In this paper, we propose a novel spatial variation modeling method based on hidden Markov tree (HMT) for nanoscale integrated circuits, which could efficiently improve the accuracy of full-wafer/chip spatial variations recovery at extremely low measurement cost. Applying this method, HMT is introduced to set up a statistical model for coefficients after exploring the underlying correlated representation of the spatial variation in the frequency domain. Accordingly, two key inherent properties of the modeling coefficients, i.e., correlations and sparse presentations in the frequency domain, can be captured exactly and the modeling accuracy can be improved evidently. Then, maximum- a-posteriori  estimation is applied to formulate the original problem as a convex optimization that could be solved efficiently and robustly. Numerical results based on industrial data demonstrate that the proposed method can achieve superior accuracy over other existing approaches including orthogonal matching pursuit,    ${l} _{1}$   -norm regularization, and reweighted    ${l} _{1}$   -norm regularization.
['Changhai Liao', 'Jun Tao', 'Xuan Zeng', 'Yangfeng Su', 'Dian Zhou', 'Xin Li']
Efficient Spatial Variation Modeling of Nanoscale Integrated Circuits Via Hidden Markov Tree