The microtips of charge emitting material, which define the cathode of the flat FED screen and face the grid of the screen, are tubular and have portions with a small radius of curvature. The microtips are obtained by forming openings in the dielectric layer separating the cathode connection layer from the grid layer, depositing a conducting material layer to cover the walls of the openings, and anisotropically etching the layer of conducting material to form inwardly-inclined surfaces with emitting tips. Subsequently, the portions of the dielectric layer surrounding the microtips are removed.