Enter the wafer area, die (chip) area, and defect density into the calculator to estimate the number of good dies per wafer. (In industry, “yield” is often reported as a fraction/percentage; this calculator’s “Die Yield” field is an estimated count of good dies per wafer.)

Die Yield (Good Dies per Wafer) Calculator

Enter any 3 values to calculate the missing variable

Die Yield Formula

The following approximation is used to estimate the number of good dies per wafer from wafer area, die area, and defect density (assuming random defects with a Poisson yield model and a simple circular-wafer edge-loss correction).

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

Variables:

  • Ngood is the estimated number of good dies per wafer (dies/wafer)
  • Wa is the wafer area (e.g., mm²)
  • A is the die (chip) area (e.g., mm²)
  • D0 is the defect density (e.g., defects/mm²)
  • e is the base of the natural logarithm (~2.71828)
  • π is a mathematical constant (~3.14159)

First estimate the gross number of dies per wafer with an edge-loss correction: (Wa/A) − √(2π·Wa/A). Then estimate the yield fraction using the Poisson model e−D0A. Multiply gross dies by the yield fraction to get the estimated number of good dies per wafer.

What is a Die Yield?

In semiconductor manufacturing, die yield usually means the fraction (or percentage) of dies that are functional. A common simple model for yield is the Poisson yield model, where yield ≈ e−D0A (defect density × die area). If you also estimate how many dies fit on a wafer (gross dies per wafer), you can multiply gross dies by the yield fraction to estimate the number of good dies per wafer.

How to Calculate Die Yield?

The following steps outline how to estimate good dies per wafer using the formula above:

  1. Gather the values of Wa (wafer area), A (die area), and D0 (defect density).
  2. Compute the estimated gross dies per wafer: Gross ≈ (Wa/A) − √(2π·Wa/A).
  3. Compute the yield fraction using the Poisson model: Yield fraction ≈ e−D0A.
  4. Multiply to get estimated good dies per wafer: Ngood ≈ Gross × Yield fraction.
  5. After calculating the result, check your answer with the calculator above.

Example Problem:

Use the following values as an example problem to test your knowledge:

Wa = 1000 mm²

A = 10 mm²

D0 = 0.05 defects/mm²

Gross ≈ (1000/10) − √(2π·1000/10) ≈ 74.93 dies/wafer

Yield fraction ≈ e−(0.05·10) = e−0.5 ≈ 0.60653

Ngood ≈ 74.93 × 0.60653 ≈ 45.46 good dies/wafer