An SE electron source for an apparatus utilising an electron beam, such as an electron microscope or electron beam lithography machine, has a needle with a tip having a cone angle of less than 15° and a radius of curvature of less than 0.5 µm. In an electron gun using such an SE electron source, the range of variations in probe current caused by a given variation in control voltage increases. Therefore, one extraction voltage setting is sufficient. Furthermore, the value of the extraction voltage decreases. Damage to the needle tip due to electric discharge is prevented. This adds to the stability of the electron gun.