Spatial Pattern Detection¶

For: developers enabling pattern classification, and engineers wanting to know what the pattern labels mean and how far to trust them.

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

Statistical region analysis (covered in Guide: Adding statistical findings) 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, the fail rate in five rings of equal width, centroid position, edge-zone coverage, and the width and length of the salient region along its own principal axis (with the fragments that continue it along the same line)
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 production, collected across 46,393 lots (Wu et al., IEEE Transactions on Semiconductor Manufacturing, 2015).

Overall exact-match accuracy: 71%

Detection rate: 88.0% — the more operationally useful number. This means that for 88 out of 100 wafers with a genuine spatial pattern, the library correctly flags some pattern (even if the specific label is occasionally wrong). 12% 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 12% 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¶

A donut is read from its radial profile. A band of failures at mid-radius, at least 15 points above both the centre and the rim, is a donut whatever its connected groups look like; a symmetric pattern on the centre that is not one is a centre cluster. A faint or partial donut can still read as a centre cluster or as random.

Scratch recall is 41%, precision 87%. A scratch is a thin line at any angle: at most 0.8 die pitches across its own axis, at least 8 pitches and 0.3 of the radius long, reaching in from the rim, with the fragments that continue it along the same line counted together. A faint scratch whose pieces are more than three pitches apart, or a short one, falls through to "random"; a thin line along the rim is edge-local, not a scratch.

Calibrated on WM-811K. The thresholds were derived from one fab's production data. 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. Clusters are also looked for in each failing hard bin on its own, so a spot of one bin that touches other failures (an edge ring of another bin, say) is still reported as that bin's cluster. 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 '@wafertools/wafermap';

const result = buildWaferMap({ results, waferConfig, dieConfig });
const summary = analyzeWaferMap(result);

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);
const withoutPattern = summary.findings.filter(f => f.comparison.family !== 'spatial-pattern');

Using the geometry features directly¶

To label a wafer, the classifier first measures the shape of its failing dies — how much of the wafer and of its edge is failing, where the failing cluster sits radially, how elongated and how line-like it is. analyzeWaferMap returns that measurement for every wafer as stats.spatialPattern, alongside the label and confidence:

import { buildWaferMap } from '@wafertools/wafermap';
import { analyzeWaferMap } from '@wafertools/wafermap/stats';

const result  = buildWaferMap({ results, waferConfig, dieConfig });
const summary = analyzeWaferMap(result);

summary.stats.spatialPattern;
// { pattern: 'edge-ring', confidence: 'high',
//   features: { globalRdd, edgeRdd, centroidDistNorm, minDistNorm, maxDistNorm,
//               p25DistNorm, innerOuterRatio, eccentricity, linearScore, ... } }

It is present on every wafer the classifier could measure, including those labelled 'random' or 'none', which raise no finding — so a set of summaries gives you features for negative examples as well as patterned ones. It is absent only when the map has no bin data, or too few failing dies to have a shape (fewer than 5, or 0.3% of the wafer).

The features are radially normalised and work at any wafer size or die pitch, which makes them suitable input for a trained classifier if you need more accuracy for your own process. Published CNN-based classifiers reach 96–99% exact-match accuracy on WM-811K when trained on labelled examples; these features are a compact, interpretable alternative to pixel-level wafer images.