Statistical wafer-level characteristic variation modeling offers an attractive method for reducing the measurement cost in large-scale integrated (LSI) circuit testing while maintaining test quality. In this method, the performance of unmeasured LSI circuits fabricated on a wafer is statistically predicted based on a few measured LSI circuits. Conventional statistical methods model spatially smooth variations in the wafers. However, actual wafers can exhibit discontinuous variations that are systematically caused by the manufacturing environment, such as shot dependence. In this paper, we propose a modeling method that considers discontinuous variations in wafer characteristics by applying the knowledge of manufacturing engineers to a model estimated using Gaussian process regression. In the proposed method, the process variation is decomposed into systematic discontinuous and global components to improve estimation accuracy. An evaluation performed using an industrial production test dataset indicates that the proposed method effectively reduces the estimation error for an entire wafer by over 36% compared with conventional methods.

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Wafer-level performance prediction has been attracting attention to reduce measurement costs without compromising test quality in production tests. Although several efficient methods have been proposed, the site-to-site variation, which is often observed in multi-site testing for radio frequency circuits, has not yet been sufficiently addressed. In this paper, we propose a wafer-level performance prediction method for multi-site testing that can consider the site-to-site variation. The proposed method is based on the Gaussian process, which is widely used for waferlevel spatial correlation modeling, improving the prediction accuracy by extending hierarchical modeling to exploit the test site information provided by test engineers. In addition, we propose an active test-site sampling method to maximize measurement cost reduction. Through experiments using industrial production test data, we demonstrate that the proposed method can reduce the estimation error to 1/19 of that obtained using a conventional method. Moreover, we demonstrate that the proposed sampling method can reduce the number of the measurements by 97% while achieving sufficient estimation accuracy.