Discovering deposition process regimes: leveraging unsupervised learning for process insights, surrogate modeling, and sensitivity analysis

TL;DR

This work tackles the challenge of identifying deposition-regime regimes in CVD reactors by integrating CFD-derived data with a data-driven workflow that combines PCA, hierarchical clustering, and Polynomial Chaos Expansion. By partitioning the Arrhenius-Plot behavior into reaction-limited, transition, and diffusion-limited regimes, the authors construct regime-specific surrogates and perform Sobol' sensitivity analysis to quantify input influences within each regime. The approach yields accurate, low-cost predictions of near-surface precursor concentrations and reveals how temperature and pressure differently govern regime behavior, offering a principled tool for reactor design and optimization without costly experiments. The results align with experimental observations and provide actionable insights into gas-phase and surface mechanisms across regimes, supporting data-driven reactor innovation.

Abstract

This work introduces a comprehensive approach utilizing data-driven methods to elucidate the deposition process regimes in Chemical Vapor Deposition (CVD) reactors and the interplay of physical mechanism that dominate in each one of them. Through this work, we address three key objectives. Firstly, our methodology relies on process outcomes, derived by a detailed CFD model, to identify clusters of "outcomes" corresponding to distinct process regimes, wherein the relative influence of input variables undergoes notable shifts. This phenomenon is experimentally validated through Arrhenius plot analysis, affirming the efficacy of our approach. Secondly, we demonstrate the development of an efficient surrogate model, based on Polynomial Chaos Expansion (PCE), that maintains accuracy, facilitating streamlined computational analyses. Finally, as a result of PCE, sensitivity analysis is made possible by means of Sobol' indices, that quantify the impact of process inputs across identified regimes. The insights gained from our analysis contribute to the formulation of hypotheses regarding phenomena occurring beyond the transition regime. Notably, the significance of temperature even in the diffusion-limited regime, as evidenced by the Arrhenius plot, suggests activation of gas phase reactions at elevated temperatures. Importantly, our proposed methods yield insights that align with experimental observations and theoretical principles, aiding decision-making in process design and optimization. By circumventing the need for costly and time-consuming experiments, our approach offers a pragmatic pathway towards enhanced process efficiency. Moreover, this study underscores the potential of data-driven computational methods for innovating reactor design paradigms.

Figures (14)

• Figure 1: The Arrhenius plot of a CVD reactor for the Fe from Fe(CO)$_5$ and a fixed pressure $P = 10$ Torr 14aviziotis2017combined. Experimental measurements (squares) and computational results (line) are shown.
• Figure 2: The dataset comes from a CFD model for the Fe CVD reactor. The input parameters are the substrate temperature $T_s$ and the chamber pressure $P$. This computational model simulates seven variables at each discretization point, including the distributions of the x-y velocities $u$ and $v$, pressure $p$, temperature $t$, and three different precursor concentrations presented in \ref{['Tab:surface-reactions']}.
• Figure 3: PCA decomposes the covariance matrix of $Y$ (cov($\tilde{Y}$)) into $n$ dominant principal components (PCs): ($PC_1, PC_2, \cdots, PC_n$), from which we can obtain the reduced space $\Upphi$.
• Figure 4: HC gradually merges smaller clusters to form a nested tree structure (dendrogram) where each branch corresponds to a group (or cluster). The three largest clusters are colored, while the number of elements in each cluster is shown in parentheses at the bottom.
• Figure 6: Nodes of the spatial discretization (all points) considered to solve the computational model. Data from the nodes close to the deposition surface (orange area) are used in the data-driven analysis.