Wafer Yield Console
Drag die area or defect density and watch yield move along the curve in real time, across all five standard models — Poisson, Murphy, negative-binomial (clustering), Seeds and Bose–Einstein. The clustering-aware negative-binomial is the fab sign-off standard; the rest show the spread.
Die area + defect density → yield, instantly.
Yield-vs-area console
- Poisson92.2%
- Murphy92.3%
- Negative binomial (α=3)92.3%
- Seeds92.5%
- Bose–Einstein (n=12)39.3%
The five yield models
| Model | Formula | Best for |
|---|---|---|
| Poisson | Y = e^(−A·D0) | Quick pessimistic bound; random defects. |
| Murphy | ((1−e^(−A·D0))/(A·D0))² | Classic; averages a triangular D0 spread. |
| Negative binomial | (1 + A·D0/α)^(−α) | Fab standard; α fits real clustering. |
| Seeds | 1/(1 + A·D0) | Heavy-clustering limit (α → 1). |
| Bose–Einstein | 1/(1 + A·D0)^n | Multi-layer; n = critical mask layers. |
Where the money is
Cost-per-good-die = wafer cost ÷ (dies × yield). A drop from 80% to 60% yield raises the cost of every shipped chip by a third — before anything else changes.
A node launches near D0 ≈ 0.3 and marches toward 0.05 over a couple of years. The same die that yields 50% at launch can yield 85% at maturity — pure profit, no redesign.
Yield falls exponentially with area: double the area and the chance of a killer defect roughly squares. A reticle-limit AI die yields far worse than a mobile SoC on the same line.
Poisson assumes perfectly random defects and is pessimistic; the negative-binomial model with a clustering factor α matches measured fab data far better — the gap can be 10+ points of yield.
Yield: the number that decides whether a chip is a business
Two fabs can run the same design on the same node and one makes money while the other doesn't — the difference is yield. Of all the levers in chip economics, the fraction of dies that actually work most directly turns a wafer's fixed cost into sellable product, and it's the one engineers can move most.
The foundation is one elegant idea: if killer defects land randomly at an average rate, the chance a die escapes them all follows the Poisson distribution — Yield = e^(−A·D0), where A·D0 is the mean defects per die. It's clean and slightly wrong, because real defects cluster. Capturing that is what Murphy's triangular average and especially the negative-binomial model (with an explicit clustering parameter α) do — and the gap between Poisson and a calibrated negative binomial can be ten points of yield, the difference between a viable product and a canceled one.
Die size dominates because of the exponential: a die that yields 90% at 1 cm² yields ~67% at 4. That's why a reticle-limit AI accelerator has brutal economics where a mobile SoC prints money, and the strongest argument for chiplets. Yield is also a curve over time — a new node improves along a learning curve as the fab hunts defects, so the same design gets cheaper to make every quarter with no redesign.
Use this as the second leg of the cost tripod: Die Per Wafer gives the gross count, this gives the working fraction, and multiplying them feeds Wafer Cost — the figure that actually matters: cost per good chip.
Trusted by Yield, Process & Cost Teams
“Finally a yield tool that shows all the models side by side on a live curve. Toggling Poisson vs negative-binomial with our α makes the clustering point land instantly with design teams. Matches our internal sign-off numbers.”
“The yield-vs-area curve is exactly the picture I draw on whiteboards, now live. Dragging D0 and watching our die move along the curve made the defect-reduction roadmap concrete for the whole team.”
“Pairs perfectly with the die-per-wafer console. Gross × this yield × wafer cost gives cost-per-good-die in under a minute across nodes. The reality anchors connect yield to dollars better than my old spreadsheet.”
“Clean, fast, genuinely educational. For memory I'd love a redundancy-uplift input, but as a defect-limited baseline across Poisson/Murphy/NB it's the best free option I've found.”
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Defect-limited yield models (Murphy 1964; Stapper negative-binomial) · Last reviewed: 2026-06