Article

Wafer Quality Monitoring using Spatial Dirichlet Process based Mixed-Effect Profile Modeling Scheme

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The objective of this work is to develop a profile-based statistical process control scheme for efficaciously monitoring wafer thickness profiles with non-normality in an industrial wafer slicing process. This is an important research area because the geometric quality of semiconductor wafers in a slicing process has a direct impact on the functional integrity of semiconductor parts and the efficiency of the production. Since non-normality in profiles indicates the existence of inter-cluster variations (i.e., the profiles cannot be represented by a single mean profile with normally-distributed random noise), it deteriorates the effectiveness of many traditional statistical process control methods with normality assumption. To realize the objective of this work, a mixed-effect profile monitoring (MEPM) scheme is proposed. The MEPM scheme adaptively groups profile data into clusters and models the inter-cluster variations, consequently, enabling a robust statistical process control scheme for detecting deviant profile data. Capturing the clustering information of the profile data leads to a deep understanding and an accurate modeling of the spatial data. It is a significant improvement over the current practice of monitoring the geometric product quality by summary quality features (such as total thickness variation) or by profiles neglecting inter-cluster variations. In this paper, the MEPM scheme is tested for detecting the out-of-control wafers from a wafer slicing process. Based on wafer thickness profiles, the MEPM scheme outperforms other benchmark methods and identifies the deviant wafers with low average type II error (missed detection rate) as 0.039. This profile monitoring scheme is extensible to geometrical quality assurance for products in other processes.
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... Principal component analysis [23][24][25] and independent component analysis [26] methods are used to separate the components of geometric specifications and analyze the causes of error. Some machine learning methods such as neural network algorithms [27] and Gaussian processes [28,29] have been proposed to detect changes in the profiles. ...
... Yu and Liu [32] proposed a new control chart to monitor the mean shifts of autocorrelated manufacturing processes. For profiles' data violating the assumption of normal distribution, Liu et al. [29] proposed a mixed-effect profile model to monitoring wafer thickness. However, few studies have focused on the case that the observations are spatially correlated. ...
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... Qiu et al. [13] proposed a nonparametric mixed-effects model that focuses on nonparametric profile monitoring when within-profile data are correlated. The profiles cannot be represented by a single average profile of normally distributed random noise, so a mixed-effects profile monitoring (MEPM) scheme that considers the presence of inter-cluster variation is proposed [14]. Gu and Ma [15] proposed a nonparametric mixed-effects model in which fixed effects are modeled by a P-spline. ...
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... Different kernels, such as Bessel additive variogram [21], have been developed to extend the capability of kriging methods to model different spatial variation patterns. These methods have been widely adopted in manufacturing applications, including wafer profile monitoring in semiconductor industry [22], quality control in additive manufacturing [23], and tool condition monitoring in ultrasonic metal welding [2,4,3]. Because these methods estimate missing values from nearby locations, their effectiveness relies on adequate measurement data. ...
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... Zheng et al. (2011) and Chuang et al. (2013) used splines to model profiles, whereas Amiri et al. (2010) used polynomials. More complex models such as mixed effects model (Jensen et al., 2008;Liu et al., 2018) and Gaussian process model (Zhang et al., 2015;Zhang et al., 2016), have also been applied. Most existing research works use parametric models. ...
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