A novel robust optimization method of exposure and mask conditions for beyond 65 nm- node lithography

Parameter optimization is a key issue to develop low-kl lithography processes, in which the number of control and error factors has been increasing. This holds especially true for alternating phase-shifting mask (alt-PSM) techniques; i.e., for this technique, not only exposure conditions but also mask structures should be optimized under various error factors (or noise factors), such as defocus, dose fluctuations, lens aberrations, mask making errors and so on. This paper describes a novel method of performing such optimization, which is developed based on a method of design of experiments (DOEs). Stabilities of target performance for various combinations of parameters are simulated by varying noise factor levels which are assigned to an orthogonal array. Optimum values of parameters are determined so as to maximize the stabilities of target performance. This method is applied to a 45-nm node alt-PSM (alternating phase-shifting mask) technique. Optical conditions, such as NA (numerical aperture) and σ-value, and mask structures, such as trench depth and undercut size, are optimized under various noise factors by applying our method for optimization. As a result, high stability of critical dimension (CD) is obtained together with sufficient suppression of image placement errors. The optimized result is further verified by statistic calculations. Finally, we conclude that our method is a very powerful tool to simultaneously optimize lithographic conditions for low-kl lithography processes.