Parametric Operator Inference to Simulate the Purging Process in Semiconductor Manufacturing

TL;DR

This work addresses the computational bottleneck of predicting purge-flow in a PECVD chamber for particle contamination control. It applies parametric OpInf to learn a data-driven, nonintrusive quadratic ROM after reducing dimensionality with POD and interpolating across two process parameters, $\mu_q$ and $\mu_p$. The approach achieves up to $9.32\%$ maximum error and about a $142\times$ online speedup compared with full CFD simulations, enabling fast multi-query predictions of the purge flow. These fast surrogates support rapid process design and control decisions in semiconductor manufacturing, and they pave the way for coupling flow predictions to particle transport analyses for improved contamination mitigation.

Abstract

This work presents the application of parametric Operator Inference (OpInf) -- a nonintrusive reduced-order modeling (ROM) technique that learns a low-dimensional representation of a high-fidelity model -- to the numerical model of the purging process in semiconductor manufacturing. Leveraging the data-driven nature of the OpInf framework, we aim to forecast the flow field within a plasma-enhanced chemical vapor deposition (PECVD) chamber using computational fluid dynamics (CFD) simulation data. Our model simplifies the system by excluding plasma dynamics and chemical reactions, while still capturing the key features of the purging flow behavior. The parametric OpInf framework learns nine ROMs based on varying argon mass flow rates at the inlet and different outlet pressures. It then interpolates these ROMs to predict the system's behavior for 25 parameter combinations, including 16 scenarios that are not seen in training. The parametric OpInf ROMs, trained on 36\% of the data and tested on 64\%, demonstrate accuracy across the entire parameter domain, with a maximum error of 9.32\%. Furthermore, the ROM achieves an approximate 142-fold speedup in online computations compared to the full-order model CFD simulation. These OpInf ROMs may be used for fast and accurate predictions of the purging flow in the PECVD chamber, which could facilitate effective particle contamination control in semiconductor manufacturing.

Figures (11)

• Figure 1: Illustration of the impact of particle contamination on subsequent wafer manufacturing processes.
• Figure 2: (a) Computational domain of a simplified PECVD chamber. B.C.1: mass flow inlet boundary condition, B.C.2: pressure outlet boundary condition, B.C.3: symmetric boundary condition. The side view represents the $xy$-vertical plane where $z = 0$ mm. (b) Profiles of the mass flow inlet, pressure outlet, and heater surface temperature over time $t \in [0, 1]s$.
• Figure 3: Left: velocity field, Right: streamlines at the onset of the purging process, initiated upon plasma deactivation.
• Figure 4: (a) Normalized singular value decay. (b) the cumulative energy $\mathcal{E}_{\text{cum}}(r)$ and the residual energy that represents the projection error $\mathcal{E}_{\text{proj}}(r)$, with respect to the reduction dimension $r$. The vertical black line illustrates the chosen ROM dimension $r=5$.
• Figure 5: (a) Datasets used for training and testing. Of the 25 datasets, nine (36%) are used for training, while 16 (64%) are reserved for testing. (b) Projection error for all 25 simulations. (c) Average relative state error between the FOM and ROM predictions.