Spatial variation decomposition via sparse regression

In this paper, we briefly discuss the recent development of a novel sparse regression technique that aims to accurately decompose process variation into two different components: (1) spatially correlated variation, and (2) uncorrelated random variation. Such variation decomposition is important to identify systematic variation patterns at wafer and/or chip level for process modeling, control and diagnosis. We demonstrate that the spatially correlated variation can be accurately represented by the linear combination of a small number of “templates”. Based upon this observation, an efficient algorithm is developed to accurately separate spatially correlated variation from uncorrelated random variation. Several examples based on silicon measurement data demonstrate that the aforementioned sparse regression technique can capture systematic variation patterns with high accuracy.