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The mechanical response of alternating phase-shift mask (APSM) microstructures subjected to dynamic pressure loadings relevant to those encountered in megasonic cleaning was analyzed with the finite element method (FEM). A parametric study of the effects of microstructure dimensions, pressure amplitude, and loading frequency on the mask structural integrity was performed for two typical chromium/quartz APSM patterns. Failure due to microfracture and plastic deformation processes which may occur during megasonic cleaning was examined for loading frequencies of 1, 5, and 10 MHz. The FEM results provide insight into possible failure modes and critical microstructure dimensions for instantaneous microstructure damage. Different failure scenarios revealed by the FEM results are in qualitative agreement with experimental observations. The results of this study have direct implications to the design of extreme ultraviolet lithography masks and the optimization of the megasonic cleaning process.