growing a plurality of first carbon nanotubes on a first substrate having a catalyst material layer formed thereon;

separating the first carbon nanotubes from the first substrate and immersing the first separated carbon nanotubes into a dispersion solution;

sequentially forming a cathode electrode, an insulating layer, and a gate electrode on the second substrate and forming an emitter hole to expose a part of the cathode electrode;

coating a top surface of the gate electrode and an inner wall of the emitter hole with photoresist to cover them and patterning the photoresist to expose the cathode electrode beneath the emitter hole;

coating the photoresist and the exposed cathode electrode with the dispersion solution and baking them at a predetermined temperature;

removing the photoresist to leave the first carbon nanotubes on the exposed cathode electrode; and

growing a plurality of second carbon nanotubes from a plurality of nano catalyst particles on the surface of the first carbon nanotubes.