Abstract
This paper will obtain a physical derivation for a very useful empirical emission formula. Thermionic emission has long been understood, by the supply side limited regime, described by Richardson-Dushman’s equation and the space charge regime by Child-Langmuir’s equation. These equations adequately describe thermionic emission and provide a measure of internal parameters, such as work function, over a limited range and in special designed devices. They fail in the intermediate region between the two laws where most measurements are required, as well as in practical devices. This theory places the well known empirical emission formula on a solid physical foundation.
Highlights
Thermionic emitters have been known and used for over one hundred years
Understanding and controlling the manufacturing processes and determining the proper operation of the dispenser cathode has had a major impact on their useful life, extending the useful life of many space technologies by significant amounts
In this paper a very useful empirical emission formula is derived from basic principles
Summary
Thermionic emitters have been known and used for over one hundred years. The development of semiconductor technology was thought to bring an end to their use. The Richardson-Dushman (RD) equation described electrons with sufficient energy to escape from hot solids Their temperature limited current density is given by JTL(T, Φ) = AT2e−βΦ,. Emitter research in part studies various cathode materials and atomic dipoles that lower the surface work function, as well as means of delivering the dipoles and keeping them on the surface at elevated temperatures. Langmuir-Child (LC) equations describes the behavior of electrons outside the cathode material. Space charge current density is dependent on geometry, described by the constant K = 2.334 × 10−6amp/volt3/2, that is determined by elementary constants. The function ψ(x) is controlled by the spacial distance x measured from the cathode to the anode This function is determined by the Poisson’s equation d2ψ(x) dx. The solution determines a function ζ(x) and defines the space charge current to first order, given by Eq 2.
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