Shared reticle floorplan
heuristic shelf packing
Wafer step-and-repeat
full reticle field edge exclusion
| Project | Die (mm) | Area mm² | ×reticle | Reticle share | Gross/wafer | Yield | Good/wafer | Wafers→target | Indicative cost | $/good die |
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How the math works (and what it ignores)
Reticle packing
Each project places×reticle copies of its die into the shared field. Dies are arranged with a first-fit decreasing-height shelf heuristic (each die padded by the scribe width). Utilisation = Σ(die area)/field area. The shelf packer is a fast approximation, not an optimal 2D bin-pack — real reticle floorplans are hand-tuned, so treat the layout as illustrative.
Wafer step-and-repeat
The whole reticle field is stepped across the wafer on a(fieldW × fieldH) pitch. A field counts only if all four corners fall inside the usable radius r = wafer⌀/2 − edge exclusion. We try four half-pitch grid phases and keep the densest — mimicking how a stepper grid is centred. Gross dies for a project = (copies in reticle) × (fields per wafer).
Yield (random-defect-limited)
Per-project die areaA (cm²) and defect density D₀ give the random-defect yield, then multiplied by a systematic factor Y₀:
· Poisson:
Y = e^(−A·D₀)
· Murphy:
Y = ((1−e^(−A·D₀))/(A·D₀))²
· Seeds:
Y = e^(−√(A·D₀))
· Neg-binomial (clustered):
Y = (1 + A·D₀/α)^(−α)
This captures only random-defect loss × a flat systematic factor. It excludes parametric yield, edge-die effects beyond the corner test, test/assembly loss, and reticle-stitching. Bigger dies yield worse — that's real and intentional.