Spatial Pattern Detection¶

The library provides two complementary analysis systems that both surface results as findings in the summary panel:

Statistical region analysis (covered in §10 of the User Guide) compares specific zones of the wafer — rings, quadrants, angular sectors, contiguous clusters, and edge arcs — against the rest of the wafer using significance tests. It answers: "is this ring statistically worse than the rest?" or "is there a contiguous cluster of failures here?" These findings are driven by p-values and effect sizes, so they have explicit statistical backing.

Spatial pattern classification (this page) looks at the overall shape of the failing die population and labels it with a named pattern: edge-ring, center cluster, scratch, and so on. It answers: "what kind of spatial failure is this wafer showing overall?" This is geometry-based, not statistical — it characterises the whole-wafer failure signature rather than testing individual zones.

Both systems run together when you call analyzeWaferMap. The spatial pattern finding appears alongside the statistical findings in the same panel — you will often see a spatial-pattern headline ("Edge-ring") supported by correlated statistical findings ("Ring 4 (edge) yield is 34 points lower than the rest"). The statistical findings are the evidence; the pattern label is the interpretation.

The library automatically analyses each wafer's failing die distribution and classifies it into one of several common spatial failure patterns. The result appears as a finding in the summary panel, with the affected dies highlighted on the wafer map. Engineers can use this as a first-pass triage signal — a prompt for investigation, not a definitive process diagnosis.

Patterns detected¶

How it works¶

The classifier uses pure geometry — no trained model, no external dependencies, no network calls. For each wafer it:

1. Finds the largest connected cluster of failing dies (the "salient region")
2. Computes geometric features: radial distance distribution, centroid position, eccentricity, edge-zone coverage, and linear/diagonal collinearity
3. Applies a rule-based classifier calibrated against real wafer data

Because it works directly from die coordinates and bin data, it functions on any wafer regardless of diameter, die size, or coordinate system.

Benchmark results¶

The classifier was tested against the WM-811K dataset — 25,519 labelled wafers from real-world TSMC 300mm fabrication, collected across 46,293 lots (Wu et al., IEEE Transactions on Semiconductor Manufacturing, 2015).

Overall exact-match accuracy: 64%

Detection rate: 86.2% — the more operationally useful number. This means that for 86 out of 100 wafers with a genuine spatial pattern, the library correctly flags some pattern (even if the specific label is occasionally wrong). Only 14% of patterned wafers are missed entirely (returned as random).

The distinction matters: an engineer reviewing a panel where a center-cluster wafer is labelled as "donut" still gets a useful signal pointing to a symmetric, wafer-centre-related process issue. A wafer labelled "random" when the pattern is borderline scratch gets no spatial hint at all — those are the true misses.

Combined detection rate: 99% — when the spatial pattern classifier and the statistical regional analysis (rings, sectors, clusters, edge arcs) are considered together, 99 out of 100 patterned wafers produce at least one relevant finding. The 14% of wafers the classifier misses are largely recovered by the regional analysis firing on the same underlying signal through a different mechanism. See the detection analysis notes for the full investigation.

Known limitations¶

Center and donut are easily confused. Both patterns have their failing dies near the wafer centre with low edge loading. At real wafer noise levels their geometric signatures overlap heavily — the classifier achieves only 60%/15% recall respectively and will sometimes call one the other. If center vs donut discrimination matters for your analysis, treat these two labels together as "symmetric centre/annular pattern" and use the wafer map visually to distinguish them.

Scratch recall is limited (~26%). Real scratch patterns often fragment into many disconnected die-sized pieces along the scratch path, particularly at typical semiconductor die pitches (5–15mm). The geometry features work best on clean, contiguous scratches — fragmented or faint scratches tend to fall through to "random".

Calibrated on WM-811K (TSMC 300mm). The thresholds were derived from one specific fab and process node. Wafers from significantly different die pitches, wafer sizes, or process types may show different geometric signatures. The geometry features are radially normalised so they transfer well across different wafer diameters and die pitches; the classifier thresholds themselves are fixed at the WM-811K calibration.

Multi-pattern wafers get one headline label. The spatial-pattern finding reports the single geometrically dominant pattern. However, the independent statistical findings — cluster, edge-arc, ring, and sector analyses — run separately and will surface both signals. For example, a wafer with both an edge-ring and a scratch will show one spatial-pattern headline ("Edge-ring" or "Scratch", whichever dominates) but will also carry a cluster finding for the scratch and ring findings for the edge loading. The full picture is in the findings list, not just the headline.

The label is a prompt, not a diagnosis. The classifier has no knowledge of your process, equipment, or lot history. A detected edge-ring finding means "the failing die distribution is consistent with an edge-ring pattern" — not that any specific piece of equipment is faulty.

Using it¶

Pattern classification runs automatically as part of analyzeWaferMap and appears in the findings panel. No configuration is required.

import { buildWaferMap, analyzeWaferMap } from '@paulrobins/wafermap';

const result = buildWaferMap({ results, waferConfig, dieConfig });
const summary = analyzeWaferMap(result, { passBins: [1] });

const patternFindings = summary.findings.filter(
  f => f.comparison.family === 'spatial-pattern'
);
// patternFindings[0].comparison.left  → e.g. "Edge-ring"
// patternFindings[0].summary          → human-readable description
// patternFindings[0].highlight.dieKeys → the failing dies

To disable it:

const summary = analyzeWaferMap(result, {
  passBins: [1],
  enablePatternClassification: false,
});

Using the geometry features directly¶

The geometry features computed for each wafer are exposed in the PatternClassification return value from classifyPattern. You can call this function directly and use the features object as input to your own model or reporting pipeline:

import { buildWaferMap } from '@paulrobins/wafermap';
import { classifyPattern } from '@paulrobins/wafermap/stats';

const result = buildWaferMap({ results, waferConfig, dieConfig });
const classification = classifyPattern(result.dies, result.wafer, {
  passBins: [1],
});

// classification.features contains:
// globalRdd, edgeRdd, p25DistNorm, centroidDistNorm,
// eccentricity, linearScore, edgeAngularSpread, innerOuterRatio, ...

These features are radially normalised and work at any wafer size or die pitch, making them suitable as input to a trained classifier if higher accuracy is needed for your specific process. Published CNN-based classifiers achieve 96–99% exact-match accuracy on WM-811K when trained on labelled examples — the PatternFeatures struct provides a compact, interpretable feature vector that can serve as input to such a model without requiring pixel-level wafer images.