半導體晶圓允收測試參數與重要機台即時監控數據項目關聯性、預測分析及機台控管參數優化研究

Abstract

半導體晶圓(Wafer)製程涉及上百道步驟，當晶圓完成所有的製造程序後，會針對晶圓上的特定測試結構進行電性測試 (Wafer Acceptance Test, WAT)，是製程末(End-of-Line, EOL) 的良率控管。 製程過程中的機台運行狀態會導致相對應製程步驟產生物理特性改變，進而影響電性，導致每片晶圓間的電性數值浮動增大。因此，每一製程環節機台的控管是EOL良率的基礎，當下控管好遠勝問題產生再處理。 目前製程整合工程師藉由分析WAT參數，依照歷史經驗或逐一分析製程站點機台的即時感測數據(Real Time Monitor, RTM)與WAT參數線性相關性來找出導致變異變大的原因，此處的變異表示為每片晶圓的WAT電性參數平均數值差異。檢測方法有四點不足：(D1) 傳輸RTM數據出現缺漏，RTM Database在傳輸數據時會出現隨機缺漏，可能會導致分析出現偏差，(D2)機台狀況RTM項目眾多，且機台狀況RTM項目與WAT參數間關係複雜，兩者可能有相依與非線性函數關係，尚未釐清導致WAT參數偏移的重點項目，(D3)WAT預測模型建立，尚未建立機台重要狀況RTM項目值與WAT電性參數間的預測模型，以提前得知WAT電性參數，(D4)RTM數值調整延後性，無法在某道製程可能導致WAT參數偏移當下即時對機台狀況進行控管，導致多批次(Lot)晶圓WAT參數受到影響。對此，我們分析機台狀況RTM和WAT參數歷史數據，提出利用RTM對WAT參數預測並優化RTM控管參數 (WAT Prediction with RTM and Optimizing RTM Control Parameters, WAPOR )架構來改善上述不足。 本研究WAPOR旨在探討如何建立重要RTM項目與WAT參數的預測模型並設定RTM控管區間上下界來降低WAT電性參數標準差。此外，本論文以實際半導體廠的RTM數據與臨界電壓電性測試項目做為案例研究，以驗證方法的有效性。主要研究問題(P)、 相對應的挑戰(C)和本論文提出的解決方法(M)如下: (P1)傳輸 RTM Data缺失問題:向RTM Data Base所要求的資料會對應Wafer ID的RTM Item隨機出現缺漏，如何填補資料以解決(D1)中資料不完整的不足? (C1) RTM數據隨機缺漏的項目並無一定的規律，導致平均每個RTM Item在資料數目的缺漏比率為20%至40%，若只取無RTM Item缺漏的Wafer數目，則會喪失約80%的資料量，如何維持原始資料數量並改善缺漏比率唯一挑戰。 (M1)提出Python-Based Multi-Request and Duplicates Removal (PB-MRDR)方法，利用多次向RTM Data Base要求相同規格資料，在Python環境中匯聚多筆資料，自動化刪除重複資料、補齊不足資料，原因為原始資料為csv檔案，在Excel中最多只能處理1,048,576行的數據，但在Python環境中並沒有限制。 (P2)重要RTM數據項目挑選問題:如何萃取對於影響WAT參數偏移之重要RTM數據項目提升關聯性掌握度，並去除無關項目，以克服(D2)中RTM數據項目眾多問題並掌握重點項目? (C2)以研究案例中所使用的機台RTM數據項目有28個，RTM數據項目間有相互關聯性。目前以工程師逐一對RTM項目與WAT參數做二維散佈圖(Scatter Plot)關聯性分析，耗時且難以斷定重要RTM數據項目。 (M2)為了提升RTM與WAT參數的關聯性掌握度、縮減需要分析的RTM維度，我們設計Hybrid RTM Item Selection Model(H-RIS)方法，結合Stepwise Regression線性特徵挑選模型與Bagging Tree、Boosting Tree的非線性特徵挑選模型找出Selected Important RTM Items(SIRIs)並設計各別模型重要RTM項目挑選門檻，與製程工程師確認所選出的6個SIRIs的物理意義與對WAT參數偏移確有重要影響。 (P3) SIRIs與WAT參數關係模型建立問題: SIRIs與WAT參數現行並無明確數學關係，如何建構兩者間的預測模型，藉由預測模型以製程中的SIRIs提前預測製程末WAT參數，以減輕(D3)WAT提前預測問題? (C3)現行工程師僅有WAT參數浮動變異增大時，回推某製程站點機台RTM數據項目，以Scatter Plot逐一檢查線性關聯性的紀錄表，但並沒有在某製程步驟結束後，結合量測到的多維RTM數據提前預知WAT參數數值紀錄。要掌握RTM數據與製程末WAT參數的關聯性需要考慮RTM對製程物理特性的影響以及RTM間的相依性與非線性函數關係，如何得知兩者間的數學函數關係為一挑戰。 (M3)考慮深度BPN的發展成熟性以及在多領域的回歸任務上的成效，設計預測WAT參數深度BPN模型(WAT Prediction through Deep BPN Model, WPBM)，利用H-RIS由歷史RTM數據找出的SIRIs與WAT參數建立監督式反向傳遞深度神經網路模型，以神經網路中的激活函數與多隱藏層結構擬合SIRIs與WAT參數非線性轉換特性，找尋SIRIs與WAT參數間多維複雜函數關係。 (P4)SIRIs控管參數優化問題:如何依照SIRIs與WAT參數的關係模型，設定SIRIs數值控管上下界，以克服(D4)無法即時對機台狀況進行控管的不足? (C4)目前實務方法是將SIRIs的數值控制在歷史SIRIs數據的平均值加減六倍標準差的範圍區間，但WAT參數在目前SIRIs控制區間仍會有偏移現象(WAT參數超過歷史平均加減3倍標準差)。如何在龐大搜索空間與多變數相互影響的情況，優化SIRIs數值控管上下界以緊縮WAT參數浮動區間為一挑戰。 (M4)考慮基因演算法的啟發式搜索與多變數優選的特性，設計基於基因演算法的RTM區間設定(RTM Region Setting by Genetic Algorithm, RRS-GA)方法，利用WPBM找出SIRIs與WAT參數的函數關係，設計WAT參數規格區間導向的適應度函數(Fitness Function)，在可接受的計算時間內找到SIRIs控管區間上下界數值。 本論文的研究發現與貢獻包含: (1) 創新設計於Python環境自動化刪除重複資料、補齊不足資料的PB-MRDR方法，在7969片Wafer數據中將平均缺漏比率由20%~40%降低至0.004 %。 (2) 創新設計混合線性與非線性模型為基礎的重要RTM項目挑選H-RIS方法，由28項RTM項目縮減至6個SIRIs，減少所需分析維度、增加關聯性掌握度。 (3) 利用H-RIS選出的SIRIs，建構多維度SIRIs和單一WAT參數的深度BPN預測模型WPBM，預測值與實際數值關聯性係數達0.505，超越實務上的顯著關係標準25%，用於控管參數的優化。 (4) 創新設計基於WAT參數規格為適應度函數的SIRIs控管參數優化方法RRS-GA，利用學得的WPBM預測模型模擬數據顯示單一WAT參數數值可以降低標準差達49%，具有降低WAT參數標準差的潛力。 (5) 以實際半導體廠臨界電壓電性測試參數數據與機台RTM數據為案例研究，並提供所提出方法對現行半導體廠的可行性。

Semiconductor wafer processing involves over a hundred steps. After the completion of all manufacturing processes on the wafer, specific test structures on the wafer undergo electrical testing, known as the Wafer Acceptance Test (WAT). This test is a crucial part of end-of-line (EOL) yield control. Abnormalities in equipment during the process can cause physical property deviations in the corresponding process steps, impacting electrical properties and potentially leading to the scrapping of an entire batch of eight-inch wafers, each valued at around $800. Therefore, controlling the equipment at each process step is fundamental for EOL yield, as proactive control is far superior to reactive problem-solving. Currently, process integration engineers analyze WAT parameters and identify causes of anomalies by correlating Real Time Monitor (RTM) data from process equipment with WAT parameters, based on historical experience or individual analysis. However, this detection method has four main shortcomings: (D1) Transmission errors in RTM data can lead to analysis bias. (D2) Numerous machine state RTM items exist, and their complex relationship with WAT parameters isn''t fully understood. (D3) Delayed detection of WAT anomalies and (D4) delayed adjustment of RTM values, which can affect multiple wafer batches. To address these issues, we propose an approach called WAT Prediction with RTM and Optimizing RTM Control Parameters (WAPOR) to analyze historical data of machine state RTM and WAT parameter. The WAPOR study aims to establish predictive models between crucial RTM items and WAT parameters and set RTM control ranges to reduce the standard deviation of WAT electrical parameters. Using critical voltage electrical test parameters and RTM data from an actual semiconductor factory as a case study, the method''s effectiveness is verified. The main research problems (P), corresponding challenges (C), and proposed solutions (M) are as follows: (P1) RTM Data Transmission Loss: How to compensate for missing data in RTM data requested from the RTM Database corresponding to Wafer ID''s RTM Item? (C1) The challenge is maintaining the original data volume while improving the missing data rate, which varies between 20% to 40% per RTM Item. (M1) A Python-Based Multi-Request and Duplicates Removal (PB-MRDR) method is proposed to repeatedly request the same data from the RTM Database and merge, deduplicate, and supplement data in a Python environment. (P2) Selection of Crucial RTM Data Items: How to extract important RTM data items that influence WAT parameter deviation? (C2) The challenge lies in narrowing down from 28 RTM data items used in the case study to key items without losing essential information. (M2) A Hybrid RTM Item Selection Model (H-RIS) is developed, combining Stepwise Regression and Bagging Tree, Boosting Tree models to select important RTM items and set selection thresholds. (P3) Relationship Modeling between SIRIs and WAT Parameter: How to construct a predictive model between Selected Important RTM Items (SIRIs) and WAT parameter? (C3) The challenge is understanding the mathematical relationship between RTM data and WAT parameter at the end of the process. (M3) A Deep Back Propagation Neural Network (BPN) model(WPBM), is designed for predicting WAT parameter using SIRIs, accounting for their complex, multi-dimensional relationship. (P4) Optimization of SIRIs Control Parameters: How to set the control range for SIRIs based on their relationship with WAT parameter? (C4) The challenge is optimizing the control range in a vast search space with multiple variables. (M4) A method based on Genetic Algorithm (GA) for RTM Region Setting (RRS-GA) is proposed, utilizing the WPBM model and a fitness function oriented towards WAT parameter specifications. Key findings and contributions of this study include: (1) Innovative PB-MRDR method in Python environment to reduce data missing rate from 20-40% to 0.004% in 7969 wafers. (2) H-RIS method to select 6 crucial SIRIs from 28 RTM items, enhancing correlation and reducing analysis dimensions. (3) WPBM model using SIRIs to predict WAT parameter with a correlation coefficient of 0.505, surpassing the 25% significance threshold in practice. (4) RRS-GA method based on WAT parameter specifications for optimizing SIRIs control parameters, showing a potential 49% reduction in WAT parameter standard deviation. (5) Case study validation using actual semiconductor factory data, demonstrating the feasibility of the proposed methods in real-world scenarios.