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Wafer Yield (Murphy Model) Calculator

Work out wafer yield (murphy model) instantly with clear inputs, formula shown and shareable results.

About Wafer Yield (Murphy Model) Calculator

Murphy's model assumes defect density varies across the wafer, giving Y = ((1 - e^-AD)/AD) squared. It sits between the pessimistic Poisson model, which assumes uniform random defects, and the negative binomial model that explicitly parameterises clustering. All three show yield collapsing as die area grows.

Formula

Murphy yield

Y = ((1 - e^(-A D0)) / (A D0))^2, with A in cm2 and D0 in defects per cm2

Worked example

With the default values below, Wafer Yield (Murphy Model) Calculator returns Murphy model yield of 84.734%. Change any input above and every figure here is recalculated in your browser.

Inputs used

Die area
48 mm²
Defect density
0.35 defects/cm²
Gross die per wafer
1,150 die
Clustering factor
2

Results

Murphy model yield
84.734% %
Good die per wafer
974 die
Poisson model yield
84.535% %
Negative binomial yield
85.102% %

Step by step

  1. 1Values used
  2. 2Murphy yield
  3. 3Murphy model yield= 84.734 %
  4. 4Good die per wafer= 974 die
  5. 5Poisson model yield= 84.535 %
  6. 6Negative binomial yield= 85.102 %

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why does Poisson under-predict yield?

Because defects cluster. Clustering means some regions carry many defects while others are clean, so more die escape entirely than uniform statistics predict.

Why is die area so critical?

Yield falls roughly exponentially with area. Doubling die area can easily halve yield, doubling cost per good die on top of the halved die count.

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