Tuning of Atomic Layer Deposition Pulse Time through Physics-Informed Bayesian Active Learning

Abstract

Atomic Layer Deposition (ALD) process development is often hindered by time-consuming and precursor-intensive tuning cycles required to identify saturation conditions. We introduce a physics-informed Bayesian Active Learning (BAL) framework that autonomously tunes precursor pulse times by integrating a Langmuir adsorption model directly into the Gaussian Process (GP) kernel. A key innovation is a two-stage parameter estimation strategy that decouples noise filtering from physical parameter extraction: the GP first smooths noisy data through standard prediction, then Langmuir parameters are fitted to the noise-filtered GP predictions. This approach effectively separates signal from experimental noise. We evaluate the framework against a standard data-driven GP across four simulated regimes, demonstrating convergence within five iterations, up to fourfold improvement in prediction accuracy, and two to fourfold reduction in precursor usage. Experimental validation using TiO2 deposition via Tetrakisdimethylamido Titanium (TDMAT) and ozone confirms that the physics-informed model accurately identifies saturation times for high-coverage targets ($\geq$95\%), with observed deviations at lower saturation levels providing valuable insight into non-ideal desorption behaviors.

Figures (13)

• Figure 1: Flowchart of the Physics-Informed Bayesian Active Learning framework. The red highlighted section details the novel two-stage parameter estimation strategy, where physical parameters are extracted from the smoothed GP surrogate to ensure robustness against experimental noise.
• Figure 2: Exploration behavior comparison for fast saturation regime ($K_{\text{true}} = 100$) over 20 iterations. Physics-informed Matérn kernel (top) prioritizes high-slope regions of the Langmuir curve, while pure Matérn kernel (bottom) explores based solely on GP uncertainty. Gray shaded regions represent 95% confidence intervals. Colors indicate iteration number.
• Figure 3: Monte Carlo statistical analysis for fast saturation regime ($K_{\text{true}} = 100$) over 100 independent runs after 20 iterations. Left bar: physics-informed Matérn achieves 18.7$\pm$13.5% error. Right bar: pure Matérn shows 70.3$\pm$53.2% error. Physics-informed approach reduces precursor usage by approximately fourfold. Error bars represent mean $\pm$ standard deviation after outlier removal via IQR method.
• Figure 4: Exploration behavior comparison for moderate saturation regime ($K_{\text{true}} = 10$) over 20 iterations. Physics-informed Matérn kernel (top) shows distributed exploration as saturation extends into the search domain. Pure Matérn kernel (bottom) explores based on GP uncertainty. Gray shaded regions represent 95% confidence intervals. Colors indicate iteration number.
• Figure 5: Monte Carlo statistical analysis for moderate saturation regime ($K_{\text{true}} = 10$) over 100 independent runs after 20 iterations. Left bar: physics-informed Matérn achieves 11.5$\pm$9.0% error. Right bar: pure Matérn shows 53.3$\pm$30.7% error. Threefold reduction in precursor usage for physics-informed approach. Error bars represent mean $\pm$ standard deviation after outlier removal via IQR method.