Analysis of edge effects in attenuating phase shift masks using quantitative phase imaging

Thick mask electromagnetic edge effects in attenuating phase-shift masks (ATT-PSM) are analyzed by extracting optical phase at the wafer plane from a series of through focus aerial images with 193nm light. The thick edges of an ATT-PSM can lead to phase distortions, creating asymmetric intensity contrast on either side of focus. Here we use through focus intensity images from an AIMS tool to quantitatively recover phase via the Transport of Intensity Equation (TIE). The TIE can recover the effective phase across the mask due to edge effects by analyzing the through focus image stack. We verify a previously proposed model for edge effects by adding quadrature phase boundary layers at the edges during simulation and compare the simulated through focus images with experimental data. After tuning the real and imaginary part of the boundary layer and the angle of the substrate, the simulated through focus behavior agrees with experiment, giving a measure of the edge effects. This leads to comparable quantitative phase profiles recovered at the wafer plane for simulation and experiment with the ATT-PSM. We expect that the method is applicable for the approximation of topographical effects in other types of thick masks as well.