Thermosonic Wire Bonding FAB & MIL-STD-883 Pull Formula

Pulling a flat low-loop bond wire upward with a 9.2 gf hook actually stresses the gold neck past 24 gf—snapping good bonds via trigonometric amplification!

**Thermosonic Ball-Wedge Wire Bonding** sparks an Electronic Flame-Off (`EFO`) plasma wand at the tip of `4N` Gold or Pd-coated Copper wire of Diameter `d` (`um`, `25.4` um = `1.0` mil) to form a spherical **Free-Air Ball `D_{FAB} ≈ 2.1 * d`** (`um`), then scrubs `120` kHz ultrasonic energy on a `175 °C` aluminum die pad to mash a **Bonded Ball Diameter `D_{mash} ≈ 2.8 * d`** (`um`)—compared against **Intrinsic Wire Tensile Strength `F_{UTS} = UTS_{MPa} * ((PI() / 4) * (d / 1,000)^2) * (1,000 / 9.80665)`** (`grams-force gf`)! During **MIL-STD-883 Method 2011 Destructive Wire-Pull QC**, a micro-hook lifts the loop apex with Vertical Gauge Reading `F_{hook}` (`gf`) at Die-Side Slope `theta_1` and Lead-Side Slope `theta_2` (`deg`). Static pulley equilibrium resolves **True Axial Wire Tension `T_{wire} = F_{hook} / (SIN(theta_1) + SIN(theta_2))`** (`gf`)—proving that shallow ultra-thin package loops (`theta < 15°`) record artificially low gauge readings even when the wire neck hits `100%` UTS!

Verify on a `25.4` um (`1.0`-mil) Annealed `4N` Gold Wire Bond—Wire_Diameter `d` = 25.4 um (B2 -> `D_{FAB} = 53.3` um in E2 & `D_{mash} = 71.1` um in E3), Wire_Tensile_Strength `UTS` = 240 MPa (B3 -> Breaking Load = `12.40` gf in E4), Hook_Gauge_Pull `F_{hook}` = 9.20 gf (B4, far above the `3.0` gf MIL-STD-883 minimum!), Ball_Leg_Angle `theta_1` = 32.0° (B5), and Stitch_Leg_Angle `theta_2` = 24.0° (B6): Resolved Axial Wire Tension equals `9.82` gf (`79%` of wire UTS, E5)!

Wire-Bond Ball Geometry & MIL-STD-883 Trigonometric Hook-Pull Resolution Formula

Validate `Wire_Diam d` in `[12, 500]` um, `UTS` in `[100, 1,200]` MPa, `Hook_Pull > 0.2` gf, and loop leg angles `theta_1, theta_2` in `[5°, 75°]`!

=LET(dw_u, B2, ut_m, B3, fh_g, B4, t1_r, B5 * (PI() / 180), t2_r, B6 * (PI() / 180), IF(OR(dw_u < 12, dw_u > 500, ut_m < 100, ut_m > 1200, fh_g <= 0.2, B5 < 5, B5 > 75, B6 < 5, B6 > 75), "Invalid Wire-Bond Input", ROUND(fh_g / (SIN(t1_r) + SIN(t2_r)), 2)))

Ultra-Low QFN Loop Profile (theta1 = 12°, theta2 = 10°) Trigonometric Neck-Snap Check

Flatten loop height on an ultra-thin QFN (`theta_1` B5 = 12°, `theta_2` B6 = 10°): `1 / (SIN(12°) + SIN(10°)) = 2.62x` magnifies `9.20` gf hook force to **`24.11` gf** in E5 (nearly `2x` the `12.40` gf wire breaking load—meaning the wire actually snaps at just `4.7` gf on the pull tester!)—explaining why low-loop packages use **Ball-Shear Testing (`JESD22-B116`)** alongside wire pull!

=IF(ISTEXT(E5), E5, ROUND((B3 * (PI() / 4) * ((B2 / 1000) ^ 2)) * (1000 / 9.80665), 2))

Further reading

• Arte Sheets Lesson — Two-Leg Bridle Sling Angle Tension & WLL Formula
• Arte Sheets Lesson — SMT Solder-Paste Stencil Area Ratio, Aspect Ratio & Volume