Wafer Yield & Economics

Gross Die per Wafer

N = πD(D/4S − 1/√(2S)), D = usable diameter, S = die area incl. scribe.

Wafer diameter (mm)

Edge exclusion (mm)

Die width (mm)

Die height (mm)

Scribe (mm)

Defect-Limited Yield

Four standard models from die area & defect density D₀.

Die area (mm²)

Defect density D₀ (/cm²)

Clustering α (negative-binomial)

Cost per Good Die

Wafer + per-die back-end cost, divided by yielded die.

Wafer cost ($)

Gross die / wafer

Yield (%)

Package+test / die ($)

Known-Good-Die Stacking

3D / chiplet composite yield = Y_die^N · Y_bond^(N−1).

Per-die yield (%)

Die in stack N

Per-bond yield (%)

Formula reference

Gross die/wafer: N=πD(D/4S − 1/√(2S)) where D=diameter−2·edge-exclusion, S=(w+scribe)(h+scribe). The second term subtracts edge-die loss.

Yield models (let x=A·D₀, A in cm²): Poisson Y=e⁻ˣ; Murphy Y=[(1−e⁻ˣ)/x]²; Seeds Y=e⁻√ˣ; negative-binomial/Bose-Einstein Y=(1+x/α)⁻ᵅ (α = clustering).

Cost/good die: = wafer$/(gross·Y) + back-end$.

KGD stacking: Y=Y_die^N·Y_bond^(N−1) — each added die multiplies the yield loss (the known-good-die problem).