Due to the extensive applications of microdosimeters, the purpose of this paper is a feasibility study of a new design as a neutron microdosimeter. A cylindrical microdosimeter using the GEANT۴-۱۰-۴ code is simulated for a neutron source with three different energies. In order to accurately select the materials, frequency-mean lineal energy, dose-mean lineal energy, and these statistical uncertainties in each case were calculated and compared to the standard configuration. It was observed that for microdosimetric walls, polyethylene and polypropylene, in addition to tissue-equivalent solids such as A-۱۵۰ plastic are suitable. To solve the problem of the nonconductivity of these materials, metals such as aluminum, copper, and layers of graphene can be used as a cathode. The optimal maximum thicknesses of these metals are ۰.۵, ۱, and ۱ micron, respectively, that in addition to solving the problem of nonconductive polyethylene and polypropylene, the microdosimetric spectra do not change. It should be noted that using the results of these simulations, an experimental sample of this microdosimeter with a Physical Vapor Deposition coating (PVD) was made in the Shahrood University of Technology, and further studies are being performed on this sample.