Previously, we theoretically investigated the charging of free standing dielectric thin films irradiated by 100 keV electrons and formulated kinetic equations describing the dynamic process [M. Mkrtchyan et al., Microelectron. Eng. 46, 233 (1999)]. It was shown that in the currently used SCALPEL(R) masks comprising a 1000-Angstrom-thick amorphous SiNx film supported by a grillage of Si struts, the membrane charging could be significant and might have an adverse effect on the system performance. The membrane charging, sensitive to both the conductivity and the geometry of conductive path, can be regulated in a straightforward manner by tailoring both of them; for instance, by applying a top surface conductive layer (TSCL) with an appropriate thickness and doping level. Here we discuss the results obtained on the basis of our charging model modified to be applicable to the case of a SiNx membrane with a TSCL (e.g., a 10-nm-thick amorphous Si or poly-Si film doped by boron). The results presented demonstrate that this modification of the membrane is sufficient to avoid the adverse effect of the mask-membrane charging. The required structure can be generated simply by regulating the gas hows in the low-pressure chemical vapor deposition process to produce a thin final layer of a:Si or poly-Si which can be doped during or after deposition.