Electromigration Lifetime Calculator
Work out electromigration lifetime instantly with clear inputs, formula shown and shareable results.
About Electromigration Lifetime Calculator
Black's equation makes median time to failure proportional to J^-n times exp(Ea/kT), with n about 2 for copper. Both terms bite hard: doubling current density quarters life, and every 10 degrees of temperature rise costs roughly a third of it at Ea = 0.9 eV.
Formula
Black's equation
MTF = A x J^-n x exp(Ea / kT), n approx 2, Ea approx 0.7-1.0 eV for copper
Worked example
With the default values below, Electromigration Lifetime Calculator returns Expected lifetime of 4.80. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Current density
- 1.2 MA/cm²
- Metal temperature
- 105 °C
- Activation energy
- 0.9 eV
- Reference life at 1 MA/cm² and 100 C
- 10 years
Results
- Expected lifetime
- 4.80 years
- Acceleration factor
- 0.4796 x
- Current density factor
- 0.6944 x
- Thermal factor
- 0.6907 x
Step by step
- 1Values used
- 2Black's equation
- 3Expected lifetime= 4.80 years
- 4Acceleration factor= 0.4796 x
- 5Current density factor= 0.6944 x
- 6Thermal factor= 0.6907 x
Assumptions and limits
- The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, fees or charges or compounding frequency into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Why is electromigration a scaling problem?
Wire cross-sections shrink faster than currents fall, so current density rises with each node, and copper grain boundaries and liner thickness make it worse.
How is it mitigated in design?
Current density rules per metal layer, wider wires or multiple parallel wires on high-current nets, and via arrays instead of single vias.
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