Advanced CD uniformity correction using radial basis function (RBF) models

Critical dimension uniformity (CDU) control using dose correction is well established and has relied on traditional polynomial models like Zernike and Legendre for a long time. As process margins are shrinking and CD (and CDU) control becomes a significant contributor to edge placement error (EPE), the dose correction models need to be enhanced to represent the systematic behavior of the fingerprints more precisely. In this paper we show that many CD signatures over the exposure field or over the wafer cannot be corrected efficiently using classical polynomials. As the CD signatures can come from a variety of processes like etch, CVD, polish, or deposition, a flexible model approach is required. Furthermore, making the right decision when choosing the correct model order of the classical polynomial based model is complicated as we need to handle the balance between the degrees of freedom and minimizing the residuals. With this problem statement in mind, we introduce a novel radial basis function (RBF) modeling approach for dose corrections that can correct a wide range of signatures. The new modeling approach is verified on real CD signatures on product, reducing CDU significantly. Additionally, we demonstrate that this approach can make the life of the engineers easy again, as there are no prior decisions about model type and order needed.