Model-based clustering for integrated circuit yield enhancement

Hwang, Jung Yoon; Kuo, Way

doi:10.1016/j.ejor.2005.11.032

Cited by 73 publications

(33 citation statements)

References 30 publications

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“…A Markov random field is used to characterise the clustered defects. A similar approach was used by Hwang and Kuo (2007) in a model-based clustering strategy that treats the observed defects as the composition of both global defects resulting from random causes and local defects resulting from assignable causes. A spatial non-homogeneous Poisson process is used to model the global defects; a bivariate normal distribution or principal curve is then used to model the local defects.…”

Section: Modelling 2d Discrete Datamentioning

confidence: 99%

A hierarchical model for characterising spatial wafer variations

Bao

Wang

Jin

2013

International Journal of Production Research

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Silicon wafers are commonly used materials in the semiconductor manufacturing industry. Their geometric quality directly affects the production cost and yield. Therefore, improvement in the quality of wafers is critical for meeting the current competitive market needs. Conventional summary metrics such as total thickness variation, bow and warp can neither fully reflect the local variability within each wafer nor provide useful insight for root cause diagnosis and quality improvement. The advancement of sensing technology enables two-dimensional (2D) data mapping to characterise the geometric shapes of wafers, which provides more information than summary metrics. The objective of this research is to develop a statistical model to characterise the thickness variation of wafers based on 2D data maps. Specifically, the thickness variation of wafers is decomposed into macro-scale and micro-scale variations, which are modelled as a cubic curve and a first-order intrinsic Gaussian Markov random field, respectively. The models can successfully capture both the macro-scale mean trend and the micro-scale local variation, with important engineering implications for process monitoring, fault diagnosis and run-to-run control. A practical case study from a wafer manufacturing process is performed to show the effectiveness of the proposed methodology.

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Section: Modelling 2d Discrete Datamentioning

confidence: 99%

A hierarchical model for characterising spatial wafer variations

Bao

Wang

Jin

2013

International Journal of Production Research

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“…Each local defect cluster can be categorized, according to its spatial pattern, into its defect generation cause. For example, a cluster with a curvilinear shape is probably caused by a material handling scratch (Hwang and Kuo, 2007). Most yield/reliability improvement efforts are focused on finding and removing assignable causes.…”

Section: Introductionmentioning

confidence: 99%

“…However, defect clusters with curvilinear patterns are observed on wafers and global defects may not be homogeneous for some manufacturing processes. Hwang and Kuo (2007) propose the use of spatial non-homogeneous Poisson processes, bivariate normal distributions and principal curves to model the distributions of global defects, the distributions of local defects in clusters with ellipsoidal patterns and the distributions of local defects in clusters with curvilinear patterns, respectively. In the first step of their algorithm, they cluster the defects assuming that all of the local defect clusters are modeled by bivariate normal distributions.…”

Section: Introductionmentioning

confidence: 99%

“…Wang et al (2006) propose a hybrid clustering method to simultaneously recognize both convex and non-convex patterns. Hwang and Kuo (2007) propose a two-step method using model-based clustering. Compared to other approaches, model-based clustering has the following advantages: (i) it is flexible enough that no training data are needed for new defect patterns to be easily detected; and (ii) the clustering results can be used for yield estimation and prediction via advanced yield models based on spatial point processes (Hwang, 2004).…”

Section: Introductionmentioning

confidence: 99%

“…Spatial defect pattern recognition is to detect the existence, shape, location and orientation of the defect clusters. The spatial defect patterns are thought to result from the superposition of both global defect patterns and local defect patterns (Hwang and Kuo, 2007). Global defects are generated by random causes, such as particles in clean rooms, thermal variations in annealing processes and variations in deposition and etching processes, etc.…”

Section: Introductionmentioning

confidence: 99%

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A model-based clustering approach to the recognition of the spatial defect patterns produced during semiconductor fabrication

Yuan

Kuo

2007

IIE Transactions

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Defects on semiconductor wafers tend to cluster and the spatial defect patterns of these defect clusters contain valuable information about potential problems in the manufacturing processes. This study proposes a model-based clustering algorithm for automatic spatial defect recognition on semiconductor wafers. A mixture model is proposed to model the distributions of defects on wafer surfaces. The proposed algorithm can find the number of defect clusters and identify the pattern of each cluster automatically. It is capable of detecting defect clusters with linear patterns, curvilinear patterns and ellipsoidal patterns. Promising results have been obtained from simulation studies.

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Identification of spatial defects in semiconductor manufacturing

Borgoni

Galimberti

Zappa

2021

Appl Stoch Models Bus & Ind

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In this article, we investigate the occurrence of defects in integrated circuit fabrication and show how spatial analysis can be effective in grasping and representing spatial regularities in defect patterns on the silicon supports, called wafers, used to produce microchips. Defects occurring on the wafer surface are the main cause of yield loss in the semiconductor industry; hence, to promptly detect an excess of defects and identify their spatial structure is crucial to the entire fabrication process. To address this hard-to-solve problem, this article proposes a concatenation of different methods, namely, a control chart, a clustering algorithm, and a graphical tool. First, a control chart based on the p-value of an appropriate test recognizes spatially structured defects on the wafer area.Then a clustering procedure grounded on the minimum spanning tree algorithm is adopted to identify those regions more prone to defect occurrences. Finally, alpha-shapes are employed to display their shape effectively. The suggested procedure proves to be extremely fast and effective, allowing its implementation in-line during the fabrication process. This provides a great advantage in modern microelectronics where items tend to be highly specialized and often produced in small lots. In particular, due to the Monte Carlo nature of the procedure, the control chart proposed hereafter does not require gold standard data to be set. This is particularly advantageous for small lot production, which is typically limited in time and does not permit to collect long time series of the charting statistics. K E Y W O R D Salpha-shapes, integrated circuits fabrication, minimum spanning tree algorithm, p-value control charts INTRODUCTIONSpatial statistics has long played a fundamental role in environmental, agriculture, and ecological studies as well as in economics, epidemiology, and other human sciences. Less usual are applications in industry and technology where the spatial dimension is often crucial to assess the quality of production processes. In this article, we investigate the spatial structure of defects occurring in integrated circuit fabrication. Integrated circuits are built through several different physical and chemical steps that are performed on thin silicon slices of a few 878

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Model-based clustering for integrated circuit yield enhancement

Cited by 73 publications

References 30 publications

A hierarchical model for characterising spatial wafer variations

A hierarchical model for characterising spatial wafer variations

A model-based clustering approach to the recognition of the spatial defect patterns produced during semiconductor fabrication

Identification of spatial defects in semiconductor manufacturing

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