| 摘要: | 控片（Control Wafer）於半導體製程量測中扮演關鍵角色，其薄膜狀態可作為製程
與量測系統穩定性之重要指標。然而，隨著時間推移，控片表面薄膜會因氧化效應而
產生結構與光學性質變化，進而影響量測結果之準確性與一致性。若能有效預測控片
之氧化趨勢與剩餘壽命（Remaining Useful Life, RUL），將有助於提升製程監控效率並
降低量測風險。
本研究以鈦薄膜控片為研究對象，結合物理模型與機器學習方法，建立一套基於
時間序列之控片氧化與剩餘壽命預測架構。首先，透過鈦薄膜氧化模型模擬鈦與氧化
鈦厚度隨時間之演化行為，並依據已知薄膜結構之光學理論，生成對應之橢圓偏光光
譜。再利用橢圓偏光儀反推等效薄膜厚度與擬合度（Goodness of Fit），建立具物理意
義之合成時間序列資料，作為模型訓練與測試之基礎。
在模型設計方面，本研究以等效薄膜厚度與擬合度之歷史量測序列作為輸入，分
別建構多層感知器神經網路與循環式神經網路模型，進行單步預測以評估模型對即時
氧化狀態之掌握能力，並透過多步遞迴預測推估控片之剩餘壽命。此外，針對實務應
用中過度預測可能帶來之風險，本研究進一步設計具方向性之懲罰型損失函數，以引
導模型降低對剩餘壽命之過度高估行為。
實驗結果顯示，相較於多層感知器神經網路，循環式神經網路在多數懲罰倍率設
定下，於等效薄膜厚度與擬合度預測誤差上皆呈現較穩定之表現，並能有效利用歷史
時間資訊描述薄膜老化之連續性行為。在剩餘壽命預測方面，所提出之懲罰型損失函
數可有效抑制過度預測現象，使模型預測結果更符合實務風險評估需求。整體而言，
本研究所提出之方法可作為控片氧化監測與剩餘壽命預測之可行解決方案，並具備延
伸應用至不同材料與量測情境之潛力。;Control wafers are essential in semiconductor process metrology, as the condition of their
thin films serves as a key indicator of process stability and measurement system reliability.
However, over time, surface thin films on control wafers undergo oxidation-induced structural
and optical property variations, which can degrade measurement accuracy and consistency.
Accurate prediction of oxidation behavior and remaining useful life (RUL) is therefore crucial
for improving process monitoring efficiency and reducing measurement-related risks.
In this study, titanium thin-film control wafers are investigated, and a time-series-based
prediction framework is developed by integrating physical modeling with machine learning
techniques. A titanium thin-film oxidation model is first employed to simulate the temporal
evolution of titanium and titanium oxide thicknesses. Based on optical theories for known thin
film structures, corresponding ellipsometric spectra are generated. Thin-film thickness and
goodness of fit (GOF) are then extracted through ellipsometric inversion, forming physically
meaningful synthetic time-series datasets for model training and evaluation.
For model development, historical sequences of thin-film thickness and goodness of fit are
used as inputs to construct multilayer perceptron (MLP) and recurrent neural network (RNN)
models. One-step-ahead predictions are performed to evaluate the models’ capability to capture
instantaneous oxidation states, while multi-step recursive predictions are applied to estimate
the remaining useful life of control wafers. To address the practical risks associated with
overestimation of remaining useful life, a directional penalty-based loss function is further
introduced to guide the models toward more conservative and risk-aware predictions.
Experimental results indicate that, compared to multilayer perceptron models, recurrent
neural networks exhibit more stable prediction performance for both thin-film thickness and
goodness of fit under various penalty factor settings, owing to their ability to effectively utilize
historical temporal information and model the continuity of thin-film aging behavior. In terms
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of remaining useful life prediction, the proposed penalty-based loss function successfully
suppresses overestimation, resulting in predictions that better align with practical risk
assessment requirements. Overall, the proposed approach provides a feasible solution for
control wafer oxidation monitoring and remaining useful life prediction, and demonstrates
strong potential for extension to different materials and metrology scenarios. |
