formed in gaas which grows on the above linear pattern thus a triangular prism shaped linear field emission electron source 12 is formed on the above linear pattern in this case face orientations of both of the oblique surfaces of the triangular prism shaped field emission electron source 12 are set to 110 and 110 and an angle which is formed by both of the oblique surfaces is set to 90 u00b0 in the growth of gaas by the mocvd method a sharp edge point is formed in the case where a ratio of as to ga in the growing raw material is small generally speaking in the case of the growth of a iii v group compound semiconductor a sharp edge point is formed when a ratio of the v group element to the iii group element in the growing raw material is small as mentioned above according to the example the shape of the tip portion of the linear field emission electron source 12 is formed as a sharp shape which is defined by the crystal faces and a radius of curvature of the tip can be reduced by about one order of magnitude as compared with that of the conventional one therefore the voltage which is applied to the field emission electron source 12 in order to execute the field emission can be reduced by about one order of magnitude as compared with the conventional one consequently a low electric power consumption can be realized fig6 shows the case of forming a point shaped field.