Black's equation predicts electromigration lifetime — modeling how current density and temperature affect metal interconnect failure through atom migration under high current.

What Is Black's Equation?

• Formula: MTTF = A·J^(-n)·exp(Ea/kT) where J is current density, n ≈ 1-2, Ea is activation energy, T is temperature.
• Purpose: Predict interconnect lifetime under current stress.

Key Parameters: Current density (J), temperature (T), activation energy (Ea ≈ 0.7-1.0 eV for Al, 0.8-1.2 eV for Cu), current exponent (n).

Why It Matters: Electromigration causes voids and opens in metal lines, leading to circuit failure.

Design Rules: Set maximum current density (typically 1-2 MA/cm² for Cu), define wire widths, select barrier materials.

Applications: Interconnect design rules, reliability qualification, current density limits, metal stack optimization.

Black's equation is canonical model for electromigration — giving designers quantitative rules for current-limited design margins.