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Markov Random Fields for Pattern Extraction in Analog Wafer Test Data
Abstract
In semiconductor industry it is of paramount importance to check whether a manufactured device fulfills all quality specifications and is therefore suitable for being sold to the customer. The occurrence of specific spatial patterns within the so-called wafer test data, i.e. analog electric measurements, might point out on production issues. However, the shape of these critical patterns is unknown. In this paper different kinds of process patterns are extracted from wafer test data by an image processing approach using Markov Random Field models for image restoration. The goal is to develop an automated procedure to identify visible patterns in wafer test data to improve pattern matching. This step is a necessary precondition for a subsequent root-cause analysis of these patterns. The developed pattern extraction algorithm yields a more accurate discrimination between distinct patterns, resulting in an improved pattern comparison than in the original dataset. In a next step pattern classification will be applied to improve the production process control.
... With great advances of technologies, more wafer projects need to be tested since the increasing complexity of manufacturing. However, traditional wafer test methods are hard to achieve high accuracy while dealing with large-scale problems, which has a great impact on cycle time, yield, cost and final product quality [3][4][5][6]. The reliability of wafer test has always been one of the main difficulties in semiconductor production. ...
Wafer test is one of the most significant parts of semiconductor fabrication. Effective data mining technologies will improve wafer prediction performance, which will contribute to production cycle time reductions, yield enhancement and final product quality improvement. This paper presents an improved AdaBoost Tree-based method to decrease the false fail rate of defective products in wafer test. Particularly, it focuses on a discussion about the low classification accuracy for the minority class of samples due to the imbalance of wafer test data set. In addition, the novel method is proposed to identify defective products in wafer test, which achieves higher separability between the majority class and the minority class as well as shorter test time. Finally, experimental studies on wafer test data set show that our algorithm has better performance than traditional methods.
... The speed-up is even higher if multiple images of equal size and noise intensity are processed due to the constant decomposition of the equation system, which launches new possibilities of application, e.g. video processing or industrial image applications [20]. Regarding the quality of the presented analytical solution of MRFs, the mathematical optimum of the restoration is reached exactly and cannot be beaten by any other approach for the same model. ...
Image restoration and denoising is an essential preprocessing step for almost every subsequent task in computer vision. Markov Random Fields offer a well-founded, sophisticated approach for this purpose, but unfortunately the associated computation procedures are not sufficiently fast, due to a high-dimensional optimization problem. While the increase of computing power could not solve this runtime issue appropriately, we address it in a mathematical way: we suggest an analytical solution for the optimum of the inference problem, which provides desirable mathematical properties. In practice, our new method accelerates the runtime via reducing the computational complexity of the image restoration task by orders of magnitude, independent from the smoothing intensity. As a result, Markov Random Fields can be considered for modern big data problems in computer vision, especially if numerous images with equal sizes are processed.
... Denoising using MRFs. The MRF model for wafermap denoising is explained in detail in [18] which is based on the book of Li [19]. The corresponding image processing model, which was originally introduced by Geman and Geman [20], belongs to the class of Spatial Domain Filters, i.e., filtering local groups of adjacent image pixels directly from the original image to reduce noise. ...
Semiconductor manufacturing is a highly innovative branch of industry, where a high degree of automation has already been achieved. For example, devices tested to be outside of their specifications in electrical wafer test are automatically scrapped. In this work, we go one step further and analyse test data of devices still within the limits of the specification, by exploiting the information contained in the analog wafermaps. To that end, we propose two feature extraction approaches with the aim to detect patterns in the wafer test dataset. Such patterns might indicate the onset of critical deviations in the
production process. The studied approaches are: (A) classical image processing and restoration techniques in combination with sophisticated feature engineering and (B) a data-driven deep generative model. The two approaches are evaluated on both a synthetic and a real-world dataset. The synthetic dataset has been modelled based on real-world patterns and characteristics. We found both approaches to provide similar overall evaluation metrics. Our in-depth analysis helps to choose one approach over
the other depending on data availability as a major aspect, as well as on available computing power and required interpretability of the results.
... In addition, preprocessing and feature extraction are crucial to guarantee that the ML technique provides useful results. Therefore, a Markov Random Field (MRF) method for image denoising is applied to the wafermaps, which can be treated like images [1]. Afterwards, Local Binary Patterns (LBP) [2] and Rotated Local Binary Patterns (RLBP) [3] are extracted as image features. ...
Semiconductor manufacturing is a highly complex and competitive branch of industry, comprising hundreds of process steps, which do not allow any deviations from the specification. Depending on the application area of the products, the production chain is subject to strict quality requirements. While heading towards industry 4.0, automation of production workflows is required and hence, even more effort must be spent on controlling the processes accordingly. The need for data-driven indicators supporting human experts via monitoring the production process is inevitable, but lacks adequate solutions exploiting both, profound academic methodologies and
domain-specific know-how.
In many cases, process deviations cannot be detected automatically during the semiconductor frontend production. Hence, the wafer test stage at the end of frontend manufacturing plays a key role to determine whether preceding process steps were executed with the necessary precision. The analysis of these wafer test data is challenging, since process deviations can only be detected by investigating spatial dependencies (patterns) over the wafer. Such patterns become visible, if devices on the wafer violate specification limits of the product. In this work, we go one step further and investigate the automated detection of process patterns in data from analog wafer test parameters, i.e. the electrical measurements, instead of pass/fail classifications, which brings the benefit that deviations can be recognized before they result in yield loss - this aspect is a clear difference to state-of-the-art research, where merely specification violations are observed. For this purpose, an indicator for the level of concern associated with process patterns on the wafer, a so-called Health Factor for Process Patterns, is presented. The indicator combines machine learning techniques and expert knowledge.
In order to develop such a Health Factor, the problem is divided into three major components, which are investigated separately: ecognition of the pattern type, quantification of the intensity of a pattern and specification of the criticality associated with each pattern type. Since the first two components are intrinsically present in the wafer test data, machine learning systems are deployed for both, while criticality is specified by introducing expert and domain knowledge to
the concept. The proposed decision support system is semi-automated and thus, unifies pattern recognition and expert knowledge in a promising way.
The effectiveness of the proposed Health Factor is underlined by experiments conducted on simulated as well as real-world datasets. The evaluations show that the system is not only mathematically valid, but also practically applicable and fulfills the demands raised by a real-world production environment. Moreover, the indicator can be transferred to various product types or even related problem setups given a reliable training dataset.
Countless learning tasks require awareness of time. Image captioning, speech
synthesis, and video game playing all require that a model generate sequences
of outputs. In other domains, such as time series prediction, video analysis,
and music information retrieval, a model must learn from sequences of inputs.
Significantly more interactive tasks, such as natural language translation,
engaging in dialogue, and robotic control, often demand both.
Recurrent neural networks (RNNs) are a powerful family of connectionist
models that capture time dynamics via cycles in the graph. Unlike feedforward
neural networks, recurrent networks can process examples one at a time,
retaining a state, or memory, that reflects an arbitrarily long context window.
While these networks have long been difficult to train and often contain
millions of parameters, recent advances in network architectures, optimization
techniques, and parallel computation have enabled large-scale learning with
recurrent nets.
Over the past few years, systems based on state of the art long short-term
memory (LSTM) and bidirectional recurrent neural network (BRNN) architectures
have demonstrated record-setting performance on tasks as varied as image
captioning, language translation, and handwriting recognition. In this review
of the literature we synthesize the body of research that over the past three
decades has yielded and reduced to practice these powerful models. When
appropriate, we reconcile conflicting notation and nomenclature. Our goal is to
provide a mostly self-contained explication of state of the art systems,
together with a historical perspective and ample references to the primary
research.
Edition 1
Since its beginning, image analysis research has been evolving from heuristic design of algorithms to systematic investigation of approaches. Researchers have realized: (1) The solution to a vision problem should be sought based on optimization principles, either explicitly or implicitly, and (2) contextual constraints are ultimately necessary for the understanding of visual information in images. Two questions follow: how to define an optimality criterion under contextual constraints and how to find its optimal solution.
Markov random field (MRF), a branch of probability theory, provides a foundation for the characterization of contextual constraints and the derivation of the probability distribution of interacting features. In conjunction with methods from decision and estimation theory, MRF theory provides a systematic approach for deriving optimality criteria such as those based on the maximum a posteriori (MAP) concept. This MAP-MRF framework enables us to systematically develop algorithms for a variety of vision problems using rational principles rather than ad hoc heuristics. For these reasons, there has been increasing interest in modeling computer vision problems using MRF’s in recent years.
This book provides a coherent reference to theories, methodologies, and recent developments in solving computer vision problems based on MRF’s, statistics, and optimization. It treats various problems in low- and high-level computational vision in a systematic and unified way within the MAP-MRF framework. The main issues of concern are how to use MRF’s to encode contextual constraints that are indispensable to image understanding; how to derive the objective function, typically the posterior distribution, for the optimal solution to a problem; and how to design computational algorithms for finding the optimal solution.
As the first thorough reference on the subject, the book has four essential parts for solving image and vision analysis problems using MRF’s: (1) introduction to fundamental theories, (2) formulations of various image models in the MAP-MRF framework, (3) parameter estimation, and (4) optimization methods.
This paper studies a combination of generative Markov random field (MRF)
models and discriminatively trained deep convolutional neural networks (dCNNs)
for synthesizing 2D images. The generative MRF acts on higher-levels of a dCNN
feature pyramid, controling the image layout at an abstract level. We apply the
method to both photographic and non-photo-realistic (artwork) synthesis tasks.
The MRF regularizer prevents over-excitation artifacts and reduces implausible
feature mixtures common to previous dCNN inversion approaches, permitting
synthezing photographic content with increased visual plausibility. Unlike
standard MRF-based texture synthesis, the combined system can both match and
adapt local features with considerable variability, yielding results far out of
reach of classic generative MRF methods.
Device Level Maverick Screening
- A Zernig
A. Zernig, "Device Level Maverick Screening," Alpen-Adria-University
Klagenfurt, Klagenfurt-Austria, 2016.