black's equation

**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.