Industrial Defectivity Prediction (IDP) V6: A Two-Layer Yield Cliff Framework for Cross-Industry Mass-Production Forecasting

Version 4: Added explicit comparison with 

existing HDE models and expanded semiconductor 

yield prediction section as primary contribution.

Version note (V5, 2026.04.27)

V5 is a substantial redesign of the semiconductor yield model introduced in V4. The cosmological component (Landauer-Holographic coupling, k ≈ 0.206) is unchanged.

Key changes from V4:

1. Collinearity fix — The V4 information-cascade term (ΔS) was found to be strongly correlated with defect density D, providing no independent predictive signal. V5 replaces it with an EUV-fraction term (f_EUV), which is structurally orthogonal to D and identically zero on pre-EUV nodes.
2. Learning-curve term added — V5 introduces a maturity attenuation factor L(t) to capture the 20–30pp yield variation between risk production and high-volume manufacturing — a dynamic absent from V4.
3. Parameter reduction — Three free parameters (k, β, γ) reduced to two (θ, τ), improving parsimony and reducing overfitting risk.
4. Expanded and cross-validated dataset — Validation extended from 11 data points (V4, in-sample only) to 55 samples across 17 process nodes with 5-fold cross-validation. V4's reported +6.9% MAE gain does not survive cross-validation (degrades ~10% vs. baseline under LOO); V5 achieves +30.1% CV-validated improvement.
5. EUV-specific performance — V5 reduces MAE by 61.2% on the EUV node subset (7nm–2nm, n=20), where the redesigned correction is structurally active.

Version note (V6, 2026.05.06)

V6 extends the V5 framework with a second-layer cliff threshold transition, introducing both single-cliff and two-cliff valley variants. The V5 first-layer information-loss correction (with Landauer-Holographic coupling) is retained unchanged. V6 adds explicit cliff-transition phenomenology and generalizes validation from semiconductor-only to nine industries.

Key changes from V5:

1. Two-layer structure formalized — V5 captured maturation-driven yield attenuation through L(t); V6 adds an explicit cliff-threshold layer multiplied on top, separating two phenomena that V5 conflated. The single-cliff variant uses a sigmoid threshold; the two-cliff valley variant is structurally compatible with the Imec stochastic valley framework (De Bisschop, Leray; SPIE 2020) while extending it through V5's maturation factor.

2. Cross-industry validation expanded — V5 was validated on semiconductor only (n=55, 17 process nodes). V6 extends validation to nine industries: semiconductor (n=40), pharmaceutical (n=15), quantum computing (n=15), solar PV (n=14), battery NMC (n=14), display (n=13), defense (n=12), solid-state battery (n=12), battery LFP (n=10). Six of nine show strong fit (rho > +0.98); two-cliff variant required only for semiconductor.

3. Function-form equivalents formalized — sigmoid threshold form is universally optimal across nine industries; tanh, probit, and Hill variants admitted as doctrine-of-equivalents extensions. Tanh provides -10% improvement for battery NMC; probit provides -3 to -6% improvement for pharmaceutical and defense; Hill is uniformly inadequate.

4. Six-method validation protocol introduced — Pearson correlation, leave-one-out MAE, permutation test, function-form variation, variance inflation factor (VIF), and AIC/BIC vs NB baseline. Strong validation defined as five-of-six methods passing.

5. Honest limitations section expanded — V5 limitations focused on collinearity (resolved via f_EUV redefinition). V6 explicitly documents five additional limitations: (a) simulation-based validation pending in-house wafer/cell-level redrop, (b) VIF elevated in some industries due to t-derivation in simulators, (c) Display and Battery LFP show simulation sample-dependence, (d) two-cliff valley achieves AIC parity with Imec benchmark on semiconductor (Delta AIC +2 to +3, indicating compatibility not supersession), (e) self-referential risk in simulation generators partially mitigated but not eliminated by permutation tests.

6. Industry-specific cliff selection guidelines — single-cliff sigmoid recommended for pharmaceutical, solar, battery NMC, quantum, display, defense, battery LFP. Two-cliff valley recommended for semiconductor forecasting niche. SSB validated on V5 first-layer only (mass production not yet reached for second-layer activation).

7. Patent supplemental claims under preparation — Korean Patent KR 10-2026-0077383 (filed 2026.04.29) covers V5 first-layer and Claim 12 single-cliff sigmoid combination. PCT international filing (deadline 2027.04.29) will add supplemental claims for two-cliff valley variant, function-form equivalents, pharmaceutical industry generalization, and investment research / cross-industry strategy use cases.

V6 is intended as a complementary public-disclosure forecasting tool, not as a replacement for established industry-specific in-house process control models (Imec, IBM, KLA, Synopsys, PDF Solutions in semiconductor; NREL, Argonne in battery; KIT, HZB, Imec EnergyVille in solar; FDA QbD/PAT in pharmaceutical), which retain superior precision through underlying physics-based parametrization.