基於時間序列窗口分治架構之虛擬量測模型及其可釋性分析

Abstract

隨著資訊技術與大數據分析概念逐漸普及，半導體製造業的製程控管發生了顯著變革。在當前APC (Advanced Process Control) 架構下，錯誤檢測與分類 (FDC, Fault Detection and Classification) 能即時檢測製程異常，減少不良品產生。然而全面檢測成本高昂，且耗時甚巨影響交期，因此虛擬量測 (VM, Virtual Metrology) 的功能被提出，用以即時預測和監控晶圓品質。然而半導體製程的複雜性和各階段的動態特性，使得從不平穩的時間序列資料中提取隱性特徵並提高模型預測準確度成為一項挑戰。過去研究主要依賴統計摘要特徵和手動擷取特徵 (hand-designed features) 的方法，難以全面捕捉非線性關係和複雜動態特性，限制對製程中複雜關係的理解。 本論文提出時間序列窗口分治的架構，期望針對製程中不同階段的資料進行個別分析，建立「基於加權虛擬量測模型」以及「基於長短期記憶虛擬量測模型」。兩模型的整體架構主要分為時間序列分治窗口與合併兩個部分，成功地提取各階段隱含的時間序列特徵，並透過圖結構訊息傳遞，分析變數在不同製程階段展現的動態交互作用關係。合併分治窗口特徵後，全面地提取資料中的重要模式和複雜的特徵關係。將驗證集置於測試集之前的方法，進一步強化模型對時間序列資料的特徵萃取能力，更有效地應對現實製程中的複雜情況。 本研究通過化學機械研磨 (Chemical-Mechanical Polishing, CMP) 製程公開資料集實證，並與基準模型進行比較，展示所提出的模型框架在窗口分治方面的效能。透過窗口權重和變數之間交互作用的深度分析，以及Deep SHAP深度學習可解釋性方法進行模型解釋性分析，提升對模型決策過程的理解和可靠性。

With the widespread adoption of information technology and big data analytics, there has been significant implementation in process control systems for the semiconductor manufacturing industry. Under the current Advanced Process Control (APC) framework, Fault Detection and Classification (FDC) can promptly identify process anomalies, thus reducing the production of defective products. Since thorough inspection is costly and time-consuming, greatly affecting delivery schedules, Virtual Metrology (VM) modeling has been proposed to predict and monitor wafer quality in real time. However, the complexity and the dynamics among operating stages in one process make it challenging to extract implicit features from the nonstationary time series data and enhance model prediction accuracy. Previous studies mainly relied on statistical summary features and hand-crafted features, which struggle to fully capture nonlinear relationships and complex dynamic characteristics, limiting the understanding of intricate relationships within the process. This paper proposes a framework of time-series window partitioning, aiming to conduct individual analysis on data from different stages of the process, and establish "VM Model with Weighted Sum" and "VM Model with LSTM.” The overall structure of both models is mainly divided into time-series partitioning windows and merging sections, successfully extracting implicit time-series features from each stage and analyzing the dynamic interactions of variables across different process stages through graph structure information propagation. By merging partition window features, important patterns and complex feature relationships within the data are comprehensively extracted. The method of placing the validation set before the test set further strengthens the model's ability to extract features from time-series data and more effectively cope with the complexities of real-world processes. This study is empirically validated using publicly available data sets from the Chemical-Mechanical Polishing (CMP) process and compared with benchmark models, demonstrating the performance of the proposed model framework in window partitioning. Through in-depth analysis of window weights and interactions among variables, as well as the model interpretability based on Deep SHAP algorithm, the understanding and reliability of the model decision-making process are enhanced.