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.

Nano-scale VLSI design is facing the problems of increased test data volume. Small delay defects are becoming possible sources of test escapes, and high delay test quality and therefore a greater volume of test data are required. The increased test data volume requires more tester memory and test application time, and both result in test cost inflation. Test pattern ordering gives a practical solution to reduce test cost, where test patterns are ordered so that more defects can be detected as early as possible. In this paper, we propose a test pattern ordering method based on SDQL (Statistical Delay Quality Level), which is a measure of delay test quality considering small delay defects. Our proposed method orders test patterns so that SDQL shrinks fast, which means more delay defects can be detected as early as possible. The proposed method efficiently orders test patterns with minimal usage of time-consuming timing-aware fault simulation. Experimental results demonstrate that our method can obtain test pattern ordering within a reasonable time, and also suggest how to prepare test sets suitable as inputs of test pattern ordering.