It is generally believed that if an n-type semiconductor with negative electron affinity could be found, it would act as an ideal 'cold cathode'. A model is proposed to describe the conditions at an ideal surface between such a semiconductor and the vacuum. When such an interface is created, electrons will have to exit the semiconductor owing to the difference in energy χ between the conduction band and the vacuum level. They leave a positively charged depletion layer behind, within which a barrier to further electron egression is generated. A self-consistent potential well has to form, which bounds the emitted electrons within quantum states such that they remain within an 'electron-charge' layer adjacent to the surface. Together with the depletion layer, the electron-charge layer forms a dipole that screens the field caused by the initial offset χ between the energies of the conduction band and vacuum level. When applying an electric field to extract electrons, the barrier in the depletion layer increases. This impedes electron flow through the semiconductor into the vacuum.