Efficient spatial pattern analysis for variation decomposition via robust sparse regression

In this paper, we propose a new technique to achieve accurate decomposition of process variation by efficiently performing spatial pattern analysis. We demonstrate that the spatially correlated systematic variation can be accurately represented by the linear combination of a small number of templates. Based on this observation, an efficient sparse regression algorithm is developed to accurately extract the most adequate templates to represent spatially correlated variation. In addition, a robust sparse regression algorithm is proposed to automatically remove measurement outliers. We further develop a fast numerical algorithm that may reduce the computational time by several orders of magnitude over the traditional direct implementation. Our experimental results based on both synthetic and silicon data demonstrate that the proposed sparse regression technique can capture spatially correlated variation patterns with high accuracy and efficiency.