Statistical Yield Modeling for Sub-wavelength Lithography

Photolithography is at the heart of semiconductor manufacturing process. To support continued scaling of transistors, lithographic resolution must continue to improve. At today's volume manufacturing process, a light source of 193 nm wavelength is used to print devices with 45 nm feature size. To address sub-wavelength printability, a number of resolution enhancement techniques (RET) have been used. While RET techniques allow printing of sub-wavelength features, the feature length itself becomes highly sensitive to process parameters, which in turn detracts from yield due to small perturbations in manufacturing parameters. Yield loss is a function of random variables such as depth-of-focus, exposure dose, lens aberration and resist thickness. The loss-of-yield is also a function of systematic components such as specific layout structure and out-of-band radiation from optical source. In this paper, we present a yield modeling technique for a given layout, based on a statistical model for process variability. The key issues addressed in this paper are (i) layout error modeling, (ii) avoidance of mask simulation for chip layouts, (iii) avoidance of full Monte-Carlo simulation for variational lithography modeling, (iv) building a methodology for yield estimation based on existing commercial tools. Results based on our approach show that yield sensitivity increases at smaller feature sizes.