時間與空間上之變異分析及其在半導體工程資料分析上的應用

Temporal and Spatial Variation Analysis and Its Applications to Semiconductor Engineering Data Analysis

藍俊宏(Jakey Blue)

指導教授 ： 陳正剛

國立臺灣大學/工學院/機械工程學研究所/博士(2010年)

https://doi.org/10.6342/NTU.2010.00186

摘要

在半導體製造過程中，為了最佳化製程產能與設備利用率，以致能提升良率，系統變異的分析研究是一個相當基本且重要的課題，傳統上，工程師以統計學中的樣本變異數來估計資料的隨機變異，但該統計量在資料呈現特殊走勢或來自非平穩的分配時，往往會遭到曲解失真，以致於影響接下來進行的製程分析與最佳化。本研究提出了計算平移變異數的概念以消彌由於資料呈特殊走勢、或來自非平穩分配所造成的影響，平移變異數主要觀念在於只計算時間軸上小區間中連續(或空間中小區域內相鄰)觀測值的樣本變異數，再藉由移動該區間(或區域)來覆蓋所有觀測值，以匯整各區間(或區域)中的變異資訊。在處理時間軸變化為主的資料，例如機台在製造過程中可即時收集的參數與訊號，本研究以平移變異數為基礎發展了一機台狀態指標，以評估當前機台狀況、找出可能的機台錯誤，使後續的機台維護保養排程能夠更適當、更有彈性；而為了處理空間座標對應的觀測值，例如晶圓臨界尺度取樣量測值等，我們則利用平移變異數發展了一空間變異頻譜來描繪晶圓量測值內含的系統變異，並在空間變異頻譜之上建立了數個指標來量化整體資料的系統變異量，使後續因果分析的進行能更有效率。同時，我們亦探討了平移變異數相關的性質與理論，並試著與傳統的樣本變異數比較，證明在資料呈特殊走勢或來自不同分配時，使用平移變異數能有較精準的估計。本研究在最後並利用了國內數家半導體製造業者提供的真實數據來驗證所提出的各項理論。

關鍵字

錯誤偵測與分類 ； 平移變異數 ； 機台狀態指標 ； 空間變異 ； 系統變異 ； 隨機變異 ； 晶圓臨界尺度量測值

並列摘要

Investigation of system variation is always critical to process/equipment optimization and yield enhancement in semiconductor manufacturing. Conventional variation estimate, usually the sample variance, cannot truthfully reveal the random variation if data exhibits a patterned profile or is of non-stationary distribution. The biased random variation estimate could then impact the subsequent analysis greatly. In this research, the concept of moving variance, which calculates the variance of a small number of consecutive/adjacent observations within a temporal/spatial moving window, is proposed to eliminate the impact of the pattern-induced (systematic) variation. By applying the moving variance technique to temporal profiles, such as the process states or tool signals, the tool condition can be evaluated by the proposed tool condition indicator. When dealing with spatial topography, such as the wafer metrology data, systematic variations can be identified and characterized by the proposed spatial variation spectrum (SVS) comprised of the spatial moving variances. Diagnosis methodologies are developed to facilitate uncovering abnormal tool conditions or systematic patterns. Properties and theories are studied as well to justify how the moving variance outperforms the conventional sample variance. With the tool condition indicator, possible tool faults can be identified and proper maintenance measures can be scheduled accordingly. With the SVS and its summarized indices, systematic variations can be characterized and the causal analysis for finding root causes can be further explored. The proposed methodologies are further validated through the real cases provided by local semiconductor companies.

並列關鍵字

fault detection and classification (FDC) ； moving variance ； tool condition indicator ； spatial variation ； systematic variation ； random variation ； wafer CD metrology

參考文獻

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