單維轉二維卷積神經網路虛擬量測模型及其可釋性發展

Abstract

因應市場高度需求，半導體製程的發展速度已經演進到超越摩爾 (More Than Morre) 的世代。為了有效應對更複雜製程設計，先進的製程控管技術已經是製造商不可或缺的基本能力。如今，半導體製造通常由數千道製程所組成，每道製程步驟都有特定的品質標準，而做完關鍵製程之後，品質量測是評估製程能力的基本且必要手段。因為製程愈趨精密，單片晶圓的測量時間亦越來越長，致使大量抽測已不符合生管標準，因此使虛擬量測模型成為更受重視的技術。

虛擬量測系統旨在利用錯誤偵測與分類 (Fault Detection and Classification, FDC) 資料預測晶圓的量測值，使每片晶圓都有相對的量測品質能被即時監控，而藉由模型預測可同時保持製程效率。回顧過往的虛擬量測相關文獻，在面對處理多變量時間序列的 FDC 資料時，主流方法是先利用領域知識從 FDC 資料中萃取出物理或統計特徵，然而過於主觀的特徵萃取與轉換會丟失大量的潛在資訊，使得模型準確度無法進一步提升，同時也容易失去製程變數和輸出測量值之間的連結。因此本研究提出了一整合卷積神經網路與圖神經網路的虛擬量測模型，並進一步發展此模型背後的可解釋性。

首先使用一維卷積層加強資料的時間特性，並經由圖神經網路萃取變數之間的交互作用關係，最後透過二維卷積與全連接層神經網路預測量測結果。為針對工業機台之特性進行可解釋性之設計，利用 DeepSHAP 演算法剖析模型的決策邏輯與各個製程變數對量測結果之影響，另外透過圖神經網路訓練的圖結構可以了解製程變數之間的交互作用關係。此外，在研究過程中發現使用相關矩陣 (correlation matrix) 來近似真實圖結構的可行性，在模型訓練最佳化的過程中取得變數之間的真實交互作用關係，發展出同時兼具準確度與解釋性之虛擬量測模型。

本研究以 2016 PHM Data Challenge 之半導體化學機械研磨製程公開資料進行案例分析，將本研究提出之模型預測結果與當前國際學術研究成果進行比較，目前在預測準確度方面與最佳結果相近，惟本研究提出之模型具有泛化與可解釋性之優勢。

In response to the urgent demand of the consumer market, the semiconductor technology node has evolved to the More Than Moore generation. In order to effectively deal with more complex process designs, advanced process control technology has become an indispensable capability for IC makers. Nowadays, semiconductor manufacturing usually consists of thousands of operations that have specific quality standards. After processing the critical operations, quality inspection is a basic and necessary manner to evaluate process capability. Due to the more and more complex design, the measuring time of a single wafer is getting longer and longer, making it impossible to do a full-spectrum inspection. As a result, virtual metrology is coming to the center of the stage.

Virtual Metrology (VM) system is designed to predict the measurements of a wafer by using Fault Detection and Classification (FDC) data, such that the relative wafer quality can be monitored in real-time. FDC data are collected in the format of multivariate time series per wafer. In reviewing the recent literature related to VM, the mainstream usually starts by using domain knowledge to extract physical or statistical features from FDC data. However, subjective feature extraction and conversion often lead to information loss or distortion. Not to mention the link between process variables and output measurements can be broken. Therefore, this study proposes a 1-2D CNN-based VM model integrating the convolutional neural network and graph neural network, and further develops the interpretability of this model.

We first use the 1D convolutional layer to enhance the temporal information. The interactions among variables are extracted through a Graph Neural Network (GNN). Finally, the measurements are predicted through the 2D convolutional layer and fully connected neural network. In order to interpret the VM model, DeepSHAP algorithm is employed to infer the decision logic and the importance of process variables. In addition, the trained graph structure can be used to understand the interactions among variables. It can be regarded as a model that combines prediction accuracy and explainability at the same time.

The 2016 PHM Data Challenge open dataset on the chemical mechanical polishing process is used for the case study. The performance of the proposed VM model is compared with that on the leaderboard. Our accuracy is close to the best ones, and the proposed model has the advantages of generalization and explainability.