Die Yield Calculator - Calculator Academy

Calculate good dies per wafer, wafer area, die size, or defect density from any three values using circular wafer yield equations.

Die Yield Formula

The calculator estimates good dies per wafer by first estimating gross dies per wafer with an edge-loss approximation, then multiplying by a Poisson yield fraction based on defect density and die area.

G = \left(\frac{W_a}{A} - \sqrt{2\pi\frac{W_a}{A}}\right)e^{-D_0A}

N_g = \frac{W_a}{A} - \sqrt{2\pi\frac{W_a}{A}}

Y = e^{-D_0A}

D_0 = \frac{-\ln(G/N_g)}{A}

W_a = A\left(\frac{\sqrt{2\pi}+\sqrt{2\pi+4N_g}}{2}\right)^2,\quad N_g = Ge^{D_0A}

G = \left(\frac{W_a}{A} - \sqrt{2\pi\frac{W_a}{A}}\right)e^{-D_0A}\quad\text{solved numerically for }A

G = estimated good dies per wafer
W_a = wafer area
A = die or chip area
D₀ = defect density
N_g = estimated gross dies per wafer before defect losses
Y = die yield fraction from the Poisson defect model

The calculator converts wafer area and die area to mm² internally. It converts defect density to defects/mm² internally.

Good dies per wafer: uses gross dies multiplied by the Poisson yield fraction.
Defect density: calculates gross dies first, then solves the Poisson equation for defect density.
Wafer area: backs out the required gross die count, then solves the edge-loss gross die equation for wafer area.
Die area: solves the full good-dies equation numerically because die area appears in both the gross die term and the exponential yield term.

Common Wafer Areas and Yield Fractions

If you know wafer diameter but not wafer area, use the full circular area as a starting point. Real usable area may be lower if edge exclusion or process-specific limits apply.

Wafer Diameter	Full Circular Area	Area in cm²
100 mm	7,854 mm²	78.54 cm²
150 mm	17,671 mm²	176.71 cm²
200 mm	31,416 mm²	314.16 cm²
300 mm	70,686 mm²	706.86 cm²
450 mm	159,043 mm²	1,590.43 cm²

Defect Density	Yield Fraction, 50 mm² Die	Yield Fraction, 100 mm² Die	Yield Fraction, 200 mm² Die
0.0001 defects/mm²	0.9950	0.9900	0.9802
0.0005 defects/mm²	0.9753	0.9512	0.9048
0.0010 defects/mm²	0.9512	0.9048	0.8187
0.0050 defects/mm²	0.7788	0.6065	0.3679

Example Problems

Example 1: Calculate good dies per wafer

Suppose you enter:

Wafer area = 10,000 mm²
Die area = 100 mm²
Defect density = 0.001 defects/mm²

Gross dies are estimated as:

N_g = 10000/100 - \sqrt{2\pi(10000/100)} = 74.9337

The Poisson yield fraction is:

Y = e^{-0.001(100)} = 0.904837

Estimated good dies per wafer:

G = 74.9337(0.904837) = 67.803

Example 2: Calculate defect density

Suppose you enter:

Wafer area = 10,000 mm²
Die area = 100 mm²
Good dies per wafer = 60

Using the same gross die estimate of 74.9337, the yield fraction is:

Y = 60/74.9337 = 0.800706

Defect density is:

D_0 = -\ln(0.800706)/100 = 0.002223\text{ defects/mm}^2

FAQ

Why is the gross die count lower than wafer area divided by die area?

Wafer area divided by die area assumes every part of the circular wafer can be filled with complete rectangular dies. In practice, dies near the curved edge are partly outside the wafer and cannot be counted as complete dies. The calculator uses an edge-loss approximation to subtract those partial dies.

Can the result be a decimal number of good dies?

Yes. The result is an expected average, not a physical count from one wafer. A real wafer produces a whole number of good dies, but the model can return a decimal because it estimates the average result from area, die size, and defect density.

How do defects/cm² convert to defects/mm²?

There are 100 mm² in 1 cm², so divide defects/cm² by 100 to get defects/mm². For example, 0.05 defects/cm² equals 0.0005 defects/mm². The calculator handles this conversion when you choose the defect density unit.

Die Yield (Good Dies per Wafer) Calculator