Lithographic process optimization using process capability analysis

A capable process fulfills many requirements on e.g. depth of focus, exposure latitude, and mask error factor. This makes a full optimization complicated. Traditionally only a few parameters are included in the optimization routine, such as the focus-dose process window, while other parameters like the (NA,σ ) illumination conditions are fixed at a specified value. In this paper we present an analytical model for describing the effect of variations in dose, focus and mask CD. We optimize the overall CD distribution, both the target value and the CD variation, taking the statistical variations of focus, dose and mask line width variations into account. The improved CD control is measured quantitatively, using the well-known process capability index ( C pk ). The results are compared to traditional optimization schemes and brute force Monte Carlo simulations. Process latitudes can be better optimized while calculating the OPC curve. This is achieved by tuning the mask corrections to the process variations and simultaneously optimizing the global mask bias. Furthermore, the optimization method enables a trade off between mask error and process control. Simulated aerial image data is used to determine the optimum mask bias and illumination condition for different levels of process variation, including mask CD variation. The effect of optimizing the global mask bias is calculated. Finally, the results will be compared to experimental data for a number of illumination settings.