# Sequential and Comprehensive Algorithm for Fault Detection in Semiconductor Sensors
###### Abstract  
The semiconductor manufacturing processes have been evolved to improve the yield rate. Here, we studied a sequential and comprehensive algorithm that could be used for fault detection and classification (FDC) of the semiconductor chips. A statistical process control (SFC) method is employed for inspecting whether sensors used in the semiconductor manufacturing process become stable or not. When the sensors are individually stable, the algorithm conducts the relational inspection to identify the relationship between two sensors. The key factor here is the coefficient of determination (R\({}^{2}\)). If R\({}^{2}\) is calculated as more than 0.7, their relationship is analyzed through the regression analysis, while the algorithm conducts the clustering analysis to the sensor pair with R\({}^{2}\) less than 0.7. This analysis also provided the capability to determine whether the newly generated data are defective or defect-free. Therefore, this study is not only applied to the semiconductor manufacturing process but can also be to the various research fields where the big data are treated. defect classification; machine learning; Voronoi diagram; statistical process control Article  
Sequential and Comprehensive Algorithm for Fault Detection in Semiconductor Sensors  
[PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], B.G. Sequential and Comprehensive Algorithm for Fault Detection in Semiconductor Sensors. _Appl. Sci._**2021**, _11_, 10419. [[https://doi.org/10.3390/app112110419](https://doi.org/10.3390/app112110419)]([https://doi.org/10.3390/app112110419](https://doi.org/10.3390/app112110419))  
Academic Editors [PERSON], [PERSON] and [PERSON]  
Received: 26 August 2021  
Accepted: 2 November 2021  
Published: 5 November 2021  
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**1. Introduction**  
Advances in the semiconductor industry have enormously contributed to other contemporary high-innovative industries such as wireless communication, aerospace, and pharmaceuticals [1; 2; 3]. Moreover, the semiconductor-based devices have a huge potential to achieve an advancement for wearables, robotics, and healthcare [4]. The emerge of smartphones has accelerated the development in the semiconductor industry and recently led to explosive demand in personal interest for Internet of Things (IoT) or home healthcare [5; 6]. Biomedical microelectromechanical system (BioMEMS) is one of the representative areas that has progressed with the development of the semiconductor industry. Various biochips have previously been developed using the semiconductor fabrication process [7; 8; 9]. The front-end fabrication process of the semiconductor silicon chips was classified into seven main processes: photolithography, etching, deposition, chemical mechanical planarization, oxidation, ion implantation, and diffusion, as previously described [10]. When the back-end process (e.g., packaging of the die) and test step are considered, the whole process flow of the semiconductors can involve over 500 steps, which may require approximately 30-60 days [11; 12]. The semiconductor industry has craved to identify the root causes of the faults in a real-time manner to reduce the process time and enhance the yield rate. However, the tremendous amounts of the data are generated during the long and complex semiconductor manufacturing process. The algorithm-based fault detection and classification (FDC) has been proposed in the previous studies [13; 14]. The key challenge is an effective and rapid interpretation of the valuable information hidden in the vast and complex microfabrication data [15]. The FDC methods are commonly divided into three types: model-based, knowledge-based, and data-based methods, as previously described [16]. The model-based and knowledge-based methods have generally used for understanding the process input and output relationship through the mathematical calculation.