57 research outputs found
Performance analysis of demand planning approaches for aggregating, forecasting and disaggregating interrelated demands
No full textSpatial Variance Spectrum Analysis and Its Application to Unsupervised Detection of Systematic Wafer Spatial Variations
No full text
Temporal and Spatial Variation Analysis and Its Applications to Semiconductor Engineering Data Analysis
No full text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。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
Spatial Variance Spectrum Analysis and Its Application to Unsupervised Detection of Systematic Wafer Spatial Variations
No full textInternational audienceInvestigation of wafer spatial variations is critical for semiconductor process/equipment optimization and circuit design. The objective of spatial variation study is to differentiate the systematic variation component from the random component. This is usually done by contrasting with a set of known systematic patterns based on engineering knowledge. However, there could exist unknown systematic components remaining in the unexplained residuals and overlooked by the conventional spatial variation study. In this paper, we develop a novel spatial variance spectrum (SVS) to analyze the systematic variations without any priori information of the systematic patterns. The SVS is a series of spatial variations over a range of spatial moving window sizes from the smallest spatial moving window consisting of only two metrology sites to the largest one covering all metrology sites of the entire wafer. The SVS can be used to characterize the wafer spatial variations and to detect existence of systematic variations by a proposed hypothesis test. We also propose an index to summarize from the SVS the systematic proportion of the spatial variation. The proposed test and index of systematic variations will be demonstrated and validated through both hypothetical examples and actual cases of wafer critical dimension (CD) metrology data
Performance analysis of demand planning approaches for aggregating, forecasting and disaggregating interrelated demands
No full textPerformance Analysis of Demand Planning Approaches for Aggregating, Forecasting and Disaggregating Interrelated Demands
No full textInternational audienceA synchronized and responsive flow of materials, information, funds, processes and services is the goal of supply chain planning. Demand planning, which is the very first step of supply chain planning, determines the effectiveness of manufacturing and logistic operations in the chain. Propagation and magnification of the uncertainty of demand signals through the supply chain, referred to as the bullwhip effect, is the major cause of ineffective operation plans. Therefore, a flexible and robust supply chain forecasting system is necessary for industrial planners to quickly respond to the volatile demand. Appropriate demand aggregation and statistical forecasting approaches are known to be effective in managing the demand variability. This paper uses the bivariate VAR(1) time series model as a study vehicle to investigate the effects of aggregating, forecasting and disaggregating two interrelated demands. Through theoretical development and systematic analysis, guidelines are provided to select proper demand planning approaches. A very important finding of this research is that disaggregation of a forecasted aggregated demand should be employed when the aggregated demand is very predictable through its positive autocorrelation. Moreover, the large positive correlation between demands can enhance the predictability and thus result in more accurate forecasts when statistical forecasting methods are used
Performance analysis of demand planning approaches for aggregating, forecasting and disaggregating interrelated demands
No full textA synchronized and responsive flow of materials, information, funds, processes and services is the goal of supply chain planning. Demand planning, which is the very first step of supply chain planning, determines the effectiveness of manufacturing and logistic operations in the chain. Propagation and magnification of the uncertainty of demand signals through the supply chain, referred to as the bullwhip effect, is the major cause of ineffective operation plans. Therefore, a flexible and robust supply chain forecasting system is necessary for industrial planners to quickly respond to the volatile demand. Appropriate demand aggregation and statistical forecasting approaches are known to be effective in managing the demand variability. This paper uses the bivariate VAR(1) time series model as a study vehicle to investigate the effects of aggregating, forecasting and disaggregating two interrelated demands. Through theoretical development and systematic analysis, guidelines are provided to select proper demand planning approaches. A very important finding of this research is that disaggregation of a forecasted aggregated demand should be employed when the aggregated demand is very predictable through its positive autocorrelation. Moreover, the large positive correlation between demands can enhance the predictability and thus result in more accurate forecasts when statistical forecasting methods are used.Top-down forecasting Demand aggregation Disaggregation Bivariate VAR(1) time series
Recipe-Independent Health Indicator for Tool Predictive Maintenance and Fault Diagnosis
No full textInternational audienceAdvanced sensor and information technologies have made real-time tool data readily accessible to tool and process engineers. A significant number of tool parameters (SVID’s) is collected during wafer processing and a large amount of tool data is acquired and available for fault detection and classification (FDC). Many IC makers have substantially improved the process capabilities by implementing FDC. With the real-time tool data, one can also evaluate the overall tool condition so that tool maintenance can be more effectively scheduled and the post-maintenance tool condition can be more easily qualified. However, due to the frequent change of recipes and the diversity of operations, the overall tool health is very difficult to evaluate. In this paper, we propose a recipe-independent health indicator based on the generalized moving variance. It is shown that the indicator faithfully reveals the tool condition regardless of recipe/operation changes. With the tool health indicator, possible tool faults can be identified and proper maintenance measures can be scheduled accordingly. The proposed indicator will be demonstrated and validated through the case studies of a PECVD and a PVD tool from a local fab
Wafer Spatial Pattern Decomposition and Diagnosis Based on Processing Characteristics
No full textInternational audienceIn semiconductor manufacturing, Integrated circuits are produced by building functional modules on top of silicon disks called wafers. The increasing complexity of processes as the nano-technology advances has caused the wafer quality diagnosis even more difficult. Quality monitoring is usually performed via physical measurements and electric tests at selected (and limited) locations on the wafers. The relationship between the measurements and their corresponding locations can be modelled by a Universal Kriging model, including a polynomial trend and an interpolation based on a Gaussian process. A wafer-to-wafer comparison of the reconstructed patterns shall firstly reveal fundamental differences among the wafers such as the product types or process recipes. Furthermore, the impacts from manufacturing equipment, feedback/feedforward process regulations and real time process signals/states are also critical for the quality of wafer measurements.In this study, the spatial reconstruction of wafer measurements is firstly presented. The trend is modelled as a linear combination of Zernike polynomials (Zernike, 1934), in terms of a set of orthogonal functions over the circular domain, i.e. a wafer. Spatial correlation is also investigated in the model with a Gaussian process regression (Rasmussen and Williams, 2006). Links between the modelled patterns and corresponding process parameters are then established for key factors detection and wafer profile prediction. The proposed methodology is tested with industrial datasets
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