A novel electron-gun design is proposed with a single carbon nanotube grown in a microfabricated conducting crater within a conducting substrate separated by an insulating layer from an apertured gate. The operating field-emission parameters for such a device are chosen from experiments by using geometric scaling resulting from electrostatic arguments. With these parameters the electron-beam formation and propagation was simulated using a ray-tracing code. The novel design produces a nearly parallel electron beam of high source brightness, low-power leakage, and negligible wall encounters, advantageous for microcolumn scanning electron microscopy, lithography, and other applications.