Advanced IC Packaging & Heterogeneous Integration, Flip-Chip C4 Underfill & DNP Strain
Flip-Chip C4 DNP Shear Strain & Capillary Underfill Formula
Calculate Corner-Bump CTE Differential Displacement (um), Un-Underfilled Bump Shear Strain (%), Young-Laplace Gap Driving Pressure (kPa), and Washburn-Hele-Shaw Fill Time (s).
Without silica-filled epoxy underfill, a 17 mm silicon flip-chip shears its corner C4 micro-bumps by 20%–40% on the VERY FIRST thermal cycle!
Direct **Flip-Chip (`C4` Controlled Collapse Chip Connection)** mounts low-expansion Silicon (`alpha_{Si} ≈ 2.6` ppm/K) face-down onto organic build-up substrates (`alpha_{sub} ≈ 16.8` ppm/K -> Differential CTE `Delta_alpha = 14.2` ppm/K) across Standoff Bump Height `h` (`um`). At the corner solder joint (`Distance to Neutral Point DNP` mm), thermal swing `Delta_T` (`K`) imposes **Differential Shear Displacement `Delta_x = (DNP * 1,000) * (Delta_alpha * 10^{-6}) * Delta_T`** (`um`) and **Un-Underfilled Shear Strain `gamma% = (Delta_x / h) * 100%`** (`>15%` cracks solder in `<50` cycles!). Dispensing silica-filled liquid epoxy (`Viscosity mu` Pa·s, `Surface Tension sigma` mN/m, `Wetting Angle theta` deg) along one die edge wicks across Chip Width `L` (`mm`) driven by **Parallel-Plate Capillary Pressure `Delta_P_c = (2 * sigma * COS(theta)) / h`** (`kPa`) in **Hele-Shaw Washburn Fill Time `t_{fill} = (3 * mu * (L / 1,000)^2) / ((h * 10^{-6}) * (sigma / 1,000) * COS(theta))`** (`s`)—coupling die and substrate to cut bump strain `5x–10x`!
Verify on a `12 x 12` mm (`DNP = 8.50` mm) Flip-Chip ASIC on Organic BGA—Corner `DNP` = 8.50 mm (B2), `Delta_alpha` = 14.2 ppm/K (B3), Thermal_Swing `Delta_T` = 125.0 K (B4), Bump_Standoff `h` = 75.0 um (B5), Flow_Span `L` = 12.0 mm (B6), Epoxy_Surface_Tension `sigma` = 28.0 mN/m (B7), Flux-Cleaned_Contact_Angle `theta` = 25.0° (B8), and `90 °C` Dispense_Viscosity `mu` = 0.45 Pa·s (B9): Corner Displacement hits `15.09` um (E2 = `20.12%` un-underfilled shear strain in E3!), Capillary Suction equals `0.677` kPa (E4), and Complete Underfill Wicking takes `102.1` s (E5)!
| Flip-Chip Underfill KPI (DNP=8.5 mm, L=12 mm, mu=0.45 Pa·s, Standoff h=75 vs 38 um) | Formula | Verified Output |
|---|---|---|
| Corner CTE Displacement dx (um) | (DNP_mm * 1000) * (dAlpha * 1e-6) * dT_K | 15.09 um |
| Un-Underfilled Shear Strain (%) | (Corner_Displacement_um / Standoff_h_um) * 100 | 20.12% (39.70% @ 38 um Cu-pillar!) |
| Capillary Suction Pressure (kPa) | (2 * (sigma/1000) * COS(rad)) / (h_um * 1e-6) / 1e3 | 0.677 kPa (1.336 kPa @ 38 um) |
| Washburn Underfill Time (s) | (3 * mu * L_m^2) / (h_m * sigma_N_m * COS(rad)) | 102.1 s (201.6 s = 2x slower @ 38 um!) |
DNP Thermal Shear Strain & Parallel-Plate Hele-Shaw Capillary Underfill Formula
Validate `DNP > 0.5` mm, `Delta_alpha > 0.5` ppm/K, `Delta_T > 10` K, `Standoff h` in `[10, 500]` um, `Chip_Span L > 1` mm, `Surface_Tension sigma > 5` mN/m, wetting `Contact_Angle` in `[0°, 80°]`, and `Viscosity mu > 0.01` Pa·s!
=LET(dn_m, B2, da_p, B3, dt_k, B4, hs_m, B5 * 0.000001, lc_m, B6 / 1000, sg_n, B7 / 1000, th_r, B8 * (PI() / 180), mu_p, B9, IF(OR(dn_m <= 0.5, da_p <= 0.5, dt_k <= 10, B5 < 10, B5 > 500, B6 <= 1, B7 <= 5, B8 < 0, B8 > 80, mu_p <= 0.01), "Invalid Flip-Chip Input", ROUND((3 * mu_p * (lc_m ^ 2)) / (hs_m * sg_n * COS(th_r)), 1)))Fine-Pitch 38 um Copper-Pillar Standoff Bottleneck Check (Set Bump Standoff B5 = 38 um)
Shrink standoff height to `h` B5 = 38 um for fine-pitch copper pillars: Un-Underfilled Strain E3 doubles to `39.70%`, AND even though Capillary Suction E4 doubles (`1 / h` -> `1.336` kPa), Poiseuille viscous resistance grows as `1 / h^2`—DOUBLING Underfill Flow Time E5 to `201.6` s and motivating molded/wafer-level no-flow underfills!
=IF(ISTEXT(E5), E5, LET(dx_u, (B2 * 1000) * (B3 * 0.000001) * B4, ROUND((dx_u / B5) * 100, 2)))Try the example
Use the original values or change them to test your understanding.