Two new tools: die layout and block harvesting yield

I’ve added two calculators to the site. Both started with questions I often run into when looking at chips, so I built tools to explore them and made them available for everyone to try.

The first is the Die Layout Optimizer (OWE / MFU). The second is the Block Harvesting Yield Demo. The harvesting tool is still under testing and currently covers manufacturing defects only. PVT and frequency yield are excluded.

Same area, different dimensions: does it matter?

Take a 100 mm² die. A 10 × 10 mm square and a rectangle with the same area can fit differently on a wafer and inside an exposure field.

The layout calculator starts at 100 mm². Set the wafer diameter, edge exclusion, scribe lanes and maximum exposure-field dimensions, then search for candidate layouts. If you already know the die dimensions, use fixed-dimensions mode. You can inspect the wafer map and export PNG or CSV results.

Here is what the metrics mean in this tool:

Metric	Calculation
DPW	Number of complete dies that fit on one wafer
OWE	DPW × die area ÷ total wafer area
MFU	Dies per exposure field × die area ÷ maximum exposure-field area
MOWE	OWE × MFU, used as a combined ranking score

MFU uses the exposure-field area, not the area of the mask glass. MOWE is a ranking score, not a yield or manufacturing-cost estimate.

In area mode, the search enumerates dimensions on a 0.01 mm grid and evaluates different placement offsets. A die is counted only if all four corners lie inside the usable wafer circle and it clears the notch keep-out boundary. The exposure array must fit the field limits, with scribe lanes included in its footprint.

Litho shots means the number of exposures per wafer, for one reticle and one lithography layer, under the selected layout. The tool adjusts array grouping on the selected die grid to compare how many exposures are needed to cover all complete dies.

The highest DPW, highest MFU and fewest shots may come from different layouts. Offset sampling is finite, so these are candidates within the search settings, not a guaranteed global optimum over every possible placement. If you allow area tolerance, check the actual die area too: some DPW gains may come from a smaller die rather than a better aspect ratio.

Can disabling defective modules recover usable dies?

The second tool asks a different question: if a CPU or GPU can operate with some modules disabled, how many otherwise unusable dies could still meet the retained-module requirement?

Enter total die area and defect density D₀. For each module group, provide a name, count, area per module and maximum number that may be disabled. CPU and GPU blocks can have separate groups and limits. All remaining area is treated as shared circuitry that must function.

Shared area = total die area − sum of (module count × area per module)

For example, eight disableable cores at 2 mm² each occupy 16 mm² of a 100 mm² die. The remaining 84 mm² must be free of fatal defects.

The calculation first estimates each module’s probability of a fatal defect, then checks whether the failed-module count stays within that group’s limit. Every group must pass, and the shared region must pass as well.

For the Poisson model, D₀ is measured in defects/cm². Divide areas in mm² by 100 to convert them to cm² before applying the formulas:

Probability that one module passes: p = exp(−D₀ × module area)
Group allowing at most m failures: sum the probabilities of 0, 1, …, m failures
Whole-die pass probability = shared-region pass probability × product of group pass probabilities

Failed-module counts follow a binomial distribution within each group. Several defects in one module still count as one failed module. A spare CPU disable allowance cannot compensate for an extra failed GPU module.

In Murphy mode, the whole die shares a random defect density. The tool calculates the joint pass probability at each density and then takes a weighted average; it does not multiply separately averaged Murphy yields for each group. The density multiplier follows a triangular distribution from 0 to 2, peaking at 1, and scales D₀. With no disabling allowed, this returns the baseline formula [(1 − exp(−A × D₀)) / (A × D₀)]², where A is total die area in cm². At D₀ = 0, defect yield is 100%.

For the eight-core example, with D₀ = 1, Murphy mode and at most one disabled core, estimated defect yield rises from 39.96% to 45.36%. The difference is 45.36% − 39.96% = 5.40% of all fabricated dies. The tool allows any one failed core to be disabled; it does not simply subtract one core’s area and recalculate.

The tool is labeled Demo (Testing). It assumes equal-area, interchangeable modules within each group and reliable isolation of failed modules. Physical area approximates defect-sensitive area. The joint-density model used to extend Murphy yield to module harvesting is a modeling assumption and has not been calibrated against production silicon.

Use it to compare choices such as allowing one more module to be disabled. The result is a manufacturing-defect estimate, not final product yield or a production guarantee. PNG exports contain the parameters, main results and selected-group curve; CSV includes complete bin data for all groups. Both retain the Demo label.

Both tools are in the site’s Calculators menu. Try your own dimensions and module configurations, and let me know if anything looks off.