A one-dimensional kinetic theory of sheaths surrounding planar, electron-emitting surfaces is presented which accounts for plasma electrons lost to the surface and the temperature of the emitted electrons. It is shown that ratio of plasma electron temperature to emitted electron temperature significantly affects the sheath potential when the plasma electron temperature is within an order of magnitude of the emitted electron temperature. The sheath potential goes to zero as the plasma electron temperature equals the emitted electron temperature, which can occur in the afterglow of an rf plasma and some low-temperature plasma sources. These results were validated by particle in cell simulations. The theory was tested by making measurements of the sheath surrounding a thermionically emitting cathode in the afterglow of an rf plasma. The measured sheath potential shrunk to zero as the plasma electron temperature cooled to the emitted electron temperature, as predicted by the theory.

It has long been known that electron emission from a surface significantly affects the sheath surrounding that surface. Typical fluid theory of a planar sheath with emitted electrons assumes that the plasma electrons follow the Boltzmann relation and the emitted electrons are emitted with zero energy and predicts a potential drop of 1.03Te/e across the sheath in the floating condition. By considering the modified velocity distribution function caused by plasma electrons lost to the wall and the half-Maxwellian distribution of the emitted electrons, it is shown that ratio of plasma electron temperature to emitted electron temperature significantly affects the sheath potential when the plasma electron temperature is within an order of magnitude of the emitted electron temperature. When the plasma electron temperature equals the emitted electron temperature the emissive sheath potential goes to zero. One dimensional particle-in-cell simulations corroborate the predictions made by this theory. The effects of the addition of a monoenergetic electron beam to the Maxwellian plasma electrons were explored, showing that the emissive sheath potential is close to the beam energy only when the emitted electron flux is less than the beam flux.