Electromigration MTTF: Estimate Interconnect Lifetime with Black's Equation
What is Electromigration MTTF?
Electromigration is the directional migration of metal atoms in interconnects under high current density, leading to voids, opens or hillocks. It is one of the dominant long-term reliability failure mechanisms in integrated circuits and power devices. Lifetime is estimated with Black's equation: MTTF = A·j^(-n)·exp(Ea/kT). Actual lifetime also depends on interconnect geometry, grain structure and stress gradients, so estimates should be refined with process information.
When to Use It
Use it to assess the lifetime of IC interconnects, solder joints and power module wire bonds, and to check current density against process design rules at the design stage. It also supports interpretation of JEDEC JESD63/JEP122 electromigration test data and failure-physics lifetime estimation. For multi-stress scenarios, use the Black equation result as a baseline and add corrections such as temperature cycling or mechanical stress.
How to Use It (Step by Step)
Enter the current density j (A/cm²), the current density exponent n, the activation energy Ea (eV), the temperature T (K) and the constant A. The tool returns MTTF and the lifetime corresponding to a specified failure rate. Make sure n and Ea come from the same process or from JEDEC data, and remember that copper interconnects require via-structure effects to be considered.
Key Formulas / Example
The Black equation is MTTF = A·j^(-n)·exp(Ea/kT), where k is the Boltzmann constant. Because lifetime scales with j^(-n), doubling the current density reduces lifetime by a factor of 2^n (four times when n = 2). Lifetime data at several temperatures or current densities can be plotted on an Arrhenius chart to validate the model and its parameters.