Fermi-Dirac Statistics Applied to the Problem of Space Charge in Thermionic Emission

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Abstract
This paper develops mathematically the state of an electron gas in equilibrium with a plane electrode when the electron gas obeys the Fermi-Dirac rather than the classical distribution law. For a part of the range of integration graphical methods were found necessary, but fortunately a change of variable leads to a solution, shown graphically, which is independent of the temperature and of the nature of the emitting electrode. Thus a single graphical integration can be applied to any emitting surface at any temperature, giving the density, electric intensity, and potential at any desired distance from the surface. A simple extension of the theory makes possible the calculation of the thermionic current between plane electrodes. Numerical examples are given, and the validity of the asumptions is discussed briefly.