  This paper presents a multi-dimensional computational method to predict the
spatial variation data inside and across multiple dies of a wafer. This
technique is based on tensor computation. A tensor is a high-dimensional
generalization of a matrix or a vector. By exploiting the hidden low-rank
property of a high-dimensional data array, the large amount of unknown
variation testing data may be predicted from a few random measurement samples.
The tensor rank, which decides the complexity of a tensor representation, is
decided by an available variational Bayesian approach. Our approach is
validated by a practical chip testing data set, and it can be easily
generalized to characterize the process variations of multiple wafers. Our
approach is more efficient than the previous virtual probe techniques in terms
of memory and computational cost when handling high-dimensional chip testing
data.
