Signoff & verification

electromigration (EM)

Picture a narrow metal wire on the chip as a riverbed and the electrons flowing through it as a current of water. Normally the water just flows past the gravel. But push enough water through fast enough and it starts dragging the gravel along with it, scouring the bed thin in one spot and piling it up downstream. Electromigration is that same idea at the atomic scale: when the current density in a wire gets high enough, the moving electrons transfer momentum to the metal atoms (engineers call it the "electron wind") and slowly nudge them along, in the same direction the electrons travel. Over months and years the metal physically migrates — atoms drain away from one place, leaving a void that thins the wire until it cracks open, and pile up elsewhere as a bump (a hillock) that can push into a neighbor and short it.

The key word is density, not total current: a thin wire carrying a modest current can have a far higher current per unit cross-section than a fat bus carrying more, and it is the per-area crowding that does the damage. That makes EM a long-term reliability (wear-out) limit rather than something you see at power-on — the chip works fine on day one and fails after years in the field, which is exactly why it must be caught before tape-out. Sign-off tools check every wire and via against foundry current limits, set per metal layer, and they are stricter on power and ground rails and clock nets, where current flows one direction all the time, than on ordinary signal wires, where the back-and-forth toggling lets some displaced atoms drift back and partially self-heal. Fixes are geometric: widen the wire, split the current across more parallel wires or vias, or move to a thicker upper metal layer.

MTTF = A * J^(-n) * exp(Ea / (k*T)) (Black's equation; n is about 1 to 2)

Black's equation estimates a wire's mean time to failure: higher current density J or higher temperature T shortens lifetime sharply, which is why EM limits tighten on hot, heavily-loaded power and clock nets.

Because failure is a slow statistical process, EM is budgeted by mean-time-to-failure rather than a hard pass/fail — and it gets worse fast as wires shrink and run hotter, since the rate climbs steeply with both current density and temperature.

Also called
EMelectromigration wear-outcurrent-density limit电迁移失效電流密度上限