A carbon nanotube has a carbon network film of polycrystalline structure divided into crystal regions along the axis of the tube, and the length along the tube axis of each crystal region preferably ranges from 3 to 6 nm. An electron source includes a carbon nanotube having a cylindrical shape and the end of which on the substrate side is closed and disposed in a fine hole. The end on the substrate side of the tube is firmly adhered to the substrate. The carbon nanotube is produced by a method in which carbon is deposited under the condition that no metal catalyst is present in the fine hole and produced by a method in which after the carbon deposition the end of the carbon deposition film is modified by etching the carbon deposition film using a plasma. Therefore, an electron source excellent in the evenness of field emission characteristics in a field emission region (pixel) in the device plane and driven with low voltage can be provided, and a display operated with ultralow power consumption exhibiting ultrahigh luminance can be provided.