Electromigration (EM) simulation predicts the lifetime and failure risk of metal interconnects under current stress — modeling how sustained current flow causes metal atoms to migrate along the conductor, eventually forming voids (open circuits) or hillocks (short circuits).

What Electromigration Is

• When current flows through a metal conductor, the "electron wind" exerts a force on metal atoms, causing them to diffuse in the direction of electron flow.
• Over time, this migration creates:
• Voids: Metal atoms leave, creating gaps that increase resistance and eventually cause open-circuit failure.
• Hillocks/Extrusions: Metal atoms accumulate, forming protrusions that can short to adjacent lines.
• EM is a wear-out failure mechanism — it develops gradually over the operating lifetime of the chip.

The Physics of Electromigration

• Driving Force: The electron wind force $F = Z^ e \rho j$, where $Z^$ is the effective charge, $\rho$ is resistivity, and $j$ is current density.
• Diffusion Paths: Atoms migrate along the path of least resistance — grain boundaries, interfaces (metal/barrier, metal/cap), and surfaces.
• Black's Equation: The empirical lifetime model:

Where $t_{50}$ is median time to failure, $j$ is current density, $n$ ≈ 1–2, and $E_a$ is activation energy.

• Blech Effect: Below a critical length-current-density product ($jL_{crit}$), mechanical back-stress prevents void growth — short lines are immortal to EM.

What EM Simulation Predicts

• Current Density Distribution: Map $j$ across all metal segments — identify hot spots where current density exceeds the EM design rule limit.
• Void Nucleation Sites: Predict where voids will form based on flux divergence — typically at via connections, width transitions, and grain boundary triple junctions.
• Time to Failure: Estimate the lifetime of each interconnect segment under operating conditions.
• Temperature Effects: Higher temperature exponentially accelerates EM — thermal simulation feeds temperature data to EM analysis.

EM Design Rules

• Maximum Current Density: $j_{max}$ limits for each metal layer and via — typically 1–2 MA/cm² for DC and higher for AC (due to self-heating recovery).
• AC Enhancement: Bidirectional current flow partially reverses EM damage — AC currents can tolerate higher $j$ than DC.
• Width and Length Dependence: Wider lines and shorter segments are more EM-resistant.

Simulation Workflow

1. Extract the power grid and signal net current distributions from circuit simulation. 2. Map current densities onto the physical layout. 3. Check all segments against EM design rules. 4. Fix violations by widening metal, adding vias, or redistributing current.

Electromigration simulation is critical for reliability — at advanced nodes with shrinking metal dimensions and increasing current densities, EM is one of the primary lifetime-limiting failure mechanisms.