electromigration basics

**Electromigration (EM)** — the gradual displacement of metal atoms in interconnect wires due to momentum transfer from flowing electrons, eventually causing circuit failure. **Physics** - High current density accelerates electrons through the wire - Electrons transfer momentum to metal atoms via "electron wind" - Atoms migrate in the direction of electron flow - Voids form where atoms leave; hillocks form where atoms accumulate - Void → open circuit (fail). Hillock → short circuit to adjacent wire **Black's Equation** $$MTTF = A \cdot J^{-n} \cdot e^{E_a / kT}$$ - $J$: Current density (critical parameter) - $n$: Current exponent (~2) - $E_a$: Activation energy (~0.7-0.9 eV for Cu) - Higher temperature and current density dramatically reduce lifetime **Design Rules** - Maximum current density limits per wire width (foundry-specified) - Typical limit: 1-2 MA/cm$^2$ for copper at 105C - Wider wires and redundant vias improve EM reliability **Mitigation** - Copper (better EM resistance than aluminum) - Bamboo grain structure (grain boundaries perpendicular to current) - Metal capping layers (CoWP) block surface diffusion - Short-length effect: Very short wires are immune (back-stress) **EM** is the primary reliability concern for chip interconnects at advanced nodes.