thode structure, each of the micropoint cathodes 3 is formed of a metal such as Mo, Ta, etc. and shaped to have a bottom of a diameter equal to or less than approximately 1 .mu.m and a tip of a diameter ofapproximately 20 nm, the insulating layer 2 has a thickness of approximately 1 .mu.m, and the gate electrode 4 is formed of Mo, W, etc. having a thickness of approximately 0.4 .mu.m, and each ape