A flat display includes a front glass plate, substrate, cathode, gate electrode, a phosphor screen and metal-backed film, and matrix-like spacer. The front glass plate is at least partly transparent. The substrate is arranged to oppose the front glass plate through a vacuum space. The cathode is formed on the substrate and has an electron-emitting source made of nano tube fibers. The gate electrode has an electron-passing hole in a direction perpendicular to the substrate and is arranged in the vacuum space away from the cathode to oppose the substrate. The phosphor screen and metal-backed film are sequentially stacked on a surface of the front glass plate which opposes the substrate. The matrix-like spacer is stacked between the gate electrode and front glass plate and has a plurality of openings each corresponding to the electron-passing hole.