates final void size and initial stress is derived. With these results conservative estimates of the lifetime of aluminum conductor lines can be made