# A Multi-Machine and Multi-Modal Drift Detection (M2D2) Framework for Semiconductor Manufacturing
## 1 Introduction  
Wide-bandgap (WBG) materials such as gallium nitride (GaN) and silicon carbide (SiC) have transformed the semiconductor landscape by enabling higher power density, faster switching speeds, and superior thermal stability compared to conventional silicon-based devices [1]. The adoption of WBG technologies is proliferating in applications ranging from power converters and electric vehicles to emerging 5G/6G communication systems. Although these advances promise higher efficiency and performance, the accompanyingfabrication and assembly processes have grown markedly more complex. Manufacturing WBG-based devices often involves numerous tightly coupled parameters--such as plasma discharge power, chemical vapor deposition (CVD) conditions, critical temperature points, and wafer handling protocols--that must be maintained within stringent control windows to preserve device quality and yield. Parameter drift arises when these control windows begin to shift or degrade over time, occurring either slowly due to gradual wear in reactor components or abruptly due to sporadic fluctuations in gas composition or chamber pressure. If left unaddressed, drift can contribute to device performance deterioration, reduce production yield, and in severe cases trigger catastrophic system failures. Detecting and correcting parameter drift at an early stage is therefore a linchpin in ensuring the stable and profitable operation of WBG semiconductor manufacturing lines [2]. To achieve this, many FDC systems aggregate sensor data from multiple process steps (e.g., etching, deposition, cleaning) and leverage statistical process control (SPC) or machine learning algorithms to monitor device health in near real-time. Despite decades of progress, conventional FDC methods face significant hurdles in the context of modern WBG manufacturing. Early works often utilized simple control charts (e.g., Shewhart, CUSUM, or EWMA) or static thresholds, which proved adequate for smaller-scale processes with relatively stable parameter distributions [3]. However, as processes became more intricate and the number of monitored variables expanded, these classical techniques showed limited sensitivity to subtle or slowly developing drifts. Studies that introduced principal component analysis (PCA) and other linear dimensionality reduction methods [4] helped to some extent, but the prevalent nonlinearity and cross-variable dependencies in WBG device fabrication frequently undermine purely linear models. Similarly, heuristic threshold updates and domain expert fine-tuning--common in many industrial settings--cannot fully address the challenge of capturing dynamic, multi-modal correlations and complex temporal dependencies [5]. In response to these limitations, more advanced anomaly detection and drift-monitoring frameworks have been proposed in recent years. Machine learning- and deep learning-based FDC systems--ranging from random forests and support vector machines to convolutional and recurrent neural networks--have demonstrated a certain level of success in learning normal operational patterns from large archives of historical data [6; 7]. Autoencoder-based methods, in which the reconstruction error of incoming data points serves as a proxy for deviations, can detect unexpected shifts in process parameters [8]. Contrastive learning and self-supervised techniques further enhance feature extraction, especially when partial labels or similarities exist among different operation modes [9]. Online learning algorithms and adaptive thresholding strategies aim to keep detection schemes current as processes evolve, sometimes employing Bayesian updates or incremental retraining [10]. Nonetheless, few of these approaches adequately confront the acute challenges that define drift detection in WBG contexts. First, WBG processes typically generate multimodal data, including numeric sensor readings, unstructured textual logs (e.g., maintenance records or operator notes), and categorical identifiers such as batch or chamber IDs.