As shrinkage of design features progresses, the difference in best focus positions among different patterns is becoming a fatal issue, especially when many patterns co-exist in a layer. The problem arises from three major factors: aberrations of projection optics, mask 3D topography effects, and resist thickness effects. Aberrations in projection optics have already been thoroughly investigated, but mask 3D topography effects and resist thickness effects are still under study. It is well known that mask 3D topography effects can be simulated by various Electro-magnetic Field (EMF) analysis methods. However, it is almost impossible to use them for full chip modeling because all of these methods are extremely computationally intensive. Consequently, they usually apply only to a limited range of mask patterns which are about tens of square micro meters in area. Resist thickness effects on best focus positions are rarely treated as a topic of lithography investigations. Resist 3D effects are treated mostly for resist profile prediction, which also requires an intensive EMF analysis when one needs to predict it accurately. In this paper, we present a simplified Virtual Aberration (VA) model to simulate both mask 3D induced effects and resist thickness effects. A conventional simulator, when applied with this simplified method, can factor in both mask 3D topography effects and resist thickness effects. Thus it can be used to model inter-pattern Best Focus Difference (BFD) issues with the least amount of rigorous EMF analysis.
We have developed a very simple source optimization (SO) method for L/S and C/H critical layers patterning of
advanced NAND FLASH. Starting from the strong off-axis illumination shape which is optimized for the finest
structure of the mask pattern, a systematic procedure is performed to extract the optimum parameters of additional assist
sources to balance the imaging performance (DOF, contrast and optical proximity effect, etc.) of dense/sparse/rough
patterns. Performance equations (linear optimization) with performance map (sensitivity) are utilized to search the best
combination of intensity for each assist source. For C/H pattern, the optimization procedure is modified to solve the
non-linearity and non-continuity problems on the relationship between assist source intensity and each imaging
performance. Finally, optimized source shapes have been successfully demonstrated and verified on 40 nm node NAND
FLASH L/S and C/H critical patterns despite the simplicity of the optimization method, without utilizing SO dedicated
software.
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