Microbump Electromigration Life Calculator
Advanced Packaging Reliability: Determine electrical current density ($J$), Joule heating temperature rise ($\Delta T$), and electromigration Mean Time to Failure (MTTF) via Black's Law.
Bump Geometry & Applied Current
Thermal Operating Environment
Electromigration & Reliability Output
Recommended Tools & Equipment
Tested hardware and components for high reliability
Semiconductor Microbump Electromigration Physics
Microbump and copper pillar scaling down to $10\,\mu\text{m} - 25\,\mu\text{m}$ pitch requires rigorous verification against electromigration (EM) voiding under high DC currents.
1. Current Density & Joule Heating
J_avg = I_dc / [ π · (D/2)² ] J_peak = c_crowding · J_avg ΔT_joule = I_dc² · R_bump · θ_thermal
2. Black's Law for Electromigration MTTF
MTTF = A · J_peak^(-n) · exp( E_a / (k_B · T_kelvin) )
Frequently Asked Questions
What is electromigration in semiconductor microbumps and copper pillars?
Electromigration is the gradual transport of metal atoms in a conductor caused by momentum transfer from high-density flowing conduction electrons ("electron wind"). Over time, atomic migration depletes metal at the cathode, forming microscopic voids and crack openings, while accumulating hillocks and whiskers at the anode that can cause short circuits.
Why does current crowding occur at the corners of microbumps?
Electric current enters the vertical microbump from a thin horizontal trace or redistribution layer (RDL) with much smaller cross-sectional area. Because electrons turn a 90° corner into the cylindrical pillar, current lines bunch up severely at the entry corner, magnifying current density ($J_{max}$) by $3\times$ to $8\times$ compared to the average.
How does Black's equation estimate MTTF for microbumps?
J.R. Black formulated the standard empirical model for electromigration: $\text{MTTF} = A \cdot J^{-n} \exp(E_a / (k_B T))$. The exponential dependence on temperature means that even modest Joule heating ($+10^\circ\text{C}$) cuts operational life in half, making thermal management vital for high-power AI accelerators and GPUs.