Semiconductor device having a cold cathode

A semiconductor device for producing an electron beam, having at least one cathode comprising a semiconductor body having a major surface, an electrically insulating layer with at least one opening at said major surface, at least one acceleration electrode on the insulating layer at the edge of the opening, and a p-n junction in the semiconductor body within the opening, within the opening the semiconductor body comprising at least one projecting portion, whose cross-section parallel to the major surface decreases as the distance from said major surface increases, and said p-n junction comprising a nonplanar junction whose contour substantially follows the contour of said projecting portion, said device comprising an n-type surface region adjoining the surface of the semiconductor body within said opening and a p-type region therebelow, said n-type and p-type regions forming said p-n junction, so that, when a voltage is applied in the reverse direction across the p-n junction, electrons are generated which emanate from the semiconductor body, said p-n junction locally having a part with a lower breakdown voltage within said opening than over the remaining part of the p-n junction, an n-type surface layer, the junction part with the lower breakdown voltage being separated from the surface by said n-type surface layer, said surface layer having a thickness and doping concentration such that at the breakdown voltage the depletion zone of the p-n junction does not extend as far as the surface, but remains separated therefrom by a distance which is sufficiently thin to allow the generated electrons to pass, the acceleration electrode, viewed in a direction perpendicular to the major surface, leaving free the part of the p-n junction with the lower breakdown voltage, and voltage control means for limiting the electric field strength at the end of the projecting portion to a value of at most 2.times.10.sup.9 V/m.