Thermal and structural deformation of extreme-ultraviolet lithography (EUVL) masks during the exposure process may become important issues as these masks are subject to rigorous image placement and flatness requirements. The reflective masks used for EUVL absorb energy during exposure, and the temperature of the masks rises as a result. This can cause thermomechanical deformation that can reduce the pattern quality. The use of very thick low-thermal-expansion substrate materials (LTEMs) may reduce energy absorption, but they do not completely eliminate mask deformation. Therefore, it is necessary to predict and optimize the effects of energy transferred from the extreme-ultraviolet (EUV) light source and the resultant patterns of structured EUV masks with complex multilayers. Our study shows that heat accumulates in the masks as exposure progresses. It has been found that a higher absorber ratio (pattern density) applied to the patterning of EUV masks exacerbates the problem, especially in masks with more complex patterns.