Enter the wafer area, chip size, defect density, and chip area into the calculator to determine the die yield.

Die Yield Formula

The following formula is used to calculate the die yield. 

Y = (Wa / (S + 2Sqrt(A * D)))^2 * e^{(-π * D * (D / A))}

Variables:

  • Y is the die yield (number of good chips)
  • Wa is the wafer area (square millimeters)
  • S is the size of the chip (square millimeters)
  • D is the defect density (defects per square millimeter)
  • A is the area of a single chip (square millimeters)
  • e is the base of the natural logarithm (~2.71828)
  • π is a mathematical constant (~3.14159)

To calculate the die yield, divide the wafer area by the sum of the chip size and twice the square root of the product of the chip area and the defect density. Square this quotient. Multiply the defect density by π and the ratio of the defect density to the chip area, then take the negative of this product. Raise e to the power of this result. Multiply these two results together to get the die yield.

What is a Die Yield?

Die yield refers to the number of good, usable chips that can be obtained from a single silicon wafer during the manufacturing process. It is a critical factor in semiconductor manufacturing as it directly impacts the cost and efficiency of production. The die yield is influenced by various factors such as the size of the chip, defects in the wafer, and the precision of the manufacturing process. A higher die yield means more functional chips per wafer, leading to lower production costs.

How to Calculate Die Yield?

The following steps outline how to calculate the Die Yield using the given formula:

  1. First, gather the values of the variables: Wa, S, D, A, e, and π.
  2. Next, substitute the values of the variables into the formula: Y = (Wa / (S + 2Sqrt(A * D)))^2 * e^(-π * D * (D / A)).
  3. Then, perform the calculations within the formula.
  4. Finally, calculate the Die Yield (Y).
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem:

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

Wa = 1000 mm^2

S = 10 mm^2

D = 0.05 defects/mm^2

A = 5 mm^2

e = 2.71828

π = 3.14159