Electromigration MTTF Calculator — Black's Equation

MTTF = A \cdot j^{-n} \cdot e^{\frac{E_a}{kT}}

MTTF = Mean Time To Failure (hours)
A = Constant (relative unless calibrated)
j = Current density (consistent units)
n = Current density exponent (positive)
Ea = Activation energy (eV)
T = Temperature (K)
k = Boltzmann constant = 8.617333262145e-5 eV/K

Material	Ea (eV)	n
Aluminum	0.5-0.7	1-2
Copper	0.7-1.0	1-2
Silver	~0.6	1-2

Current Density Unit

MTTF (hrs)Current Density (A/cm2)Temperature (C)Activation Energy (eV)n (positive)A (relative unless calibrated)

MTTF (hrs): 725.4242

Have a more complex case than this calculator covers? Get in touch.

How it works

Black's equation models electromigration — the gradual failure of metal interconnects as current physically displaces atoms over time. Mean time to failure falls as current density rises and as temperature rises:

MTTF = A \cdot J^{-n} \cdot \exp\!\left(\frac{E_a}{k T}\right)

where J is current density, nis the current-density exponent (typically 1–2), E_a is activation energy (eV), kis Boltzmann's constant, and T is temperature in kelvin.

Example:With n = 2, doubling current density cuts life to one-quarter (AF = 2² = 4). Separately, raising temperature from 105 °C to 150 °C at E_a = 0.9 eV gives a thermal acceleration of about 19×. The two effects multiply, so current and temperature together drive electromigration life hard.

Use this when sizing metal traces, vias, or bond wires for long-term current loading. For thermally activated chemical wear-out, see the Arrhenius calculator.