Solder Bump Thermal-Cycling Life

What is modelled

Silicon expands by about 2.6 parts per million per kelvin, an organic substrate by about 17. When the package heats and cools, the substrate slides under the die and each solder bump is sheared, most at the corner furthest from the die centre. Repeated shear strain makes the solder creep and crack, so the bump fails after a number of cycles that falls steeply as the strain grows. Underfill glue spreads the strain and extends the life by a large factor.

Equations

• Shear strain range Δγ = DNP (αs − αSi) ΔT / h times the underfill relief factor.
• Engelmaier strain-life law Nf = ½ (Δγ / 2εf)1/c, with c = −0.442 − 6×10−4 Tsj + 1.74×10−2 ln(1 + 360 / td).
• Weibull failures F = 1 − exp(−(N / Nf)β), B10 life Nf (−ln 0.9)1/β.

Checks run in the page

• The strain range measured on a sampled temperature cycle against the closed form.
• The strain-life law inverted back to the applied strain.
• A seeded Monte Carlo of Weibull lives against the 63.2 % and B10 values.
• The power-law scaling in temperature swing and die size.

Honest simplifications

Only the corner bump is analysed, the board is treated as a rigid reference for the shear, the underfill is a single multiplier on strain, and the strain-life law is the empirical Engelmaier fit for tin-lead and lead-free solders with a fixed ductility of 0.325. Real life depends on the alloy, intermetallics, warpage and board bending, so use this as a trend illustration, not a qualification result.

• Press Bare bumps, no underfill and see the life collapse by orders of magnitude.
• Press Large 20 mm die to watch the corner strain grow with the distance from the die centre.
• Press Ceramic substrate to reduce the mismatch and lengthen the life.