Existing analytical and numerical methodologies are discussed and then extended in order to calculate critical contamination-particle sizes, which will result in deleterious effects during extreme ultraviolet lithography E-chucking in the face of an error budget on the image-placement-error (IPE). The enhanced analytical models include a gap-dependent clamping pressure formulation, the consideration of a general material law for realistic particle crushing and the influence of frictional contact. We present a discussion of the defects of the classical de-coupled modeling approach where particle crushing and mask/chuck-indentation are separated from the global computation of mask bending. To repair this defect we present a new analytic approach based on an exact Hankel transform method which allows a fully coupled solution. This will capture the contribution of the mask-indentation to the image-placement-error (estimated IPE increase of 20%). A fully coupled finite element model is used to validate the analytical models and to further investigate the impact of a mask back-side CrN-layer. The models are applied to existing experimental data with good agreement. For a standard material combination, a given IPE tolerance of 1 nm and a 15 kPa closing pressure, we derive bounds for single particles of cylindrical shape () and spherical shape ().