Deep transfer operator learning for predicting low temperature plasma sheath dynamics in semiconductor processing

Accurate and efficient modeling of plasma behavior are essential for process control and yield optimization in advanced semiconductor manufacturing. However, the high cost of obtaining labeled data—whether through in situ diagnostics or high-fidelity simulations—limits the applicability of conventional machine learning methods in this domain. To address this challenge, we propose a plasma physics-aware neural network (PPAN) framework that leverages pre-trained deep operator networks (DeepONets) with transfer learning to predict sheath-region plasma parameters in inductively coupled plasma reactors. The DeepONet is pre-trained to learn the nonlinear operator mapping among plasma parameters in the sheath region, such as the relationship between plasma density, electric potential, and ion flux near the wafer surface. Additionally, we demonstrate that the pre-trained DeepONet can be used as a physics-informed operator loss within a neural network, guiding predictions toward physically consistent solutions even in low-data regimes. To handle domain shifts introduced by changes in process conditions (e.g., RF power and outer-to-inner coil current ratios), we employ a transfer learning strategy that fine-tunes only the trunk network of the pre-trained DeepONet, enabling efficient adaptation to new conditions with minimal data. The results show that the proposed framework achieves high predictive accuracy even with as few as 5–15 training samples, significantly outperforming models trained from scratch. These findings highlight the potential of combining operator learning and transfer learning to develop physically consistent and data-efficient surrogate models for plasma process prediction. The proposed approach offers a practical solution for real-world semiconductor manufacturing environments, where data are scarce and process conditions frequently change.