Statistics of Electromigration Lifetime Analyzed Using a Deterministic Transient Model

The electromigration lifetime is measured for a large number of copper lines encapsulated in an organosilicate glass low-permittivity dielectric. Three testing variables are used: the line length, the electric current density, and the temperature. A copper line fails if a void near the upstream via grows to a critical volume that blocks the electric current. The critical volume varies from line to line, depending on line-end designs and chance variations in the microstructure. However, the statistical distribution of the critical volume (DCV) is expected to be independent of the testing variables. By contrast, the distribution of the lifetime (DLT) strongly depends on the testing variables. For a void to grow a substantial volume, the diffusion process averages over many grains along the line. Consequently, the void volume as a function of time, V(t), is insensitive to chance variations in the microstructure. As a simplification, we assume that the function V(t) is deterministic, and calculate this function using a transient model. We use the function V(t) to convert the experimentally measured DLT to the DCV. The same DCV predicts the DLT under untested conditions.