To reduce both a control voltage and a leakage current at the same time in a field-emissive element.

In this field-emission element, a gate electrode 50 is formed on a resistant layer 20, which is an emitter electrode, interposing a first insulating membrane 30 and a second insulating memberane 40. The structure such that the gate electrode 50 and both insulating membranes are extended as far as the side face of a projection 25 of the emitter, and a tip of the projection 25 and an opening 55 of the gate electrode 50 face each other, interposing an aperture having the thickness of the first insulating memberane 30. Electric field applied on the projection 25 is affected, only by the thickness of the first insulating membrane 30, therefore a control voltage can be reduced by forming the first insulating membrane 30 thin. Also the second insulating membrane 40 is affected only by the distance from the gate electrode 50 to the resistance layer 20. Therefore, both the control voltage and a leakage current can be reduced at the sometime, by forming the first insulating membrane 30 thinly and the second insulating membrane 40 thickly.