On the distribution of stress-induced voiding failures under vias

A physics-of-failure model is derived for the statistics of open-failure mode stress induced voiding (SIV) for vias contacting wide lower metal leads. This model is used to fit long-term, low-temperature data from a 130 nm Cu/low-k BEOL process. Scaling forms are discussed for the temperature acceleration, via chain length, and linewidth. A single void growth model can be used to fit the apparent separate Weibull modes in the data, and for very long chains a three-parameter Weibull is found as a limiting distribution. Monte Carlo integration over the via size is also used to verify the model. The presence of early transient statistics emphasize the practical importance of the sample size and stress testing readout strategy.