93.4%
SEM Balanced Accuracy
Carinthia semiconductor SEM · 4,579 images · 5-fold CV · ties the best classical baseline (Haralick) with 15 features
94.9%
Wafer Map Accuracy
MixedWM38 · 7,015 maps · 7.59× lift over Hu moments, which collapse to chance on wafer maps
0.9477
NIST Breach Ratio
PTD-Z envelope breach tracking across 3,402 NIST SEM degradation images. Pattern topology drift confirmed.
0
Learned Parameters
All 15 coordinates derived from image formation physics. No training required across any modality.
NILS
Edge Sharpness
Normalized Image Log Slope, standard lithography metrology quantity. Strongest reference-free focus indicator (R²=0.975 against |focus|). Leads on SEM; confirms coherent defocus in aerial images.
LER
Edge Roughness
Std of lateral contour deviation, normalized by image diagonal. Identically zero on coherent simulated aerial images, an independent negative prediction confirmed before any real data was examined.
δx,y
Centroid Geometry
Intensity-weighted centroid displacement. Largest residual route after classical descriptors in Carinthia and NFFA audits. Carries mesoscale organizational signal that texture and moment descriptors do not preserve.
d_s
Spectral Spread
FFT power spectrum center of mass. Encodes spatial frequency organization, coarse vs. fine structure. Leads on density-encoded binary wafer maps where defect topology is encoded in spatial frequency.
θ
Gradient Orientation
Dominant gradient direction weighted by magnitude. Detects scratches, line patterns, oriented defects. Part of pitch/phase route, the most defensible independence route in PTD-Z audits.
Φ
Route Grammar
PTD-Z decomposes 15 coordinates into six route families, each carrying a process-facing hypothesis (overlay, pitch drift, etch bias, focus) and a refusal condition blocking unsupported causal claims.
Finding 01 — Cross-Modality Transfer
Coordinate dominance shifts systematically with imaging physics
LER leads production SEM (physical edge roughness). μ and d_s dominate wafer maps (density + spatial frequency). This shift is reproducible across three independent datasets with no retraining, the framework tracks visual organization, not domain statistics.
Finding 02 — Hybrid Complementarity
Structural organization provides residual signal after classical descriptors
Adding PTD-Z to Classical_All improves Carinthia macro F1 by +0.0214 and NFFA by +0.0144. Hybrid systems outperform either alone. image_geometry and pitch_phase are the most defensible residual routes, they persist in independence audits where signal/noise and contrast drift toward overlap roles.
Finding 03 — Refusal as Method
The system knows what it cannot say
PTD-Z treats refusal as a first-class component. Each route carries a refusal condition: when the margin is thin, when the selected channel is support-heavy, when no process-linked sequence data exists. No public image dataset provides direct fab process-cause labels. PTD-Z withholds causal language when evidence is absent.
Finding 04 — Wafer Grammar
Constrained learned layer confirms coordinate signal
WM-811K wafer pattern grammar (4,149 maps, 9 classes): hand grammar alone reaches macro F1 0.5609. A constrained logistic layer over deterministic coordinates reaches 0.8859. Null-label shuffle collapses to chance, confirming the coordinates carry real class signal, not artifact.
