Bump Electromigration

Run kinetic study at multiple currents & temperatures to estimate Ea (activation energy) & n (current density exponent) in Black's equation:
MTTF = A J ^ (-n) exp [Ea/KT]
Resistance of the EM device is measured using 4-wire Kelvin structure, and an increase in R over a predefined threshold is considered to be a failure.
As a first step, the temperature sensor (that may be an on-die resistor or diode) is calibrated in the oven (set at a certain temp, for a low constant current) to generate R v/s temp (for the resistor) or V v/s temp (for the diode) to estimate TCR.
Then the oven is set to stress temperatures, and EM test structure is powered at stress current, to note initial change in R. Knowing TCR, delta R is equated to delta T. This is 'Joule Heating'.
Device temp = Oven Temp + DeltaT (Joule heating)
TTF data is collected and fit to an appropriate statistical distribution, which is then used to estimate MTTF from CDF plot (Cumulative % fails v/s time). Common distributions used to model EM data are Lognormal & Weibull.
Lognormal = sigma -> shape parameter, gives measure of distribution width.
Weibull = beta is shape parameter, eta is characteristic time (or time when 63.2% fails) MTTF obtained for multiple stress conditions (current & temp), based on distribution parameter estimation helps estimate Ea & n in Black's Equation. Once Ea & n have been estimated, lifetime/usage requirements (for eg 95C device temp & 5 years life) is used to predict Imax.