Implementation of different cost functions for EUV mask optimization for next generation beyond 7nm

As the technology node gets smaller and smaller, the benefit from Sub-Resolution Assist Features (SRAF) becomes significant in EUV lithography which makes SRAFs a must-have tool for next generation beyond 7nm technology. When considering EUV specific effects, the metrics that need to be accounted for include Image Log-Slope (ILS), Process Variability (PV Band), common Depth of Focus (cDOF), and Image Shift (ImS) through focus. When these critical factors are accounted for during the EUV mask generation the optimization become much more complicated and challenging and necessitates the need for SRAFs beyond 7nm. SRAF helps enhance not only the PV Band, but more importantly helps boost the ILS, which is one of the key factors for improving stochastic effect in EUV. However, ILS is just one of the important image quality metric that we should focus on. For metal layers, Image Shift is another key factor which can have a big impact on overlay. ImS at the nominal condition could be compensated by Optical Proximity Correction (OPC), but image shift through focus can hardly be tuned by the main feature correction. The image shift through focus can be mitigated by SRAF insertion. Strong 3D mask effects can cause best focuses of different patterns to be far apart in EUV, which can cause an unusable cDOF even when the individual depth of focus values of all the patterns are not bad. SRAFs can be inserted to improve the individual depth of focus and align the best focuses together to help enhance the common process window. When taking account of various different EUV specific metrics mentioned above, then the most critical question for the next generation beyond 7nm is “How to define the cost function for mask optimization with SRAFs?” (Figure 1, EUV mask optimization flow for next generation beyond 7nm). In this study the image quality metrics including ILS, PVBand, cDOF, and ImS are evaluated. For each optimization schema using different cost functions, we examine the cost function metric and its impact on the other image quality metrics. We also present the potential trade-offs together with the analysis. Furthermore, multiple cross cost functions are defined for SRAF optimization and the results are analyzed accordingly. Both contact and metal layer patterns representing next generation beyond 7nm design rules are investigated. In our testing, symmetric standard sources from ASML NXE3400 is examined and the results are compared and analyzed.