• Extract the current-density exponent in Black's electromigration law from two median-time-to-failure measurements at different current densities.
• Compare fabrication or device scenarios while holding coefficients and unit conventions constant.
• Check a hand calculation before moving to a higher-fidelity process, circuit, or TCAD model.

A positive exponent means lifetime decreased as current density increased. Zero or a negative result is retained as diagnostic evidence that the two measurements do not show the usual positive current acceleration rather than being silently rejected.^[1]

• Both measurements must use the same conductor structure, temperature, failure criterion, activation mechanism, and effective prefactor. Two points determine a slope exactly but cannot quantify uncertainty, test linearity, or reveal a mechanism change.
• Use parameters measured for the same material, geometry, temperature, and operating regime whenever the result informs engineering work.

• Black Equation MTTF

  Apply the fitted current-density exponent with a compatible prefactor and activation energy to predict median lifetime at a selected stress condition.

• Linear Regression

  Fit more than two log(MTTF) versus log(current-density) points when you need a slope estimate and goodness-of-fit information rather than an exact two-point exponent.