Induced Start Dynamic Sampling for Wafer Metrology Optimization

Abstract

Metrology, which plays an important role in ensuring production quality in modern manufacturing industries, incurs substantial costs, both in terms of the infrastructure required, and the time needed to perform measurements. In particular, in the semiconductor manufacturing industry, measuring fundamental quantities on different sites of a wafer surface is associated with increased production time. To increase metrology efficiency, a typical strategy is to limit the number of sites measured and to exploit statistical models (soft sensing) to reconstruct the wafer profile. Moreover, for quality reasons, spatial dynamic sampling strategies may be employed to ensure that all regions of a wafer surface are checked periodically during production. In this work, we propose a new sampling strategy, called Induced Start Dynamic Sampling (ISDS), that adapts greedy feature selection algorithms to the spatial dynamic sampling problem such that the number of measured sites at each process run is minimized while achieving good wafer profile reconstruction accuracy and process visibility. The superiority of the proposed strategy with respect to the state-of-the-art is demonstrated using both simulated data and an industrial chemical vapour deposition case study. Note To Practitioners-In this work we tackle a practical metrology problem encountered in semiconductor manufacturing, namely, the design of a dynamic wafer measurement plan to monitor the accuracy of a process across the whole wafer surface. The measurement plan is called 'dynamic', since, the measurement locations, which are drawn from a candidate set that provides coverage of the whole wafer, change at each process iteration. Our methodology addresses the challenge of finding an optimized trade-off between the number of measurements performed on each wafer and the reconstruction accuracy that can be achieved for the unmeasured areas on the wafer, while at the same time, for quality assurance purposes, ensuring that all locations on a wafer are visited in a finite number of process runs. The major benefit of the methodology is that it can significantly reduce the number of sites that need to be measured on each wafer enabling greater throughput on metrology tools without sacrificing process monitoring and anomaly detection capability.

The MICS Project: A Data Science Pipeline for Industry 4.0 Applications

“…SS approaches are used to improve quality monitoring, control, and sampling in production [20]; • Dynamic Sampling (DS) strategies are approaches able to optimize measurement and sampling in complex manufacturing environments [21]. DS approaches typically rely on regression analysis and optimization approaches [22]; • Computer Vision-based control and monitoring is widely adopted in the industry thanks to the diffusion of low-cost effective industrial cameras and the incredible advancements of Deep Learning approaches in recent years. In this context, supervised classification and segmentation approaches to recognize defects [23] are some of the most popular techniques adopted, but unsupervised methodologies have been used in the industry [24].…”

Recovery of linear components: Reduced complexity autoencoder designs

“…Thus, further hidden layers are added to obtain a deep structure called a stacked autoencoder (SAE) [42]. Assuming the general case of an ANN having L layers, the autoencoder equation (11) becomes…”

“…The L 1 regularization term, also known as the least absolute shrinkage and selection operator (LASSO), is added to the cost function (14) in [33] to achieve input selection in a Multilayer Perceptron neural network, while [31] and [32] integrated a row-sparse regularization term and a graph regularization trace-ratio criterion, respectively, within the training of an autoencoder to indirectly obtain nonlinear variable selection. Even when using implicit approaches, the computational burden associated with nonlinear variable selection can be prohibitive in time-constrained applications such as dynamic spatial sampling for silicon wafer process monitoring [11], especially when training large neural models. This has motivated our investigation of a methodology that requires the training of less complex nonlinear models, and can be thought as a middle ground between linear and nonlinear variable selection techniques.…”

“…Rather than transforming to a new set of variables, it is often desirable to reduce dimensionality by selecting a subset of the original variables (or features) as this enhances the transparency and interpretability of models [9], and in some applications it is a necessity, for example in sensor selection and measurement plan optimisation problems [10], [11]. Since determining the best subset of variables from a candidate set, with respect to a given performance metric, is an NP-hard combinatorial optimisation problem, practical implementations of unsupervised variable selection usually involve approximate solutions such as those provided by greedy search algorithms [12], [13], [14], [15], [16].…”