In this paper, we report the design and simulation of electron sources composed of arrays of Si field emitters (FEs) that are individually ballasted by a current source. Each FE is fabricated on top of a vertical ungated field-effect transistor (FET), a two-terminal device based on a very-high-aspect-ratio Si column. The ungated FET takes advantage of the velocity saturation of electrons in silicon, the high aspect ratio of the ungated FET, and the doping concentration of the semiconductor to achieve current-source-like behavior. The proposed technology can be used to implement cathodes capable of reliable uniform and high current emission.