The failure distribution of microelectronic devices follows a
WEIBULL^{3.5} distribution. At the beginning, early failure may
occur due to fabrication faults. At the end of the device's life time, failure
is mostly due to material fatigue of one or more parts of the device.
To determine the reliability especially for metals,
BLACK [215,216] has proposed a modified ARRHENIUS law, which can be
arbitrarily adapted and calibrated to special failure mechanisms.
BLACK's equation reads

where the local mean time to failure (MTTF) is inversely proportional to a certain power of the local current density and directly proportional to , with as the activation energy. The proportionallity constant is geometry-dependent, and must be determined by measurements for different interconnect geometries.

However, BLACK's equation describes an empirical observed material behavior and is thus not valid for arbitrary use. It requires a separate calibration for each different failure mechanism. Nevertheless, BLACK's equation is still commonly used to estimate the reliability with respect to the mean time to failure [5,33,217].

Stefan Holzer 2007-11-19