A Physics-Chemistry-Informed Neural Network (PCINN) for Real-Time Spatial-ALD Coverage Prediction and Reliable Kinetics Inversion
A Physics-Chemistry-Informed Neural Network (PCINN) surrogate achieves CFD-level accuracy for spatial ALD coverage prediction at ~7 ms per query, roughly 50,000× faster than traditional CFD simulations The hybrid architecture uses a small neural network only for the operating-condition-to-near-wall-concentration closure, while known surface kinetics are hard-coded as a trainable chemistry layer integrated along the substrate trajectory Full identifiability analysis reveals E_ads and k_des are ro
Analysis
TL;DR
- A Physics-Chemistry-Informed Neural Network (PCINN) surrogate achieves CFD-level accuracy for spatial ALD coverage prediction at ~7 ms per query, roughly 50,000× faster than traditional CFD simulations
- The hybrid architecture uses a small neural network only for the operating-condition-to-near-wall-concentration closure, while known surface kinetics are hard-coded as a trainable chemistry layer integrated along the substrate trajectory
- Full identifiability analysis reveals E_ads and k_des are robustly identifiable, while k_ads is only identifiable as a product with wall concentration at single temperature
- A weakly identifiable degeneracy valley between prefactor ν and E_ads has slope 0.065 eV/decade, analytically derived as k_B T_eff ln(10), serving as a reliability diagnostic for unmodelled site heterogeneity
- The model achieves R²_log = 0.998 (leave-one-out R²_raw = 0.974) from only 30 training cases spanning four orders of magnitude in coverage
Why It Matters
This work demonstrates a practical blueprint for physics-informed surrogate modeling in industrial process optimization, where high-fidelity simulation is computationally prohibitive for real-time control. The hybrid architecture—separating learnable transport closures from hard-coded kinetics—offers a template for building interpretable, data-efficient models in other computational chemistry and materials processing domains. The identifiability analysis also provides a concrete diagnostic framework for validating kinetic parameter extraction from experimental data.
Technical Details
- Architecture: PCINN is a hybrid surrogate where a compact neural network learns only the mapping from operating conditions to near-wall concentration (the gas curtain modulation), while surface reaction kinetics are encoded as a differentiable, trainable chemistry layer integrated along the substrate trajectory. This single-scalar bottleneck design ensures interpretability and invertibility.
- Performance: Test R²_log = 0.998 with leave-one-out R²_raw = 0.974 across four orders of magnitude in coverage, using only 30 training cases. Inference time is ~7 ms per query versus ~350 seconds for a comparable CFD solve.
- Identifiability Analysis: Fisher information and profile likelihood methods show E_ads and k_des are robustly identifiable. k_ads is structurally non-identifiable at single temperature (only the product k_ads·c_wall is). Across four temperatures, ν and E_ads lie on a degeneracy valley with slope 0.065 eV/decade.
- Diagnostic Framework: A seven-chemistry mismatch matrix is invariant under single-Arrhenius parameter mismatch but shifts when a second thermally activated process is present, providing a flag for unmodelled site heterogeneity.
- Validation: Ground-truth data from simulation with known kinetic parameters inverted by the same kinetic form, verifying pipeline self-consistency and identifiability boundaries rather than recovering true physical parameters.
Industry Insight
- Physics-informed hybrid architectures that isolate learnable components to the most uncertain closures (here, transport) while hard-coding well-understood physics (surface kinetics) can achieve high accuracy with dramatically less training data—this principle generalizes to other simulation-intensive domains like combustion, semiconductor manufacturing, and catalysis.
- The identifiability diagnostic (degeneracy valley slope departure) offers a practical quality-control tool for kinetic parameter extraction: practitioners should routinely check for slope deviations as an early warning of missing physics or heterogeneous surface sites before trusting inverted parameters.
- Real-time surrogate models at 50,000× speedup enable closed-loop process control and online operating-window optimization for atmospheric-pressure ALD tools, which is a prerequisite for industrial scale-up of spatial ALD processes.
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