WaferGenie™ is a free, browser-based wafer map explorer. Pick a wafer size and die size, see how many dies fit, simulate defects and yield, estimate cost per good die, and learn how each number is worked out.
Zoom with the mouse wheel or the + and - buttons, drag to pan, hover over a die for its details and click a die to ink it. Feature requests are welcome in the comments.
Dies per wafer
The map places a grid of die "steps" (die size plus scribe line) across the wafer and counts every die that sits fully inside the usable area, which is the wafer minus the edge exclusion ring. Dies that are cut by the edge are partial dies: they are printed but cannot be sold.
A common quick estimate is DPW ≈ πd² / (4S) - πd / √(2S), where d is the usable wafer diameter and S is the die step area. The first term is wafer area divided by die area; the second subtracts the dies lost around the edge. The exact count from the map is usually close, and the difference shows why placement matters.
Why grid placement matters
Shifting the whole die grid by a fraction of a die changes how many dies fit inside the circle, often by a few percent for large dies. Optimise placement tries many offsets and keeps the one with the most full dies. Fabs and design teams do the same when they set the wafer map for a new product.
Defect density and yield models
Defect density D0 is the number of killer defects per cm². Bigger dies catch more defects, so yield falls as die area A grows. The models differ in how they treat defect clustering:
| Model | Formula | Assumption |
|---|---|---|
| Poisson | Y = e-AD | Defects are fully random; the most pessimistic for large dies |
| Murphy | Y = ((1 - e-AD) / AD)² | Defect density varies across wafers; widely used as a middle ground |
| Seeds | Y = 1 / (1 + AD) | Strong clustering; the most optimistic |
| Negative binomial | Y = (1 + AD/α)-α | Clustering set by α: small α means heavy clustering, large α approaches Poisson |
Clustering helps yield: if defects bunch together, several land on the same bad die and more dies elsewhere stay clean.
Wafer map failure signatures
Engineers read the spatial pattern of failing dies to find the root cause. Typical signatures:
- Random: particles from the environment or tools; tracked as D0.
- Clustered: a local contamination event or a tool-specific particle source.
- Edge ring: edge bead, film thickness or etch non-uniformity near the wafer edge.
- Centre spot: centre-to-edge process variation, for example in deposition, CMP or spin coating.
- Donut: a ring of failures between centre and edge, often from a radial process step.
- Scratch: wafer handling or CMP damage, seen as a line of failing dies.
Pick a signature under Defects and yield and compare the simulated yield with the model.
Cost per good die
Cost per good die = processed wafer cost ÷ good dies per wafer. It rises quickly with die size, because a bigger die means fewer dies per wafer and a lower yield at the same time. That is one reason large chips move to chiplets.
Lithography fields and shots
A scanner exposes one reticle field at a time; the largest standard field is 26 × 33 mm. Several small dies fit in one field, while a die larger than the field cannot be printed in one exposure. Fewer shots per wafer means higher scanner throughput. Turn on Show field grid to see the shots.
All results are teaching estimates using simple geometric and statistical models, not a replacement for a foundry's own wafer map and yield tools. © Murugavel Ganesan, The Digital Electronics Blog.
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