Theoretical Calculation of Mask Error Enhancement Factor for Periodic Pattern Imaging

The mask error enhancement factor (MEF) is analyzed through an imaging theory, and simple equations for finding the MEFs for partially coherent imaging are developed. Periodic line pattern images projected by an alternating phase shift mask (PSM), an attenuated PSM, and a binary mask were evaluated under several illumination conditions and the MEF for each set of mask exposure conditions was predicted using these simple equations. With a binary mask or attenuated PSM, three-beam interference imaging for equal lines and spaces was found to provide an MEF of 0.5, while the two-beam interference provided an MEF of 1.0 due to the absence of -1st or +1st order diffracted waves. When the ratio of illumination components to eliminate both the -1st and +1st order diffracted waves increased due to fine features, the MEF increased dramatically. On the other hand, the MEF of an alternating PSM was found to be 1 under two-beam interference for projecting equal lines and spaces, and increased when the -1st or +1st order diffracted wave was eliminated. Our results suggest that the phase edge PSM should be advantageous because the MEF can be reduced to less than 0.5.