- 學位論文
整合統計分析與知識推論系統的貝氏架構設計 -以半導體良率分析為例
A Bayesian Framework to Integrate Data-Driven and Knowledge-Based Inference Systems for Reliable Yield Analyses in Semiconductor Manufacturing
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摘要
本論文目的在於診斷半導體產業良率損失因子的可靠方法。本研究定義了兩個使用統計分析進行良率診斷時所存在的嚴重問題：混淆變數所產生的錯誤定義、單因子演算法分析中所造成的訊息遺失。為了同時解決這兩個問題，本研究提出一個貝式模式選擇架構，藉由統計分析和知識推論系統的整合和再使用，使半導體良率分析能有一個更可靠的良率診斷方式。 這個貝式架構包含了三個主要模組：資料事前處理、貝式分析以及結果事後處理。在資料事前處理中，整合了經由資料探勘和知識系統推論結果所篩選過的候選因子，進行配對篩選以得到候選因子。在貝式分析中，所執行的兩個貝氏演算法皆能適應。單因子貝式演算法解決了混淆變數所產生的錯誤定義。多因子貝式演算法解決了單因子貝式演算法所造成的資訊遺失。最後，在資料事後處理的模組中，為了使良率損失的因子篩選結果的排序更為可靠，本研究提出一個具有柏拉圖曲線的泡泡圖。其中，泡泡大小代表事後機率(posterior probability)。且當泡泡位於柏拉圖曲線上時，表示沒有其它因子可同時在統計顯著水準(p-value)和知識推論系統上因子錯誤的可能性(fault possibility)優於該泡泡。 最後，兩個模擬實驗被設計評估本研究所建構的貝氏架構。第一階段實驗由單因子貝式演算法藉由控制虛擬因子個數和事前知識的因子錯誤的可能性，解決因為因子增加而導致FI問題；第二階段實驗由多因子貝式演算法，藉由控制錯誤因子個數、因子彼此間影響、被懷疑的事前知識，解決因為錯誤因子增加而導致MI問題。最後結果表示，即使沒有貝氏推論的幫助，柏拉圖曲線仍然可以找出大多數的錯誤因子。但是在本研究貝氏架構下將柏拉圖曲線結合貝氏推論所得到的事後機率結果判斷，可以得到比過去資料驅動(Data-Driven)方法更好的良率診斷結果。
並列摘要
This thesis studies the reliable yield diagnosis from hundreds of suspected yield-loss factors in semiconductor manufacturing. Two problems of data-driven inference approach commonly used for yield diagnosis are identified: False Identification (FI) Due To Confounding Variables and Miss-Identification (MI) Due To One-Factor-At-A-Time Analysis. To cope with the FI and MI problems, a framework of Bayesian model selection is proposed to integrate and reuse both the data-driven and knowledge-based inference systems in industry practices for more reliable yield diagnosis. The Bayesian framework consists of three modules: Pre-Processing, Bayesian Analysis, and Post-Processing. The Pre-Processing module applies successive factor filtering and matching techniques to integrate the inference results from both data-driven and knowledge-based systems for the generation of candidate factors and corresponding beliefs. Two algorithms are then adopted for the Bayesian Analysis in the second module: One-Factor-At-A-Time Bayesian Analysis to solve the FI problem and Multi-Factor-At-A-Time Bayesian Analysis to further solve the MI problem. For reliable factor rankings, a novel Bubble Diagram with Pareto Frontier is proposed in the Post-Processing module, where the size of each bubble(factor) representing the magnitude of posterior probability while the bubbles on Pareto Frontier represents the factors non-dominated by other factors with respect to both p-value and fault possibility generated by data-driven and knowledge-based systems respectively. Two simulation experiments are conducted for evaluating the capability of the proposed Bayesian Framework. The first simulation experiment is to study the capability of One-Factor-At-A-Time Bayesian Algorithm on solving the FI problem with respect to different numbers of dummy factors and qualities of prior knowledge. The second simulation is to study the capability of Multi-Factor-At-A-Time Bayesian Algorithm on solving the MI problem with respect to different numbers of faulty factors, various effects among faulty factors, and different qualities of prior knowledge. Both simulation experiments are evaluated by the metrics derived from the Bubble Diagram with Pareto Frontier. Simulation results show that, without the aid of Bayesian inference, the interpretation of Pareto Frontier alone successfully captures the faulty factors in most cases. With the additional information of bubble size, i.e. the posterior probability derived from Bayesian inference, the proposed Bayesian framework performs much better than the data-driven approach commonly used for yield diagnosis.
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