Wafer map defect recognition is commonly formulated as a fixed-taxonomy classification problem that assigns each wafer to a single defect class. However, some wafers exhibit morphologies near class boundaries, for which forcing a single prediction may be less informative than providing plausible diagnostic alternatives. This paper proposes a morphology-aware ambiguity learning framework that supports three diagnostic actions: automatic single-class diagnosis, assisted diagnosis with two plausible defect classes, and full review. Using the radial, angular, and geometric characteristics of training wafer maps, the framework constructs a class-level ambiguity matrix representing defect-class pairs with similar morphology and plausible diagnostic alternatives. It guides the model to learn plausible alternative classes rather than treating all incorrect classes equally. During inference, the matrix determines whether an uncertain prediction can be represented by a meaningful two-class diagnostic set or should be escalated for full review. Experiments on WM-811K show that the proposed framework outperforms conventional approaches in defect recognition and diagnostic decision support, providing meaningful two-class alternatives while reserving full review for cases with unresolved ambiguity. Illustrative cost analyses further show the potential cost advantage of the proposed routing strategy. The diagnostic behavior of the framework remains consistent across different backbone architectures.
Figures & tables
Figure 1: Representative wafer maps illustrating class taxonomy and boundary ambiguity. (a) Examples of the nine WM-811K classes; no class has a single canonical morphology. (b) Wafers from different annotated classes with visually similar defect morphologies.
y
Class name
Diagnostic role
0
Nonpattern
No identifiable failure pattern
1
Center
Defect concentrated at wafer center
2
Donut
Ring-shaped defect around the center
3
Edge-Loc
Localized cluster on the wafer edge
4
Edge-Ring
Full peripheral ring
5
Loc
Localized cluster away from the edge
Table 1: Fixed class indexing used throughout the paper. Labels 1 – 8 constitute the defect block Yd .
Figure 2: Overview of the proposed framework. The ambiguity matrix Amorph derived from wafer morphology plays a key role in both training and inference. During training, it defines morphology-aware soft targets. During inference, it determines whether the top-2 predictions form a plausible two-class diagnostic set.
Figure 3: The morphology descriptor ϕ(x) on an Edge-Loc wafer. (a) Radial defect profile over ten concentric bins. (b) Defect density over twelve peripheral sectors and its rotation-invariant angular spectrum; shaded bars are not part of the descriptor. (c) The seven scalar shape cues, each with the geometry it measures overlaid.
Method
Target structure
Macro-F1
Defect macro-F1
Defect bal. acc.
CE
Hard one-hot
0.9154 ± 0.0059
0.9176 ± 0.0049
0.8934 ± 0.0060
LS
Uniform across all classes
0.9109 ± 0.0063
0.9174 ± 0.0074
0.8914 ± 0.0142
Auniform
Uniform across defect classes
0.9093 ± 0.0090
0.9120 ± 0.0097
0.8863 ± 0.0112
Apixel
Raw-pixel-derived
0.9114 ± 0.0043
0.9138 ± 0.0038
0.8855 ± 0.0095
Amorph
Morphology-derived
0.9201 ± 0.0076
0.9245 ± 0.0082
0.9009 ± 0.0153
Table 2: Classification performance and structural ablation on WM-811K using ResNet-34.
Class
Samples
Amorph
Auniform
Δ F1
Center
859
0.9512 ± 0.0015
0.9493 ± 0.0060
+0.0020
Donut
111
0.8915 ± 0.0100
0.8781 ± 0.0307
+0.0134
Edge-Loc
1,038
0.8777 ± 0.0154
0.8600 ± 0.0101
+0.0177
Edge-Ring
1,936
0.9840 ± 0.0038
0.9801 ± 0.0049
+0.0038
Loc
718
0.8431 ± 0.0085
0.8195 ± 0.0122
+0.0236
Near-full
30
0.9583 ± 0.0326
0.9546 ± 0.0348
+0.0037
Table 3: Per-class F1 on ResNet-34. Samples are test-set counts, identical across seeds because the split is stratified. Δ F1 denotes the difference between the two matrices.
Automatic
Assisted
Full review
Coverage
94.2%
1.9%
3.8%
Top-1 acc.
99.75%
77.1%
74.1%
Top-2 incl.
–
95.2%
96.1%
Table 4: Three-way diagnostic routing under Amorph at the default operating point (τconf,τA)=(0.95,0.015) using ResNet-34.
Assisted set
Full review
Annotated class
n
Share
Top-2 incl.
n
Share
Top-2 incl.
Nonpattern
21
3.2%
0.0% †
782
58.7%
100.0%
Center
66
9.9%
97.3%
78
5.8%
93.9%
Donut
43
6.5%
96.1%
3
0.2%
47.5% †
Edge-Loc
229
34.2%
99.3%
222
16.7%
93.8%
Edge-Ring
62
9.3%
99.6%
27
2.0%
88.2% †
Table 5: Composition of the assisted and full-review groups by annotated class ( Amorph , ResNet-34). Counts are seed means rounded to the nearest integer; shares are the count divided by the group total. Each entry is rounded independently, so a column need not sum exactly to its total.
Figure 4: Operating-point behavior as τA varies. The morphology-derived matrix produces a gradual change in assisted-set volume, whereas the uniform matrix exhibits a discrete cliff at its single off-diagonal value, (1−δ)/(∣Yd∣−1)=0.0286 .
Variant
τA
α=0.1
α=0.2
α=0.3
α=0.5
No assisted action
–
0.0810
0.0810
0.0810
0.0810
Amorph
0.015
0.0636
0.0656
0.0675
0.0714
Auniform
0.015
0.0711
0.0737
0.0762
0.0812
Amorph
0.040
0.0709
0.0720
0.0732
0.0754
Auniform
0.040
0.0938
0.0938
0.0938
0.0938
Table 6: Expected per-sample routing cost on ResNet-34 under a common relative cost model. “No assisted action” removes the intermediate branch: a wafer that fails the confidence test is escalated rather than given a two-class set.
Automatic
Assisted set
Full review
Method
Coverage
Top-1
Coverage
Named-patterns
Top-2 incl.
Coverage
CE + confidence
93.9%
99.76%
4.8%
24.8%
98.1%
1.2%
Our framework
94.2%
99.75%
1.9%
100.0%
95.2%
3.8%
Table 7: Comparison of confidence-based routing and our framework. “Named-patterns” denotes the share of two-class outputs in which both classes correspond to named defect patterns, rather than one class being Nonpattern . Results are averaged over four seeds.
Table 8: Representative wafers that both approaches route to assisted diagnosis.
δ
Variant
Macro-F1
Defect macro-F1
0.5
Amorph
0.9161 ± 0.0096
0.9183 ± 0.0133
0.5
Auniform
0.9189 ± 0.0043
0.9221 ± 0.0082
0.8
Amorph
0.9201 ± 0.0076
0.9245 ± 0.0082
0.8
Auniform
0.9093 ± 0.0090
0.9120 ± 0.0097
0.9
Amorph
0.9113 ± 0.0029
0.9148 ± 0.0051
0.9
Auniform
0.9120 ± 0.0057
0.9150 ± 0.0042
Table 9: Sensitivity to the diagonal mass δ using ResNet-34 at the selected mixing coefficient λ=0.6 .
Backbone
Auto cov.
Auto top-1
Asst. cov.
Asst. top-2
ResNet-18
93.4%
99.80%
2.3%
95.7%
ResNet-34
94.2%
99.75%
1.9%
95.2%
ResNet-50
93.2%
99.77%
2.4%
95.9%
MobileNetV2
93.1%
99.76%
2.3%
95.6%
ShuffleNetV2
92.1%
99.79%
2.6%
95.8%
EfficientNet-B0
93.2%
99.79%
2.1%
96.3%
Table 10: Cross-backbone behavior of the selective diagnostic system under Amorph at the default operating point (τconf,τA)=(0.95,0.015) . Each entry is a mean over four seeds; the last row is the standard deviation across the seven backbones.
Hyperparameter
Value
Optimizer
AdamW
Learning rate
10−4
Weight decay
10−4
Batch size
64
Maximum epochs
50
Learning-rate schedule
Cosine annealing
Table S1: Default training hyperparameters.
Hyperparameter
Value
Radial bins Bρ
10
Angular sectors Bθ
12
Peripheral radius threshold ρedge
0.7
Hough accumulator threshold TH
3
Descriptor dimension
23
Diagonal mass δ
0.8
Table S2: Default descriptor and ambiguity-aware training hyperparameters.
δ
λ=0.3
λ=0.6
λ=1.0
0.5
0.9227
0.9226
0.9153
0.65
0.9229
0.9252
0.9229
0.8
0.9239
0.9314
0.9210
0.9
0.9266
0.9257
0.9234
Table S3: Validation defect macro-F1 over the (δ,λ) grid, ResNet-34 with Amorph . Each entry is a mean over four seeds; the selected setting is shown in bold.
Action under CE + confidence
Action under our framework
Wafers
( Nonpattern pairs excluded)
Assisted diagnosis
Assisted diagnosis
290
Full review
Assisted diagnosis
173
Automatic diagnosis
Assisted diagnosis
206
Assisted diagnosis
Automatic diagnosis or full review
124
Table S4: Diagnostic action returned for the same wafer by the two approaches, using ResNet-34 and averaged over four seeds. The CE-based variant excludes any pair containing Nonpattern . Each row is a disjoint group of wafers; counts are seed means rounded to the nearest integer.
Spatial defect signatures on wafer bin maps (WBMs) trace yield loss to specific process faults, yet supervised classifiers recognize only the defect types seen during training, and one-class detectors built on a single mechanism tend to capture either local structural deviations or global distributional violations, but rarely both. This work proposes a hybrid one-class framework that couples a patch-based student-teacher detector (EfficientAD) with a denoising diffusion probabilistic model (DDPM) used for partial-diffusion reconstruction, and fuses their percentile-calibrated scores through a fixed convex combination. Trained on only 700 normal wafers from the WM-38K mixed-type dataset and evaluated on 18,658 held-out wafers, the fused detector reached an AUROC of 0.9985 and reduced misclassifications from 852 (DDPM) and 1,412 (EfficientAD) to 618, with all pairwise differences significant at p < 0.001. Beyond aggregate accuracy, the analysis shows that the gain arises from weakly overlapping errors between the two modules, yet fixed-weight fusion recovers only 40-70% of the correction available to an oracle selector. Under the benchmark's inverted class balance, average precision and F1 saturate, while the Matthews correlation coefficient and negative predictive value expose unreliable normal predictions. Pixel-level maps further show that strong image-level separability does not imply spatial localization, and the diffusion module succeeds as a local density prior rather than through global geometric reasoning. These findings motivate sample-adaptive fusion and imbalance-aware evaluation of hybrid wafer anomaly detectors.
Limon Bin Hossain, Md Sadib Rahman Ananta
Department of Industrial and Production Engineering, Bangladesh University of Engineering and Technology (BUET), Dhaka, 1000, Bangladesh
In semiconductor manufacturing, defect analysis is essential, but manual inspection cannot scale. However, existing automated inspection methods remain insufficient for root-cause analysis and process optimization. To this end, we present SePArate, a weakly supervised wafer defect segmentation method. SePArate enables pixel-level separation of patterns by leveraging only image-level annotations. It consists of a three-phase training: encoder pretraining, knowledge transfer to learn spatial cues, and training on synthetic mixed-defect data for accurate segmentation. Experiments demonstrate that SePArate outperforms the baselines.
Conventional wafer defect analysis relies on offline, closed-world classifiers that fail to detect novel, unseen defect signatures emerging during continuous semiconductor manufacturing. To address this, we propose WaferHDC, an online open-world wafer defect discovery framework based on hyperdimensional computing (HDC). The memory-centric architecture of WaferHDC enables rapid anomaly detection and grouping of recurring failures into compact hypervector representations. This allows the memory space to dynamically scale with new defect modes without retraining a static classifier or archiving entire raw wafer history. WaferHDC first models normal spatial distributions, then dynamically groups recurring failures into persistent defect memory without labels or predefined class counts. It outperforms the strongest online baseline by 13.3 p.p. in adjusted Rand index and 10.5 p.p. in normalized mutual information on the industry-standard WM-811K dataset. These results demonstrate the effectiveness of WaferHDC for continuous and open-world wafer defect analysis.
Quanling Zhao, Ava Emami, Tsuyoshi Idé +4
University of California San Diego · IBM Research · Anderon