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.
We determined the structural state of six plagioclase crystals from the Kobe meteorite by measuring the separation between the 13 1 and 131 X ray diffraction peaks (Δ131 parameter) using a Gandolfi camera. The formation temperature of each plagioclase crystal was then estimated by plotting the Δ131 parameter on the relation diagram between the Δ131 parameters and temperatures of plagioclase synthesis, as proposed by Smith (1972). Three of the crystals record temperatures of just under 700 °C, while the other three crystals record much lower temperatures. The temperature estimates can be regarded as representing the crystallization temperature of plagioclase, and the highest recorded temperature is thought to correspond to the peak temperature of the thermal metamorphism, close to but not exceeding 700 °C. A thermal model of the CK chondrites is proposed on the assumption that thermal metamorphism, with 26 Al decay as a heat source, began prior to accretion of the CK parent body. The model explains the homogeneous compositions of olivine and pyroxene in CK chondrites, which are inconsistent with the petrographic type suggested by their grain sizes, and explains the occurrence of silicate darkening in almost all CK chondrites.
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