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This paper presents a multi-dimensional computational method to predict thespatial variation data inside and across multiple dies of a wafer. Thistechnique is based on tensor computation. A tensor is a high-dimensionalgeneralization of a matrix or a vector. By exploiting the hidden low-rankproperty of a high-dimensional data array, the large amount of unknownvariation testing data may be predicted from a few random measurement samples.The tensor rank, which decides the complexity of a tensor representation, isdecided by an available variational Bayesian approach. Our approach isvalidated by a practical chip testing data set, and it can be easilygeneralized to characterize the process variations of multiple wafers. Ourapproach is more efficient than the previous virtual probe techniques in termsof memory and computational cost when handling high-dimensional chip testingdata.

Prediction of multi-dimensional spatial variation data via Bayesian tensor completion